Frequency of visual field testing when monitoring patients newly diagnosed with glaucoma

Article history

The research reported in this issue of the journal was funded by the HS&DR programme or one of its proceeding programmes as project number 10/2000/68. The contractual start date was in October 2011. The final report began editorial review in July 2013 and was accepted for publication in March 2014. The authors have been wholly responsible for all data collection, analysis and interpretation, and for writing up their work. The HS&DR editors and production house have tried to ensure the accuracy of the authors’ report and would like to thank the reviewers for their constructive comments on the final report document. However, they do not accept liability for damages or losses arising from material published in this report.

Declared competing interests of authors

none

Copyright statement

© Queen’s Printer and Controller of HMSO 2014. This work was produced by Crabb et al. under the terms of a commissioning contract issued by the Secretary of State for Health. This issue may be freely reproduced for the purposes of private research and study and extracts (or indeed, the full report) may be included in professional journals provided that suitable acknowledgement is made and the reproduction is not associated with any form of advertising. Applications for commercial reproduction should be addressed to: NIHR Journals Library, National Institute for Health Research, Evaluation, Trials and Studies Coordinating Centre, Alpha House, University of Southampton Science Park, Southampton SO16 7NS, UK.

Background

Chronic open-angle glaucoma (COAG) represents a major workload for UK eye hospitals. It is estimated that at least 480,000 people are affected by the condition in England alone, and they account for over 1 million related outpatient visits per year. 1 The prevalence of glaucoma rises exponentially with age, with 85% of cases of open-angle glaucoma occurring in people aged 60 years and above. 2 The ageing population means that these figures are destined to increase dramatically in future years. Glaucoma is a progressive disease and often asymptomatic, so it is vital that affected individuals are monitored routinely over time in order to control the disease and detect any signs of worsening damage. Any vision loss that occurs is irreversible, and so clinical care must aim to ultimately halt or ameliorate progression to a rate which is compatible with a sighted lifetime without significant disability. Nevertheless, at the present time, 10% of cases of registered blindness in the UK are attributed to glaucoma. This figure suggests that there is still room for improvement in terms of the efficiency of diagnosis and with regards to the quality and effectiveness of ongoing care from the point of first referral. 1

Clinical testing plays a large role in glaucoma monitoring and, therefore, much research is devoted to examining the relevance, reliability, variability and predictive powers of the various available tests for detection and progression. Standard automated perimetry (SAP), which is used to assess changes in the visual field (VF), lies at the forefront of assessments of visual function in glaucoma and is central to clinical management. Rates of VF progression in clinical populations can vary widely between patients; therefore, timely detection of progression requires accurate and consistent monitoring of the VF over time. Nevertheless, some evidence suggests a lack of consistency in terms of the rate of VF monitoring between clinics. 3,4 In 2009, guidelines for glaucoma published by the National Institute for Health and Care Excellence (NICE) highlighted a lack of evidence about how often patients with the condition should be monitored. 1 The first question in the report was:

. . . What is the clinical effectiveness and cost effectiveness of using different monitoring intervals to detect disease progression in people with glaucoma who are at risk of progression? . . .

The guidelines subsequently called for further research in this area, in order to form optimal recommendations for disease monitoring intervals. Some recent studies have attempted to address this dilemma by trying to identify practical recommendations for measuring clinically relevant rates of glaucomatous VF progression. A notable study by Chauhan et al. 5 demonstrated that the ability to detect the rate of VF change will depend on the variability of mean deviation (MD; an index of defect severity, measured in dB) over time, the number of examinations and the degree of change wished to detect. They concluded that, for a patient demonstrating average measurement variability, three examinations per year would be required to detect a change in MD of 4 dB over 2 years. This finding is supported by earlier research demonstrating that three examinations per year are needed to provide a good statistical compromise between sensitivity and specificity. 6

The evidence from these studies has subsequently informed current guidelines set by the European Glaucoma Society (EGS)7 recommending that newly diagnosed patients undergo VF testing six times in the first 2 years of their follow-up care in order to gain a more accurate depiction of the rate of progression. These guidelines complement current recommendations by NICE that the interval between VF tests should be between 2 and 6 months for newly diagnosed patients, and between 6 and 12 months for stable follow-up. However, NICE does not stipulate the period for which such monitoring should be maintained.

Objectives

This study aims to ascertain the current practice of VF testing for monitoring patients with glaucoma in England, and to evaluate this practice in relation to the EGS and NICE guidelines. Specifically, the study will test the hypothesis that follow-up intervals are highly variable in the clinic.

Methods

Analysis

All data were anonymised prior to analyses. Statistical analyses were carried out using the open-source environment, R 3.0.1 (The R Foundation for Statistical Computing, Vienna, Austria). The non-parametric Kruskal–Wallis test was used to compare data from different groups, with statistical significance defined as p < 0.05.

Ethics statement

This study was reviewed by the research and ethics committee at each hospital and is compliant with the Declaration of Helsinki. We certify that all applicable institutional and governmental regulations concerning the ethical use of human volunteers were followed during this research.

Results

Visual field testing frequency

Patients had completed a median of four VF tests (IQR 2–7 VF tests) in total since being diagnosed. This finding equates to 0.7 VF tests per year over the average 7.2 years of follow-up. Within the first 2 years after diagnosis, patients completed a median of two VF tests (IQR 2–3 VF tests), ranging from one to five tests (Figure 1a). Notably, none of the patients met the EGS objective of six VF tests in the first 2 years. The number of patients diagnosed with COAG before publication of the EGS guidelines and Chauhan et al. 5 recommendations (pre 2009) was 69, while 35 patients were diagnosed in, or after, 2009. Thirty-nine patients had completed at least six VF tests during their follow-up, but took a median duration of 4.6 years (IQR 3.7–6.0 years; range 2.2–17.5 years) to achieve this landmark (Figure 1b). No statistically significant relationship was found (using the Kruskal–Wallis test) between the number of VF tests performed and disease stage (early, moderate, advanced), adequacy of the IOP control (adequate, inadequate, not recorded), VF status (stable, progressing, unsure, not recorded), ONH appearance (stable, progressing, unsure, not recorded) or overall stability of the conditions (stable, progressing, unsure, not recorded). These results are summarised in Table 3.

FIGURE 1.

Visual field testing. (a) The number of VF tests performed in the first 2 years in patients with minimum follow-up of 2 years; (b) time taken for patients to receive six VF tests. Adapted by permission from BMJ Publishing Group Limited. [Are practical recommendations practiced? A national multicentre cross-sectional study on frequency of visual field testing in glaucoma. Fung SS, Lemer C, Russell RA, Malik R, Crabb DP. Br J Ophthalmol. 97:843–7. 2013.]9

TABLE 3 - Median number of VF tests by disease severity and IOP

Recorded parameters	Median number of VFs (IQR)
IOP status
Adequate	4 (2–7)
Inadequate	2 (1–6)
Not recorded	5 (3–6)
ONH status
Stable	4 (2–7)
Progressing	3 (2–6)
Unsure	5 (3–7)
Not recorded	3 (1–6)
Overall clinical impression
Stable	4 (2–7)
Progressing	3 (1–6)
Unsure	7 (5–7)
Not recorded	4 (3–6)
Severity of glaucoma
Early	3 (2–5)
Moderate	4 (1–7)
Advanced	6 (2–7)
VF status
Stable	5 (3–8)
Progressing	5 (2–7)
Unsure	4 (2–7)
Not recorded	2 (1–5)

Monitoring intervals

Two patients were scheduled to undergo surgery at the time of the study (one trabeculectomy and one cataract surgery) and thus they were excluded from this part of analysis. Fifty-nine patient records contained details regarding the length of time until the next VF examination, while 43 records specified only the time interval to the next appointment.

The overall median monitoring interval requested at the study visit was 7.5 months (IQR 3.8–8 months). In total, 84.5% of patients had no changes made to their management. When patient outcomes were considered according to NICE-recommended monitoring intervals for complete examination (i.e. including VF testing and ONH examination), 88 out of 101 patients (87.1%) were guidance compliant. Among the patients with non-compliant outcomes, five had be given a longer than recommended interval for IOP monitoring; three patients had longer than recommended VF monitoring intervals, while another three patients had shorter VF monitoring intervals than the NICE recommendations.

No relationship was found between stability of VF defects (Kruskal–Wallis test, p = 0.25) and the monitoring interval requested. The severity of disease also had no influence on the monitoring interval requested (Kruskal–Wallis test, p = 0.40). The median monitoring interval requested for early, moderate and advanced glaucoma was 7 months (IQR 3–8 months), 8 months (IQR 4–8 months) and 8 months (IQR 4–8 months), respectively, while the median interval requested was 8 months (IQR 3–8 months) for stable VF defects, 8 months (IQR 4–8 months) for progressing VF defects, 5 months (IQR 3–6 months) for uncertain VF progression and 8 months (IQR 4–8 months) for those with no comments on VF status (Figure 2a). In contrast, monitoring intervals were significantly shortened when patients had inadequate IOP control or when the overall clinical impression was disease progression (p < 0.001 and p < 0.001, respectively). The median monitoring interval was 8 months (IQR 3–8 months) for patients with adequate IOP control, 4 months (IQR 2–5 months) for those with inadequate IOP control and 8 months (IQR 7–8 months) for patients with no comments on IOP control (Figure 2b). For the overall impression of disease status, the median monitoring interval was 8 months (IQR 4–8 months) for stable patients, 4 months (IQR 2–5 months) for patients with disease progression, 6 months (IQR 4–6 months) for those with uncertain status and 6 months (IQR 5–8 months) for those with no comments on overall status.

FIGURE 2.

Patient monitoring in relation to clinical findings. (a) Follow-up interval by VF status; (b) follow-up interval by IOP status. (Horizontal lines represent medians. Boxes represent 25% and 75% quartiles. Each whisker extends 1.5 times the IQR and outliers are represented by dots.) NR, not recorded. Adapted by permission from BMJ Publishing Group Limited. [Are practical recommendations practiced? A national multicentre cross-sectional study on frequency of visual field testing in glaucoma. Fung SS, Lemer C, Russell RA, Malik R, Crabb DP. Br J Ophthalmol. 97:843–7. 2013.]9

This audit has its limitations. It is assumed that the six units sampled are representative of national practice. Being a cross-sectional study, sampling bias is an inherent issue. Furthermore, for each centre, the patients sampled during the study week is assumed to be representative of the general population of COAG patients seen in that unit. The number of patients from Portsmouth was only four, which is not comparable to other participating centres. However, out of the 32 patients seen in Portsmouth during the study week, 28 patients did not meet the study inclusion criteria (17 had a diagnosis other than COAG and 11 had recent intraocular surgery). It is also worth noting that patients requiring more intensive control are more likely to be included in the study, and so there are likely to be a higher proportion of patients with poor IOP control (and advanced glaucoma severity) than patients with adequate IOP control in the study population. However, this is likely to make the sample representative of the distribution of patients (in terms of proportions with different IOP control and disease severity) seen in the clinic annually. In addition, clinical note taking was often poor or incomplete; several patient records contained no comments on adequacy of IOP control, VF status or overall disease status. Inevitably with any retrospective analysis of patient records, it is difficult to draw certain conclusions, since notes are often made by multiple clinicians with varying levels of expertise. Where available, the clinician’s comments regarding optic disc and/or VF progression were assumed to be documented and an accurate representation of the patient’s clinical state in each case.

Conclusions

The results from this retrospective, multicentre cross-sectional study demonstrate that no patients received the frequency of VF testing recommended by Chauhan et al. 5 and the EGS guidelines (six VFs in the first 2 years). Instead, patients typically had only two or three VF tests in the first 2 years following diagnosis, typically taking more than 4 years on average to reach six VFs. While recommended monitoring intervals were considered as NICE compliant, it is worth noting that the intervals given by NICE are fairly wide (the permitted interval spans 2 to 6 months or 6 to 12 months), and suggested intervals were dependent on disease severity and IOP relative to target IOP. Indeed, NICE has recognised the current lack of evidence regarding the frequency of monitoring intervals for patients with glaucoma and recommended future research in this area of study to substantiate current practice. 1 From a health-care planning perspective, it is important to acknowledge that the cost of glaucoma management increases substantially with the severity of visual loss. 10,11 Therefore, there is a strong rationale for frequent monitoring from an early stage to detect rapidly progressing patients. However, a large number of patients will have stable treated disease and so there will also be cost implications for carrying out more tests than necessary. These results inform further studies regarding the effect of VF testing intervals on patient outcomes and cost-effectiveness. In addition, these findings open up the path for subsequent research into the types of factors affecting VF test frequency for newly diagnosed COAG patients in the first 2 years of follow-up.

Background

Given that COAG accounts for a major proportion of ophthalmology workload, with an estimated 1 million outpatient visits in the UK taking place every year,1 the frequency of VF testing undoubtedly has important implications for resource management and service delivery, as well as cost in the outpatient setting. The frequency of VF tests over a given period for a patient with COAG is ultimately governed by the clinician’s estimate of the likelihood and speed of progression of disease, which, in turn, may depend on the level of IOP control, and stage of disease as well as other factors such as the age of the patient and degree of VF reliability. Test intervals are essentially a risk–benefit trade-off: an interval which is too long may allow timely detection of progressive VF loss to be missed, while multiple tests at short test intervals in patients at low risk of progression may mean unnecessary extra visits and use of hospital resource.

As discussed in the previous chapter, there are limited published guidelines available regarding the expected frequency of VF testing. Results from statistical modelling suggests that six VF tests in 2 years (i.e. approximately one every 4 months) in newly diagnosed patients may be necessary to allow detection of patients who may be progressing ‘rapidly’ in terms of VF loss. 5 The EGS therefore recommend that newly diagnosed patients receive six VF tests during the first 2 years of glaucoma follow-up. 7

Nevertheless, the audit described in the previous chapter demonstrated that the majority of newly diagnosed patients are not receiving the recommended number of VF tests in the first 2 years following diagnosis. It is worth noting that the ‘six VF tests in 2 years’ approach implies that a patient doing well under treatment receives the same number of tests as a patient heading for blindness. Ultimately, it is the clinician who drives decision-making as to how often VF tests take place. A subsequent study was therefore designed to establish the attitudes of glaucoma subspecialists to the frequency of VF testing and sought to investigate perceived barriers to frequent VF testing of patients with glaucoma.

Methods

Results

The questionnaire was returned by 70 consultant ophthalmologists currently employed in England and Wales, with a self-declared specialist interest in glaucoma. For the clinical scenarios listed in question 4 for a hypothetical patient with ‘target’ IOP, 14 (20%) of responders gave follow-up intervals outside those recommended by NICE when the patient was said to show no evidence of VF progression and no change in treatment (scenario a). For clinicians asked to assign follow-up intervals for the hypothetical patient who showed evidence of VF progression and no change in treatment (scenario b), 33 (47%) responses fell outside the recommended intervals. Twenty-eight (40%) responders assigned follow-up intervals different to the NICE recommendations for a hypothetical patient showing uncertain VF progression and no change in treatment (scenario c). [The width of the 95% confidence interval (CI) associated with these estimates, with n = 70, is about ± 12%.]

Question 5 was answered by 57 out of the 70 specialists. Nearly half of these specialists (26/57, 46%) agreed that six VF tests in the first 2 years was ideal practice (Figure 3), but admitted that the practicalities of this would be challenging. Example responses that fell in this category included:

Agree but practical issues found in a busy glaucoma clinic may be a hurdle to achieve this target.

FIGURE 3.

Summary of views of responders to the suggestion that six VF tests should be performed in the first 2 years for a newly diagnosed patient with primary open-angle glaucoma.

Two delegates (3%) indicated that this was already their current practice. Six specialists (11%) disagreed with the suggestion of six VF tests, while 16 (28%) said this was ‘not possible’, again listing limited ‘capacity’ or resources as a constraining factor. (The width of the 95% CI associated with these estimates, with n = 57, is about ± 15%.) Examples of responses that fell in the latter category included:

Totally out of touch with what is possible in the current NHS clinics with such limited capacity.

A few alternatives were suggested to six VF tests, including alternating imaging and VF tests for detecting progression. For example, one responder stated:

Instead of function tests, structural ones: GDx/OCT [scanning laser polarimetry/optical coherence tomography] would be better . . .

A limitation of this and all studies of this nature is the response rate. An assumption has been made that responses from the surveyed consultants are representative of subspecialist national practice in England and Wales. There are approximately 150 consultant ophthalmologists in the England and Wales with a glaucoma subspecialist interest as estimated from a list obtained from the Royal College of Ophthalmologists. Our surveyed population would, therefore, represent nearly half of glaucoma specialists nationally.

Conclusions

The results from this survey suggests that there is a large variation in attitudes to follow-up intervals for patients with glaucoma in the UK, with assigned intervals for VF testing often inconsistent with the guidelines from NICE. Nearly half of glaucoma specialists thought the suggestion of six VF examinations in the first 2 years after diagnosis, as recommended by EGS guidelines, to be ideal practice. However, an equal proportion of those surveyed thought the idea to be impractical, or not possible, in the current health setting.

Background

Guidelines proposed by EGS recommend that six VF tests should be taken in newly diagnosed glaucoma patients within the first 2 years of follow-up. This recommendation is based on research evidence suggesting that this level of monitoring identifies patients with fast progression far quicker than annual testing. 5,6 However, the audit reported in Chapter 1 demonstrated that these guidelines are not being implemented within clinical practice, with patients typically receiving only two VF tests, on average, within the first 2 years of follow-up, and taking an average of 4 years to reach the recommended six VF tests. Furthermore, the results of the survey described in Chapter 2 revealed that VF monitoring intervals assigned by clinicians (for hypothetical patient scenarios) are very variable. While many specialists conceded that better surveillance of the VF would be helpful in managing patients, they viewed the recommendations as impractical in the current health setting. These results suggest that personal attitudes regarding the frequency of testing could play an important role in translating research into practice.

While it is the clinician who ultimately drives decision-making based on his or her estimates of the likelihood and speed of disease progression, establishing the most effective monitoring strategies may also require the input of the patients themselves. This is important because patient and public involvement in research is paramount to health care. 12,13 Wisdom gained anecdotally has, for a long time, suggested that patients dislike the VF test, and one systematic study found that patients rated the VF test poorly in comparison with other vision tests. 14 However, no study has asked patients with glaucoma, in detail, about their perceptions of the VF test and their follow-up care. Care plans that place burdens on patients may result in a reduced willingness to return for follow-up and could compromise the quality of the data obtained that is subsequently relied on during management. 15 It is, therefore, of value to consider their views to help establish the most effective strategies for glaucoma monitoring.

When considering patients’ perspective of their health condition, many studies opt to use questionnaires to quickly gather information about the perceptions of service users. However, this method can be restrictive, and patients may misinterpret the meaning of the question or simply not be given an appropriate opportunity to contribute all their views. Qualitative techniques, such as focus groups, offer an alternative method of gathering information about not only what a patient thinks, but also how they think or why they may hold a particular view. Group interaction encourages participants to explore and clarify individual and shared perspectives, and supports the participation of people who may be reluctant to contribute their views in a more formal one-to-one scenario. 16

Therefore, for the first time, the current study aims to explore patient views and experiences of glaucoma monitoring, via focus groups, particularly with regards to the type and frequency of VF testing.

Methods

Results

Data were initially indexed according to themes central to the main research questions, such as opinions of the VF test, current experience regarding the frequency of VF testing and opinions about more frequent VF testing. However, throughout the analysis a number of additional themes emerged, often with their own subthemes. These generally related to specific areas perceived to affect the follow-up experience, and included points relating to clinical constraints (waiting times, booking appointments), travel to the clinic, the testing environment and aspects of patient–clinician communication. Figure 4 summarises the key themes and subthemes that emerged from the analysis.

FIGURE 4.

Coding tree showing main themes and subthemes that emerged from the analysis, and how the categories relate to each other.

Direct quotes were taken from the transcripts and were chosen to illustrate the key themes that emerged from the focus groups. Excerpts are annotated with a pseudonym for the corresponding participant based on their gender [male (M) or female (F)] and the order in which they spoke in the interview. The location of the focus group and the session number (1 or 2) are also shown for each quote.

Explanation of results

Most patients said they had to specifically enquire about their results to find out information about their vision and whether or not their condition had progressed since the last appointment. Some patients felt too intimidated to ask the doctor for feedback as to how they had performed, feeling they were being a nuisance or wasting the doctor’s time.

My wife always says ‘how did you get on?’ and I say ‘I don’t know’, and that’s one of the problems.

M2, Portsmouth 2

I don’t think they’ve got time to listen to you, or they don’t appear to, and I don’t know whether they would listen . . . You feel pathetic asking these questions.

F3, Portsmouth 1

It was felt that a better explanation of the test results after completing the VF test would ease some of the pressure felt when performing the test.

If the doctor actually spent a bit more time discussing it with you, would it maybe ease the pressure of actually doing the test?

I would . . .

I think possibly.

Yes, I mean I would still panic, but if I knew, yes.

Patients may be more inclined to have VF tests more frequently should they be informed clearly about what the results indicate about their prognosis.

I don’t mind how many times I do it providing I get a result of the test at that time compared to what the previous one was. Is there any improvement? Is there any downgrade?

M1, Portsmouth 1

The patient–clinician relationship

The quality of relationship with the clinical staff and aspects of patient–clinician communication also emerged as key factors influencing perceptions of the follow-up process.

A major discussion point was the lack of continuity of clinical staff from visit to visit.

The doctors seem to change . . . most of them I think tend to be all right but I still see this as a weakness, that you are unable to ask to see the same doctor every time you come in.

M2, London 2

Sometimes it’s good I think. You get a different opinion from a different person.

M3, Portsmouth 2

An apparent lack of personalised care also caused some unease: there was a sentiment that sometimes the clinician simply looked at the eyes and failed to consider the person’s individual needs.

You’re not a person, you know, you’ve just got eyes, they’re just going to deal with that and that’s it.

F3, Portsmouth 1

The experience was seen to be much more bearable if they felt the staff member dealing with them was empathetic.

Even buying a chop, you know: if the butcher’s interested, it helps doesn’t it?

M3, Norwich 1

The opportunity to spend more time with their consultant ophthalmologist was a key factor that influenced whether or not patients were open to visiting the clinic more frequently.

Not just for the field test . . . But I wouldn’t mind coming in more to see the doctor.

M2, London 2

Testing environment

The testing environment was another important theme. The dark room, especially if it was warm, made focusing on the tests difficult. Patients felt they performed better in the morning when they were more alert. Ambient noise in the room made it difficult to concentrate; technicians talking and doing the test at the same time as several other patients all had an effect on their ability to focus on the task.

I will also say that the staff chatter a lot, which is difficult for concentration; the doors open and close, there’s a lot of noise.

F1, Norwich 1

The times that I’ve had the visual field test done in a room where there’s just one [machine] I felt more confident to do it and it was much quieter and more relaxed and it seemed to be a lot quicker too.

F3, Norwich 2

I think having the quieter atmosphere would generally help I’m sure . . . just that feeling of slight calm, you can relax more and then it probably would be a lot quicker because maybe you’re not going to miss as many [lights] as you haven’t got other distractions.

F3, Norwich 2

Clinic constraints

Conclusions

Research based on statistical analyses and computer simulations has typically been used to investigate VF follow-up in glaucoma. This is the first study to examine the VF test and clinic experience from the patients’ perspective using a qualitative research approach. Although patients did not like the VF test, they accepted it as a ‘necessary evil’ for maintaining their vision. However, a number of possible actionable points were raised which were perceived to impact the effectiveness of follow-up care, including distracting testing environments and hospital constraints relating to excessive waiting times and appointment booking. Some patients also expressed particular concerns about patient–clinician communication, including the quality of test instructions, explanation of results and a lack of individual-centred care. Many of the viewpoints expressed coincided with previous evidence suggesting that these factors can influence VF data obtained during the follow-up process. 21–25 Ensuring that glaucoma monitoring is as clinically effective and cost-effective as possible will inevitably require the confidence and co-operation of the person at the heart of the treatment, so that the data are of a sufficient quality to inform further treatment decisions. Therefore, patient involvement could be important to not only address some, or all, of the perceived barriers highlighted in this study but ultimately to drive further research into the most efficient strategies for VF monitoring.

Background

Accurately and precisely measuring VF progression in glaucoma patients is imperative. First, it is essential for effective clinical management of the disease. Second, VF measurements are the most commonly used end points for clinical trials in glaucoma. Monitoring VF status in the patient is achieved by SAP testing. Analyses to measure VF progression then require a sound understanding of the amount or rate of VF loss (dB per year), the period of observation, the effect of VF measurement variability, and the number of follow-up tests, as all these factors affect the ability to detect VF progression with adequate statistical power. 26 The number of VF tests required to detect change is often overlooked. VFs exhibit substantial measurement error and, therefore, clinical management decisions based on results from only one or two VF tests will, in general, be unreliable. A sufficiently long observation period and a suitable number of VF tests are essential to measure change with reasonable confidence. Furthermore, longitudinal studies5,27,28 and natural history data29,30 indicate that there is considerable between-patient variability in the rate of VF progression. The rate of VF loss cannot be well predicted at diagnosis, at an individual patient level, and is best estimated by collecting the results of several VF tests over a period of time. In a newly diagnosed patient, it would be ideal to first obtain an adequate number of reliable VF examinations over a period of time to exclude, or to detect, the presence of rapid VF progression. In this way, clinical treatment can be intensified for those patients (‘fast progressors’) that need it, thereby controlling the disease process. Until recently, there has been little research evidence concerning how frequently VF tests should be carried out to optimally detect progression. At present, the timetabling of VF tests in routine clinical practice is often intermittent and not well planned. 4

In 2008, Chauhan et al. 5 published recommendations for measuring rates of VF loss in newly diagnosed glaucoma patients based on statistical power calculations. Fundamental to their results was the key principle that an adequate number of VF tests must be performed over a given period in order to separate true disease progression from the measurement variability inherent in VF data. This conclusion is equivalent to the accepted notion that a clinical trial will not be sufficiently powered to detect an experimental effect if too few patients are enlisted. One particular finding from the Chauhan et al. study suggested that newly diagnosed glaucoma patients should undergo VF testing three times per year in the first 2 years post diagnosis. This frequency of testing identifies rapidly progressing eyes, losing average VF sensitivity (MD) of more than 2 dB per year, with greater certainty than if annual testing was implemented. Consequently, this recommendation has been adopted in the EGS guidelines on patient examination. 7 The idea that three SAP tests per year should be performed to measure visual progression is also supported by results from previous research using computer simulation6 and retrospective investigation of a large VF database. 31

This chapter aims to determine the clinical effectiveness of alternative monitoring regimes (including the recommended EGS strategy of six VF tests in the first 2 years) in newly diagnosed glaucoma patients. These questions are investigated using data from computer simulations. A second aim of this chapter is to explore the usefulness of computer simulation for optimising SAP testing when attempting to accurately detect progression in newly diagnosed glaucoma patients with different levels of baseline VF damage; this is informative about prioritising clinical management in those patients who may or may not require intensified treatment. For example, younger patients with more advanced glaucoma are at increased risk of visual disability in their lifetime compared with older patients with early VF damage.

Objectives

The objectives of this chapter are:

1. To retrospectively investigate the distribution of the rate of progression in a large cohort of patient records already archived from Moorfields Eye Hospital in London; Cheltenham General Hospital Gloucestershire Eye Unit and Calderdale Royal Hospital in West Yorkshire; and Queen Alexandra Hospital in Portsmouth. This will involve the interrogation of almost half a million VF tests, equivalent to around 25 million data points. Information about rates of progression in representative groups of glaucoma patients under clinical care will help us to model typical results achieved with currently available treatment modalities and inform about the magnitude of current and projected future visual function deficits caused by glaucoma.

2. To further develop our published model for generating virtual series of VF tests in order to explore different follow-up schemes for newly diagnosed glaucoma patients. In particular, annual testing against three tests per year in the first 2 years will be assessed for positive outcomes in determining glaucomatous progression.

Estimating rates of visual field progression

Glaucoma treatments attempt to slow the rate of progression of VF loss and generally aim to reduce IOP, which is the only known modifiable risk factor for the disease. Clearly, the key objective of clinical management is to prevent glaucoma patients advancing to visual impairment and blindness so that their quality of life remains unaffected. Once diagnosed, patients normally require lifelong treatment and monitoring so that any threatening rate of progression of VF loss can be detected and treatment can be changed accordingly. Thus, monitoring patients represents a considerable workload for glaucoma clinics. VF testing remains the only direct method for measuring patients’ visual function and, therefore, to gauge if a treatment is effective in avoiding future impairment. The amount of VF loss can be summarised using the MD measurement, which is the averaged difference between a patient’s VF and the VF from a person with healthy vision of the same age – the more negative the MD, the greater the amount of VF damage.

Many patients newly diagnosed with glaucoma are not at great risk of blindness. Retrospective analyses based on reviews of clinical notes suggest that the percentage of patients, under care, going blind is between 6% and 13%. 32–34 These studies, however, are somewhat limited at informing present-day prevalence, as VF tests were conducted using manual perimetry, and only relatively small numbers of patients (in all cases fewer than 300 patients) were investigated. Furthermore, all this research was carried out more than 10 years ago and, therefore, before the advent of new glaucoma medications, such as prostaglandins. The rate of progression of VF impairment varies greatly, but it is obvious that patients who experience rapid progression, the so-called ‘fast progressors’, are at highest risk of visual impairment, yet the incidence of fast progressors in clinical practice is uncertain. Cohort studies suggest that less than 5% of patients progress at a rate of –1.5 dB/year or worse. 35–37 However, results from retrospective studies are less optimistic, suggesting that the proportion of fast progressors varies from approximately 9% to 25% (with the use of different exclusion criteria). 38–40 In particular, a recent review by Heijl et al. 41 documented that 15% of patients investigated progressed at a rate faster than –1.5 dB/year.

Considering treatment and monitoring costs, it is essential that resources are prioritised towards patients at risk of significant visual disability in their lifetime. 42 Accordingly, a patient’s rate of VF loss over a period of time and the level of damage at presentation are extremely important factors. The research by Chauhan et al. has emphasised the clinical importance of establishing estimates of the rates of progression in glaucoma patients. 5 The first objective for this chapter is to estimate rates of MD progression, VF damage at presentation and age at presentation in a large cohort of glaucoma patients. The results of this analysis are extremely important to assess the cost-effectiveness of alternative VF monitoring regimes on long-term health outcomes. We therefore conducted a retrospective multicentre study of VF databases (PROGRESSOR Medisoft, Leeds, UK) to provide baseline population parameters for the health economic modelling discussed in the next chapter. This VF database comprised 473,252 VF tests of 88,954 patients from four separate hospitals: Moorfields Eye Hospital in London, Cheltenham General Hospital Gloucestershire Eye Unit, Calderdale Royal Hospital in West Yorkshire and Queen Alexandra Hospital in Portsmouth. In order to be included in the study, VF tests were required to utilise the 24-2 test pattern, a size III stimulus and the Swedish interactive threshold algorithm (SITA) Standard or SITA Fast testing algorithm.

This study centred on rates of VF loss progression in newly diagnosed glaucoma patients; consequently, to be included in the study, one of each patient’s eyes had to have a VF test series that was at least 2 years long, with at least six VF tests after discarding the first VF test for learning effects. This time period and number of VFs aligns with the proposed practice of testing patients six times in the first 2 years. If patients had two eyes meeting these criteria, the eye with the best (larger) MD at baseline was analysed; otherwise the patient’s single eye meeting the criteria was analysed. The patient’s better eye (the eye with the larger/healthier MD) was analysed rather than their worse eye because research suggests that the level of VF damage in a patient’s better eye has a closer relationship with functional vision and utility estimates relative to that of the worse eye. 43–46 As the analysis considered VF data and no other clinical information it was not possible to confirm whether individuals in the database were clinically diagnosed with glaucoma or were glaucoma suspects. In order to attempt to include only eyes with glaucomatous defects, the study required the eye’s MD or pattern SD value to be outside 95% normal limits in the baseline VF. We also included only patients of at least 35 years of age. Consequently, 5999 patients and 5999 eyes were left in the final analysis.

The level of VF damage at baseline, defined as a patient’s ‘health state’ in the health economic model that follows this chapter, was defined according to the Bascom Palmer glaucoma staging system. 47 This staging system identifies mild patients as those with an MD between 0 dB and –6 dB, moderate patients as those with an MD between –6 dB and –12 dB and severe patients as those with an MD between –12 dB and –20 dB, while patients with worse MDs are classified as visually impaired. Patients were therefore allocated to one of the four possible health states based on their baseline disease severity (Table 5).

Figure 5 illustrates the distribution of the 5999 patients’ age at baseline; the asymmetry of the histogram suggests that there are two distinct groups of newly diagnosed glaucoma patients – a group of patients appear to present at an earlier age than the mode of the distribution (approximately 70 years). Hierarchical clustering for parameterised Gaussian mixture models48 with two mixture components (clusters) was carried out to determine the mean age of each of the two components. This clustering suggested that the distribution of ages could be represented as two clusters (normal distributions) with mean ages of 51.2 years and 70.2 years; we defined these two groups as the ‘younger’ and ‘older’ cohorts respectively.

FIGURE 5.

Distribution of patients’ age at baseline.

Intrinsic to the overall objectives of this research is how quickly patients progress to visual impairment from their level of VF damage at presentation. A key driver for this is the progression rate of the individual. We stratified patients in the VF database by their age grouping (younger cohort or older cohort) and measured their rate of progression of MD. Rates of MD loss were calculated in decibels per year (dB/year) using standard linear regression. Next, patients were subclassified according to whether they had stable, slow, medium or fast progression of MD, following the groupings in Chauhan et al. 5 (Table 6).

In those patients in the younger cohort, it was observed that 49.2%, 36.4%, 12.2% and 2.3% of patients analysed were characterised as being stable, slow, medium and fast progressors respectively. For patients in the older cohort, it was observed as 33.8%, 41.0%, 21.0% and 4.2%, respectively (Figure 6). Our finding that a larger percentage of older patients than of younger patients are fast progressors supports results in the Canadian Glaucoma Study, which showed that increasing age was associated with a worse MD rate. 36

FIGURE 6.

(a) Distribution of MD rates in younger cohort; and (b) distribution of MD rates in older cohort (eight patients have been removed to enhance visualisation, as their rates of MD exceeded 10 dB/year).

As already pointed out, one important aim of this research is to establish how rapidly newly diagnosed glaucoma patients progress to visual impairment; clearly, the amount of VF damage at presentation is another crucial factor (Figure 7). Analysis of the VF database indicated that, of the younger cohort, 65.0% patients were specified as having mild glaucoma, 21.4% were defined as having moderate glaucoma, 10.0% were specified as having severe glaucoma and 3.7% of patients were defined as visually impaired. In the older cohort, these figures were very similar, 66.2%, 20.9%, 9.3% and 3.7% respectively. The mean level of existing VF damage for the younger cohort was –3.1, –8.3, –15.5 and –24.0 dB for the mild, moderate, severe and visually impaired subgroups, respectively, whereas these figures were –3.1, –8.4, –15.4 and –23.6 dB for the older cohort respectively.

FIGURE 7.

(a) Distribution of baseline MDs younger cohort; and (b) distribution of baseline MDs for older cohort.

The analyses of VF data outlined above provided a number of interesting findings. In particular, the distribution of rates of MD loss shown in Figure 6b is reminiscent of similar results shown in prospective studies. 30,36 However, only a small proportion of glaucoma patients progress at a rate faster than –1.5 dB/year. This is in stark contrast to the findings from Heijl et al. ,41 who estimated that 15% of patients progressed at a rate faster than –1.5 dB/year, and the New York Progression Study, in which the number was in excess of 9%. 38–40 A possible explanation for this difference is the substantial percentage of patients with pseudoexfoliation glaucoma, which in the Heijl et al. study was associated with faster disease deterioration,41 and which is a condition not commonly seen in the UK. Another potential reason is that the patients in these other studies presented with more advanced glaucoma than observed here, which may be associated with more rapid progression. 36 Nevertheless, our estimates of the percentage of ‘fast progressors’ are similar to the results from controlled clinical cohort studies. 35–37 Notably, around half of the patients investigated had a positive rate of MD change, which is likely because of a combination of high VF measurement variability49,50 and learning effects. 51 We endeavoured to prevent learning effects by discarding patients’ first recorded VF tests, but, evidently, there remains a considerable difficulty in accurately measuring rates of MD change. This has significant consequences for the utility of VF testing in clinical practice. Patients who find VF testing difficult and produce unreliable measurements, or patients who simply are learning to do the test over time, should be identified as soon as possible because they are using resources that may be better utilised elsewhere.

Clinical trials and prospective studies principally inform clinical practice and decisions regarding health service delivery. On the other hand, retrospective examination of large numbers of data collected from the everyday clinical milieu over long periods of time also offers interesting insights, as our analysis shows. It is already recognised that participants in prospective glaucoma studies better adhere to prescribed therapy than patients in routine medical care;52 consequently, prospective studies and trials may sometimes misrepresent the routine clinical situation. However, any retrospective study, including our own, will have limitations. In particular, full patient records were not available, so analyses were based purely on age and VF data. As a result, some of the patients may have concomitant eye disease, principally cataract, and it is possible that a small minority of the patients did not have glaucoma at all, although it is unlikely given that all subjects were monitored at glaucoma clinics over at least 2 years.

The primary aim of this part of the research was to estimate the rates of MD progression and baseline VF damage observed in newly diagnosed glaucoma patients under clinical care, since, in order to model progression of VF loss, it is important that any model replicates data from the real clinical situation. Of course, it is assumed that the 5999 eyes selected are representative of all the patients made available to this study. One limitation is that those selected may be a biased sample of patients who are at more risk of progression. For example, there is a danger of selecting a group of patients who have actually been monitored quite intensively, perhaps because they are perceived to have been at high risk of rapid VF loss. Still, we think the very large sample is a reasonable representation of our target population and yields valuable data on rates of visual loss in clinics. For example, the interested reader is directed towards a paper describing a subsequent study that evaluated the proportion of patients in glaucoma clinics progressing at rates that would result in visual disability within their expected lifetime. 53 The information gathered in this section is thus essential to model the clinical effectiveness and cost-effectiveness of different VF monitoring regimes.

Computer model of visual fields

Gardiner and Crabb previously developed a computer model for generating series of VF tests. 6 In short, the model simulates series of VF tests with known properties, specifically baseline VF sensitivity, the length of series, the frequency of testing and the rate of loss. Variability or ‘noise’ around each measured value (VF sensitivity) is then added to the simulation by sampling randomly from a Gaussian distribution with mean zero and with a SD which increases as the underlying sensitivity decreases. A key objective of this chapter was to advance our published model for simulating VFs and, then, use simulations to investigate the clinical effectiveness of different VF testing schemes, namely annual testing against three tests per year in the first 2 years (following the recommendations by Chauhan et al. 5 and the EGS7).

As already pointed out, interpretation of results from SAP is difficult as VF measurements are highly variable, as shown by psychophysical experiments using frequency-of-seeing (FOS) measurements54–56 and test–retest studies. 50,57–62 VF variability dictates frequent monitoring and/or an extended period of time to accurately and precisely detect glaucomatous progression. 5,6 The lack of a ground-truth VF measurement in glaucoma makes it very difficult to measure the diagnostic performance of tests, such as SAP, to evaluate disease progression. Computer simulation thus provides a way to generate artificial VF data that reflect real results obtained with SAP. Indeed, simple computer simulations have been utilised to gauge VF test strategies for over 20 years. 6,63–70 Furthermore, simulation provides a reproducible and modifiable means to investigate the characteristics of cross-sectional and longitudinal VF data in large numbers. A key component of any computer model for VFs is the simulation of variability around VF sensitivity measurements.

The relationship between variability and sensitivity in visual field data

Previous research has explored the relationship between VF variability and sensitivity. In particular, Henson et al. and Henson collected FOS data, using SAP, from four VF locations in 71 subjects with a range of VF damage. 55,71 The authors concluded that variability (SD) was greater as VF sensitivity decreased and described the relationship using the following linear function:

where A = –0.081 and B = 3.27; R² = 0.57. According to this equation, as sensitivity reduces there is an exponential increase in variability. This finding, however, is not directly relevant to clinical SAP test strategies, where measured thresholds are not constructed from FOS curves. Moreover, there was an extreme lack of measurements with reduced sensitivity and absolutely no data below 10 dB. A later study by Artes et al. overcame these limitations using test–retest data and studied the variability properties of SAP threshold estimates from the full threshold and SITA strategies of the HFA. 61 The authors investigated one eye of 49 patients with glaucoma, with a large range of VF damage, four times with each test strategy. The study found that variability increased as the ‘best available estimate of sensitivity’ (mean sensitivity from test–retesting) decreased up until about 10 dB, after which variability was found to reduce as sensitivity decreased further. For glaucomatous locations with a best available estimate of sensitivity equal to 10 dB, variability was so great that the fifth and 95th percentiles of the retest measurements covered 0 dB to 28 dB respectively.

In this section, we characterise VF variability by level of sensitivity using a statistical method to quantify heteroscedasticity in longitudinal data. The chief advantage of this approach is that inference is based on thousands of patients tested in standard clinical settings, rather than the tens of individuals reported in FOS and test–retest studies. We undertook a retrospective analysis of 14,887 VF tests from 2736 eyes in 2736 patients (if more than one eye was eligible, one eye was randomly selected) attending the Glaucoma Service of Moorfields Eye Hospital, London, between 1997 and 2009. VFs were anonymised prior to analysis. The study adhered to the tenets of the Declaration of Helsinki and was approved by the research governance committee of Moorfields Eye Hospital. All data were transferred to a secure computer database at City University London, London, UK.

All VF tests were carried out with the HFA using the 24-2 test pattern with a Goldmann size III target and the SITA Standard testing algorithm. VFs were considered unreliable and discarded according if fixation losses were ≥ 20% or false-positive errors were ≥ 15%. False-negative errors were not considered, as a higher false-negative rate is strongly correlated with field damage. 72 A patient’s series of VF tests had to number at least five and the first VF test was discarded to lessen the impact of perimetric learning effects. 51,73 The relationship between variability and sensitivity was analysed by examining the residuals from linear regression of pointwise sensitivity over time. Linear regression estimates the relationship between a predictor variable X and an outcome variable Y:

where a is the intercept, b is the slope and E is the error term. 74 The error term represents the part of the outcome variable that is not explained by the predictor variable. For the fitted function, the error term is estimated from the residuals, which are the vertical deviations from the fitted line.

The simplest and most common approach for fitting a regression line is to minimise the sum of squares of the residuals; this method is known as ordinary least squares linear regression (OLSLR). This technique assumes that the outcome variable is error free and that the error term is Gaussian distributed with mean zero and uniform variance across the range of the predictor measurement. Constant variance is known as homoscedasticity (‘equal scatter’). However, if the residuals alter according to the size of the measurement, this is referred to as heteroscedasticity (‘unequal scatter’), which indicates that the variance of the error term is not constant across observations. Linear regression coefficient estimates (i.e. the slope and intercept terms) are not biased by heteroscedasticity, but estimates of the variance of these coefficients are influenced. 75 Thus, OLSLR, in the presence of heteroscedasticity, offers an unbiased estimate for the relationship between the predictor variable and the outcome variable, but standard errors and, consequently, inferences on statistical significance may be incorrect. The residuals from OLSLR are hugely informative when examining heteroscedasticity. A scatterplot of the absolute or squared residuals against X, Y or Ŷ (the fitted value of Y) may be used to assess for non-uniform variance of the error term.

We investigated heteroscedasticity in longitudinal VF data by analysing the residuals from pointwise linear regression of sensitivity measurements (the Y variable in dB) against time (the X variable in years) for each eye’s series of VF tests using OLSLR and Tobit linear regression (TLR). 76 We previously discussed the usefulness of TLR for the analysis of VF sensitivity measurements in Russell et al. 77 When the response variable in a linear model is censored (as is the case for SAP sensitivity), the assumptions of OLSLR are not valid. TLR, on the other hand, employs a latent dependent variable, which respects left and/or right censoring and predicts the response only within the range specified. Thus, in contrast to OLSLR, TLR reconciles that a VF sensitivity measurement of 0 dB could be 0 dB, or, a value less than 0 dB (were SAP to have a larger dynamic range).

Regression models (TLR and OLSLR) were fitted to each eye’s series of VF sensitivity values (for each test point separately) against time (the patient’s age at each VF test); for an example, see Figure 8. The two locations adjacent to the blind spot were excluded, giving 52 thresholds for each VF.

FIGURE 8.

The solid line represents OLSLR of a patient’s VF measurements (at a given point in their VF) against their age. In this example the TLR line is no different to the OLSLR line.

Next, least squares residuals (Ê) were extracted:

and binned according to measured sensitivity in the range 0–36 dB. Residuals were also grouped according to the fitted sensitivity value (rounded to the nearest whole decibel), Ŷ, as this value estimates ‘true’ sensitivity. The two binning strategies ask subtly different questions. First, binning by measured sensitivity investigates variability conditional on the measured threshold and, therefore, poses the question, given a measured threshold what is the underlying range of values for the ‘true’ value? This is akin to a study by Wall et al. 57 in which retest VF thresholds were compared with baseline threshold; in this case, as the authors state, ‘the first test is not meant to be the true sensitivity, as it has its own variability’. Second, binning by fitted sensitivity analyses variability conditional on the estimated true value and asks the question, given a ‘true’ threshold value what is the range of measured thresholds expected for any given test? This approach mirrors research by Artes et al. ,61 in which thresholds were compared against the average of several retest thresholds. The difference in the two binning strategies is shown in Figure 8. In this figure, the regression residuals are all associated with an OLSLR-fitted sensitivity of 31 dB; however, when the residuals are stratified by measured threshold, they are grouped into the following bins: 30, 31, 31, 30, 33, 31, 33 and 28 dB.

Table 7 summarises the characteristics of the study sample.

In total, 142,272 (52 × 2736) regression lines were fitted and approximately 1 million residuals recorded for each linear regression method. The residuals associated with fitted and measured sensitivity levels were evaluated as histograms for both the TLR and OLSLR models (Figure 9). Figure 9 highlights significant differences in the distributions of residuals at different sensitivity levels; for both linear regression methods, distributions were relatively condensed at large VF sensitivities (26–36 dB) but variability increased substantially as sensitivity decreased to a level of 10 dB. Indeed, for the 10-dB level, residuals spanned almost the entire dynamic range of SAP. Below 10 dB, there was some disparity between the distributions of residuals for the TLR and OLSLR models (see Figures 9a and e); this suggests that any reduction in variability below 10 dB is explained by the limited dynamic range of SAP, as evidenced by the negative skew in the histograms in Figure 9. In the range of 0–21 dB, the distributions of residuals for OLSLR are negatively skewed as a result of the limited dynamic range, and this is not observed, to the same extent, in the corresponding TLR distributions. The standard deviations of the residuals for each fitted and measured sensitivity level are shown in Figures 10a and 10b respectively; the blue lines result from binning OLSLR residuals, whereas the green lines are derived from binning TLR residuals. These are compared with variability estimates from Henson et al. 55 (yellow lines) and Artes et al. 61 (red lines).

FIGURE 9.

Distributions of residuals according to fitted-values values (left column) and measured values (right column) for 0, 10, 20 and 30 dB sensitivity levels. Distributions are illustrated as ‘back-to-back histograms’: the upper histogram (black bars) are residuals derived from OLSLR, whereas the lower histogram (green bars) are residuals derived from TLR. (a) Ŷ, = 0 dB; (b) Ŷ, = 10 dB; (c) Ŷ, = 20 dB; (d) Ŷ, = 30 dB; (e) Y = 0 dB; (f) Y = 10 dB; (g) Y = 20 dB; and (h) Y = 30 dB.

FIGURE 10.

(a) Plot of the SD of residuals for each fitted sensitivity level from OLSLR (blue line) and TLR (green line); and (b) plot of the SD of residuals for each measured sensitivity level from OLSLR (blue line) and TLR (green line). In both plots, variability estimates are compared with those from Henson et al. (yellow lines) and Artes et al. (red lines). 55,61 The blue-to-red background is a smoothed colour density representation of the scatterplot for all absolute residuals; the hotter the colour, the larger the sample at that level of sensitivity.

This study is unique in its analysis of the association between variability and sensitivity in VF tests. Previous research has studied this relationship with small numbers of patients, or people with normal vision, using FOS experiments or test–retest data in a research setting. In contrast, we analysed variability using linear regression analysis of retrospective large-scale longitudinal clinical data. The results confirm that a reduction in VF sensitivity is accompanied by a large increase in variability. 50,54,57,59–61,78,79 However, there are notable differences between this study and previous investigations of VF variability. Test–retest studies assume that VF measurements remain unchanged over the testing period and take an average of threshold values to approximate true sensitivity. Here we estimate two parameters, a slope and an intercept term, whereas test–retest studies estimate only the latter parameter, as they assume that the measurement does not change in the period of time over which the data are captured. Thus, a limitation of test–retest data is that they assume the absence of a perimetric learning effect, which can persist over tens of VF tests in some patients. 50,51,80 Nonetheless, our results are in good agreement with the findings of Artes et al. ,61 but are possibly more robust because of the large number of data investigated. Moreover, our study sample consists of patients from general ophthalmic clinics and not ‘perimetry athletes’ who are acquainted with SAP and, accordingly, may record less noisy measurements. In addition, since our analysis was carried out on retrospective data, the technique could be easily applied to other perimetry and imaging devices used in glaucoma assessment.

Both our method and the test–retest approach assume that the fitted value or mean of the measurements is the ‘true’ value. Using the mean to estimate true sensitivity makes statistical assumptions about VF measurements; in particular, the arithmetic mean is greatly affected by outliers, and is not robust to skewed and/or truncated distributions. This is reinforced by inspecting estimates of VF variability in the test–retest studies by Artes et al. 61 and Wall et al. 57 – when VF sensitivity is equal to 0 dB, the arithmetic mean is not robust to the truncated nature of VF measurements and the derived variability is artificially reduced (see Figure 10a). This truncation effect is very apparent in the distributions shown in Figure 9 and in similar figures in other studies. 57,61 Thus, our results emphasise that a reduction in VF variability for thresholds below 10 dB can fundamentally be attributed to the limited dynamic range of SAP. Unlike OLSLR, TLR attempts to take into account the truncation effect of VF sensitivity measurements. This is evident in Figure 9e, in which residuals binned by a measured threshold of 0 dB are symmetrically distributed for TLR, but are negatively skewed for OLSLR. As expected, positive skew is apparent in both distributions in Figure 9a, in which residuals are binned by a fitted value of 0 dB, because no measured value can ever be less than 0 dB. Furthermore, Figure 10a demonstrates that the SD of the residuals (binned according to the fitted value) is greater for TLR than for OLSLR. This is because fewer negative residuals are associated with TLR as it respects the left-censoring of VF measurements, whereas OLSLR does not respect this phenomenon.

Unlike previous research, this study also analysed variability as a function of measured sensitivity; this relationship is informative about the range of possible ‘true’ values associated with an observed measurement. The dashed dark green and dark blue lines in Figure 10b indicate the variability associated with measured sensitivity for the TLR and OLSLR models, respectively, whereas Figures 9e–h illustrate the distribution of residuals associated with measured sensitivity. Both sets of figures suggest that variability rises rapidly as measured threshold declines. This result has important implications for SAP. Wall et al. 57 suggested that threshold estimates below 20 dB have little worth for predicting the value at retest. Our results are comparable to the findings of Wall et al. and back their suggestion that, for the purposes of detecting progression, investigation of damaged VF test points could be valueless.

Visual field variability leads to false-positive diagnoses of progression when patients actually have stable glaucoma, which may lead to needless treatment changes and costs to both patient and health-care provider. 81 Conversely, progression may be overlooked if clinicians deem any reduction is as a result of inherent measurement variability. One particularly important application of these results is in VF simulations. Presently, there is no ground truth for the assessment of glaucomatous VF progression, so our results will now be used to build a non-parametric model of VF variability. VFs with known characteristics are simulated to investigate the variability of the MD index, which is important to assess the clinical effectiveness of proposed practice (six VFs in the first 2 years) and current practice (annual VF testing). Past VF simulation models6,69,70,82 have been based on Henson et al. ’s55 equation for VF variability, which may be less suitable than the results here as Henson et al. ’s results were grounded on FOS experiments, with no measurements below 10 dB. Conversely, the results presented here are based on thousands of clinic patients, with tens of thousands of measurements across the range of SAP sensitivity.

Model for generating visual field simulations

As there is no technique for measuring ground-truth VF sensitivity, it is difficult to gauge the performance of SAP to measure glaucomatous progression. Computer simulations can be used to provide virtual VF data consistent with real SAP test results. In the previous section, we investigated the relationship between VF variability and sensitivity. These results were used to construct a novel non-parametric model for generating VF simulations. We described the model and used it to generate 1 million VF simulations from 1000 ground-truth VFs (1000 simulations per real VF test). These simulations were then analysed to investigate the variability associated with the MD summary statistic, as a function of the level of MD. 79 It is worth noting, again, that MD measures the average increase or decrease of a patient’s overall VF compared with a person with healthy vision of the same age.

Mean deviation is especially important to the overall objectives of this research, since the proposed VF testing frequency (three times per year in the first 2 years post diagnosis) is based on this measurement. In particular, proposed practice is based on identifying rapidly progressing patients, who are defined as losing MD of more than 2 dB per year, with greater certainty than current practice (annual testing). In clinical practice, MD is often analysed in order to identify VF defects and monitor progression of glaucoma. Despite its importance, the relationship between the level of MD and variability of MD is uncertain. It has been suggested that MD variability is non-stationary, growing with VF damage,81,83,84 but no research has yet reported on the impact of pointwise VF variability and, therefore, the pattern of VF damage, on MD variability; such research would not be feasible without computer simulations.

The study sample used to derive pointwise VF variability, which forms the foundation of the simulation model, is described in the previous section. The residuals extracted from OLSLR of longitudinal pointwise VF sensitivity tell us the range of measured values expected for any given ‘true’ test result, thereby allowing pointwise sensitivity to be simulated (Figure 11). For example, to simulate VF sensitivity when the true value is equal to 22 dB, we randomly sample from the distribution of residuals associated with a fitted sensitivity of 22 dB. The simulation is demonstrated in Figure 11d (Ŷ = 22 dB); this histogram consists of roughly 50,000 residuals associated with an OLSLR-fitted sensitivity value of 22 dB, while the green line signifies the result from randomly drawing a single residual from this distribution. Thus, simulated VF sensitivity would be equal to 18 dB, since the sampled residual was equal to –4.07 dB. An entire VF test can be generated using one-by-one simulations for each test point (Figure 12). Raw sensitivities were converted to total deviation values using published normative values describing the relationship between age and sensitivity in healthy individuals. 79 MD was then calculated as the weighted mean of the total deviation values, with weights equal to the inverse of the variance observed at each VF test point in the healthy reference group. 79

FIGURE 11.

Distributions of VF variability according to OLSLR-fitted sensitivity levels. The green line in (a) Ŷ = 0 dB; (b) Ŷ = 6 dB; (c) Ŷ = 14 dB; (d) Ŷ = 22 dB; illustrates a single simulated draw from this distribution.

FIGURE 12.

(a) Ground-truth VF. The left-hand grid of numbers illustrates VF pointwise sensitivity, while the right-hand image is the corresponding greyscale plot. The variability of the shaded VF point (sensitivity equal to 22 dB) is indicated in Figure 11d. (b) VF simulated from ground-truth VF shown in (a). The left-hand plot illustrates simulated pointwise sensitivities for the above VF, while the right-hand image is the corresponding greyscale plot. The shaded VF point (sensitivity equal to 18 dB) was derived by the simulated draw shown in Figure 11d.

One thousand VFs were simulated from each of 1000 patients’ VF tests (1000 eyes) visiting Moorfields Eye Hospital between 1998 and 2009; note that these patients were not included in the analysis to establish pointwise VF variability. Once again, all VFs were carried out with the HFA using the 24-2 test pattern, a Goldmann size III target and the SITA Standard testing algorithm. Pointwise VF sensitivity was simulated via random sampling from the distribution of residuals associated with each true sensitivity (excluding locations in the blind spot). Entire HFA-like VF printouts including greyscales were then generated (Figure 13).

FIGURE 13.

Simulated VF shown as a HFA-like printout. The grid of numbers in the top left are simulated sensitivities, while the adjacent greyscale plot provides a graphical representation of the VF (darker areas indicate damage). The two grids of numbers below represent the difference in the patient’s VF sensitivities and those of an individual of the same age with healthy vision: without correction for a general reduction in retinal sensitivity (‘total deviation’; left-hand side); and with correction (‘pattern deviation’; right-hand side). Below these two grids are probability maps indicating whether or not the reductions in sensitivities are significant.

Table 8 describes the characteristics of the 1000 eyes that make up the 1000 ground-truth VFs.

We analysed the relationship between MD variability, the level of MD, and the pattern of pointwise VF damage, using computer simulations. Figure 14 shows the variability of MD, according to the SD of 1000 simulated VF tests, as a function of the ground-truth level of MD. The dashed black line in Figure 14 indicates the locally weighted polynomial regression85 (‘LOESS’ regression), which illustrates how variability changes, on average, with MD. The figure suggests that variability tends to rise as MD decreases, with variability peaking around –20 dB. For early VF damage, when a significant amount of MD loss is approximately defined as –2 dB, variability is half that when MD is equal to –10 dB, which corresponds to VF loss associated with moderate glaucoma. 47 Interestingly, as revealed by the substantial scatter in Figure 14, the SD varied more than threefold between patients with roughly the same levels of ground-truth MDs, from about 0.2 dB to over 0.7 dB (see patients A–D in Figure 14).

FIGURE 14.

Variation of ground-truth MD according to level of MD and greyscale plots for four patients’ ground-truth VFs. (a) Variation of ground-truth MD; (b) patient A ground-truth MD = –11.4 dB, SD = 0.72 dB; (c) patient B ground-truth MD = –11.5 dB, SD = 0.19 dB; (d) patient C ground-truth MD = –20.4 dB, SD = 0.25 dB; and (e) patient D ground-truth MD = –20.5 dB, SD = 0.66 dB.

Standard automated perimetry is the benchmark for monitoring glaucoma in clinical practice and clinical trials of new therapies for the disease. Nonetheless, SAP measurements are influenced by factors such as learning effects and patient fatigue. 25,51 Measurement variability is also induced by errors associated with testing strategies, such as staircases, used in clinical SAP. 65,68 Several studies have shown that a decline in VF sensitivity is accompanied by a rise in variability. 50,57–62 Thus, differentiating true VF change from inherent noise is challenging, making glaucoma management and treatment decisions difficult.

Quantitatively characterising VF measurements and the performance of methods of measuring VF progression requires a gold standard, which is not available for VF contrast sensitivity. This fact is widely documented in glaucoma research so many approaches to estimating ‘true’ glaucomatous progression have been attempted. 68,86 Computer modelling of VFs permits large numbers of data to be simulated, with known characteristics. Thus, the effects of different variables on VF measurements can be investigated. Simulations have previously been used in glaucoma research to evaluate VF testing strategies and progression measurement methods. 6,63–69,87 However, these simulations have been based on imperfect VF data and may not accurately reflect clinical VF measurements. For instance, many models6,69,70,82 have been based on a linear equation for VF variability described in Henson et al. ,55 which was based on FOS curves with absolutely no VF measurements below 10 dB. The model described here is based on SAP results from thousands of clinic patients and empirical estimates of VF variability, but it is important to note that our VF simulations do not account for factors such as patient fatigue and learning effects. 25,51

Mean deviation is routinely used to summarise VF damage in patients. As MD is a weighted average, it is less sensitive to localised VF damage, but is consequently robust to measurement noise at individual test points. Some research has proposed that MD variability rises as the level of MD declines,81,83,84 but, until now, no study has looked at the influence of the pattern of VF damage on MD. Without computer simulations, such a study would be very difficult to achieve using clinical data, as it would be almost impossible to unravel the relationship between patient error, algorithm error and other measurement errors. Figure 14 shows that MD variability tends to increase as the level of MD decreases, with some evidence that variability peaks around –20 dB. For VF loss associated with early disease (MD ≈ –2 dB), variability is half that in moderate glaucoma (MD ≈ –10 dB). 47 Furthermore, variability can vary more than threefold between patients with roughly equivalent levels of MD; this suggests that the pattern of VF damage has a significant impact on MD variability. VFs with global diffuse damage (see patients A and D in Figure 14) tend to have higher MD variability than VFs with localised damage and other regions that are healthy (see patients B and C in Figure 14). This highlights the importance of measuring VF progression using individualised rather than population-based criteria.

There has been renewed interest in the MD statistic in recent years. Junoy Montolio et al. 23 showed that VF locations measuring blind on sequential tests can lead to an underestimation of MD, which could affect MD-based progression detection algorithms. This censoring will also decrease the dynamic range of MD and, therefore, reduce variability of MD. Our results are in good agreement with those from Junoy Montolio et al. ; Figure 14 suggests that MD variability starts to decrease at roughly –20 dB, which is unsurprising given that many points in the VF will probably be perimetrically blind at this level of damage. Furthermore, Junoy Montolio et al. showed that the number of VF test points excluded by the HFA ‘Guided Progression Analysis’ software (Carl Zeiss Meditec, Dublin, CA)88,89 rises with disease progression up to an MD of a proximately –20 dB but declines beyond this value. 23

A recent study by Wall et al. 84 investigated the variability of MD for Goldmann size III and size V stimuli. They found that size V MD was repeatability smaller than that for size III, but increased for both stimuli when VF damage worsened. They also suggested that, depending on the size of the stimulus and the amount of VF damage, a reduction in MD of 1.5–4 dB is necessary to be outside normal 95% confidence limits. 84 The results presented here suggest that such confidence limits also need to account for the pattern of VF damage and not just the level of MD. Wall et al. 84 concluded their research by stating that ‘further work needs to be done to determine criteria for identifying visual field change’. We consider VF simulations an excellent point of reference for gauging the performance of VF progression detection tools and developing new methods for measuring VF progression. One particularly important finding, with reference to the overall objectives of this research, is the need to account for the non-stationary variability observed with MD worsening if assessing the rate and significance of VF damage using linear regression of MD over time. In particular, detecting VF progression in newly diagnosed patients who present with advanced VF damage is challenging owing to the increased variability associated with this disease severity compared with early VF damage.

Modelling proposed practice

In this study, proposed practice consists of testing newly diagnosed glaucoma patients three times per year for the first 2 years. The recommendations by Chauhan et al. 5 purport that this VF testing strategy will result in 80% power to detect a rate of loss of 2 dB/year in MD with moderate variability. 5 As Chauhan et al. 5 comment, the ability (statistical power) to detect a given rate of MD change depends on the variability of MD over time, the number of examinations and the amount of change we wish to detect. In the research of Chauhan et al. ,5 moderate variability was defined such that the SD of MD measurements was equal to 1; this SD figure was based on retrospective analysis of glaucoma patients in a longitudinal study. 62 Our VF model described above suggests that this is an oversimplification and that MD variability also depends on the level of damage. However, a limitation of our simulations is that they do not incorporate factors such as patient fatigue and learning effects so the absolute magnitude of MD variability will be larger in clinical practice.

The VF monitoring regimes for proposed practice and current practice are summarised in Table 9.

We carried out simulations of MD over time with a SD of MD equal to 1 (‘moderate variability’) using the same methodology described in the Chauhan et al. paper. 5 However, our model was updated to account for a mistake in the simulations in Chauhan et al. , whereby the duration of follow-up was not considered. 5 Consequently, the Chauhan et al. findings were misleading, since, in order to establish whether or not such a proposed practice is a significant improvement over annual testing, the efficacy of increasing the frequency of field examinations compared with prolonging the duration of the follow-up needs to be established. 90 As already stated, the ability to detect progression, in this case a statistically significant slope, is determined by the variability of the measurement, the number of observations/examinations and the duration of follow-up. Furthermore, increasing the duration of follow-up is much more efficient, statistically speaking, than increasing the frequency of examinations. For example, six examinations in 2 years are less powerful in detecting change than six examinations in 6 years, as the total amount of change will be much lower after 1 year than after 6 years. Thus, we conducted further simulations and calculated the time period required to detect various rates of MD change with 80% power in VF tests with moderate MD variability using current practice and proposed practice (Table 10).

The substantial differences in time to detect progression between the Chauhan et al. 5 model and our own model, summarised in Table 10, is extremely important. The Chauhan et al. model exaggerates the clinical effectiveness of proposed practice to identify MD progression; this is explained by the fact that the Chauhan et al. simulations did not account for the duration of follow-up. 5,90 Since our model accounts for the duration of follow-up in its simulations, it takes longer to identify progression with proposed practice so these time periods were used in the health economic model described in the next chapter.

Conclusion

When managing newly diagnosed glaucoma patients, the clinician’s goal is to preserve patients’ visual function during their lifetime. The risk of severe visual impairment depends on the stage of disease at presentation and the patient’s life expectancy, as well as on the rate of visual deterioration. Patients with fast progression of VF loss are in greater danger of going blind than patients with slow progression. One way to identify these ‘fast progressors’ sooner is to ascertain their rates of VF loss earlier. Considering treatment and monitoring costs, it is vital that resources are prioritised towards patients who are in greatest danger of suffering visual disability in their lifetime.

Chauhan et al. 5 recommend six VF tests in the first 2 years for all newly diagnosed glaucoma patients. Notably, this recommendation does not incorporate information about each patient’s level of VF damage at presentation, which is also hugely important when trying to ensure that a patient’s visual function remains unaffected. Further research is essential to provide evidence for advantages about adaptive testing regimes for each patient; for instance, studies could investigate the effectiveness of prescribing test intervals based on the rate of VF loss progression that a clinician wishes to detect in a given patient. One statistical consideration for adaptive testing is the relationship between VF variability and the level of VF damage. In this chapter we have shown that pointwise VF variability and MD variability increase as VF loss increases; this implies that prescriptions for the frequency of VF testing should also be dependent on the patient’s individual VF and level of damage. There might be significant service delivery advantages in monitoring patients who present with advanced VF damage more frequently than patients with early or moderate VF loss; this observation awaits further research. We support comments from Heijl that glaucoma management needs to be individualised; treatment and monitoring regimes should be tailored to the preferences of each patient, based on the risk of future loss of visual function. 42

Another strategy worth investigation is the sensible idea of varying intervals between VF tests to optimise detection of progression. 91 In one approach, the length of the interval between consecutive tests depends on the outcome of previous test results. 92 Other strategies including testing at evenly spaced intervals, such as every 6 months or annually, have also been suggested as a way of improving detection rates in clinical trials. 93 Furthermore, Crabb and Garway-Heath94 recently determined that estimates of MD progression are improved if examinations are clustered at the beginning and end of a predetermined observation period (the wait-and-see approach); the authors simulated patients with fast MD progression (–2 dB/year) with added MD measurement variability and estimated progression using linear regression of MD over time. One group of patients was measured every 6 months, another every 4 months, whereas the wait-and-see group was measured either two or three times at both baseline and at the end of a 2-year period. Stable patients (MD 0 dB/year) were generated to examine the effect of the follow-up patterns on false-positive progression identification. The wait-and-see method identified more patients with rapidly progressing VF loss with fewer false positives and one fewer VF test. The idea of scheduling VF tests in this way is particularly applicable to clinical trials in which progression of VF loss is the functional marker for glaucomatous change.

It is worth noting that an assumption of the recommendations from Chauhan et al. 5 is a linear rate of progression of MD over time. This may not reflect the true nature of glaucomatous deterioration given that there is some evidence to show patients tend to progress more quickly at older ages. 5 Nonetheless, linear regression of MDs is commonly employed in clinical practice. Furthermore, a linear decline in decibels represents an exponential decay in retinal sensitivity; thus, although loss of sensitivity could occur at greater than an exponential rate, no research to date has suggested that another type of model should be used to measure the rate of decay of MD.

In conclusion, the research presented in this chapter shows that proposed practice (six VF tests in the first 2 years) identifies progression sooner than current practice; however, the clinical effectiveness of proposed practice over current practice (annual VF testing), in terms of time to detect progression, is less effective than indicated in Chauhan et al. ’s study. 5 In the next chapter we investigate the cost-effectiveness of proposed practice and current practice.

Background

Glaucoma is a chronic condition: after diagnosis the patient requires care and management for life. Careful clinical follow-up is required in order to assess stability of the disease and to provide the appropriate level of treatment. The monitoring and management of the disease represents a significant economic burden to the NHS. Statistical modelling, described in the previous chapter, highlights the potential benefits of three VF tests in each of the first 2 years of follow-up in order to detect ‘fast’ progression of VF loss in newly diagnosed glaucoma patients. 5,7 However, the economic consequences relative to the utility that would derive from such a strategy have not been evaluated. Therefore, this chapter describes a study that examined the cost-effectiveness of existing practice (annual testing) compared with the recommended practice of six VF tests in the first 2 years in the newly diagnosed patient. The benefit of moving to such a strategy is that clinicians would have earlier access to the subject’s rate (speed) of VF loss instead of relying on risk factors for progression; something that is currently not possible with any certainty. 95,96 It would certainly help clinicians to identify rapidly progressing patients. By accounting for the rate of progression, clinicians can set better target services for those individuals most likely to move into a state of visual impairment in their lifetime. 5,42,97 Consequently, the productivity of services rendered by the NHS could be improved by reducing the level of resource consumption by those least likely to have their quality of life impacted by the disease.

Methods

This section reports the methodology underpinning the health economic model described in this chapter. Detail is provided on the estimations of parameters that support the model in addition to how the decisions nodes, which inform how patients move through the model, were identified and incorporated. This section also describes how the model was validated to ensure it estimates real-world glaucoma care service in England and Wales. Furthermore, sensitivity analyses are outlined, which were carried out to analyse how uncertainty in the model’s parameters affect final outcomes.

The model

A Markov model was constructed to model the proposed practice of increased VF monitoring frequency against existing practice. The Markov model was chosen because of its relative simplicity and relative transparency in comparison with other models (i.e. discrete event simulations). All the programming for the model was implemented in Excel (Microsoft Excel 2010; Microsoft Corporation, Redmond, WA, USA).

Markov models ‘stratify’ patients to be always a member of one of its constituent Markov states, a state that reflects the subject’s existing level of well-being. The members of each state can then move into other health states dependent on the transition probability. Each Markov state is designated a utility weight and the individual accumulates utility according to how long he or she remains a member of each state. The model is run for a length of time (e.g. 25 years) known as the ‘model time horizon’. This time horizon is broken down into equal parts, denoted as Markov cycles98 (e.g. 1-year intervals). In addition, all Markov models have at least one absorbing state in which all individuals will eventually enter if the model is given a sufficiently long time horizon.

Figure 15 presents a schematic representation of the Markov model constructed in this study. Markov states represent, from left to right, increasing disease severity. Individuals can start in any of these states according to the state of their disease at diagnosis. In a particular model cycle, patients can remain within their existing state of health, or progress towards increased disease severity. Most Markov models would allow for multidirectional transitional movement, but in the case of an irreversible disease, such as glaucoma, a unidirectional movement (towards a worse disease severity) is the only transition possible. In addition, it is assumed that patients move sequentially and cannot skip states because of the relatively slow evolution of the disease and the yearly defined cycle lengths defined in our model. Patients may also leave the model and move into the absorbing state (death).

FIGURE 15.

Markov model for a glaucoma ‘pathway’.

Strategies to follow up individuals with newly diagnosed glaucoma

Within this subsection the NICE guidelines and the proposal by Chauhan et al. 5 are reviewed. The subsection ends with a summary of the strategies included in the economic model.

National Institute for Health and Care Excellence guidelines for glaucoma

Guidelines were produced by NICE to improve the prevention of visual impairment in those with or suspected of having glaucoma by establishing clinical monitoring and treatment pathways. 1 Following identification of disease, long-term monitoring of IOP fluctuation, the ONH and the VF is required (Table 11).

TABLE 11 - NICE guidelines on COAG monitoring intervals

n/a, not applicable.

IOP at target	Progression	Patient monitoring intervals (months)
		IOP only	IOP, ONH, VF
Yes	No	n/a	6–12
Yes	Yes	1–4	2–6
Yes	Uncertain	n/a	2–6
No	No	1–4	6–12
No	Yes	1–2	2–6
No	Uncertain	1–2	2–6

Those defined as experiencing disease progression should have their IOP, ONH and VF measured at 2- to 6-month intervals, while those not progressing are recommended to undergo the full spectrum of testing every 6–12 months. Those with an uncertain definition regarding progression status should be monitored at 2- to 6-month intervals irrespective of whether or not IOP is at target. Guidelines on IOP monitoring alone vary according to IOP control, with those achieving target IOP not recommended to undergo further testing unless progression is identified (1- to 4-month intervals). It is recommended that patients not achieving target IOP be monitored every 1–2 months if there is any suspicion of progression or every 1–4 months if progression is not suspected. 1

Treatment modalities offered to the patient, as with monitoring, vary according to the risk of the individual progressing to a state of visual impairment. Those newly diagnosed with early to moderate COAG and at risk of visual impairment in their lifetime should be offered pharmacological treatment depending on comorbidities and drug interactions. 1 Those with severe COAG and at risk of further visual impairment in their lifetime should be offered surgical intervention in conjunction with pharmacological treatment.

Monitoring of newly diagnosed glaucoma patients

The work described in the previous chapter supported the idea presented by Chauhan et al. 5 that performing three VF tests in each of the first 2 years of follow-up is helpful in detecting ‘fast’ progression of VF loss in newly diagnosed glaucoma patients. As discussed before, identification of these patients is hampered by the large variability of VF test results over time, and thus it was suggested that at least six VF tests are required in the first 2 years to identify those progressing rapidly (at a power of 80%). 5 Two different strategies, defined as current practice (annual VF testing) and proposed practice (three VF tests per year in the first 2 years after diagnosis), were modelled. Our specific hypothesis was constrained to investigating if the proposed practice was more cost-effective than current practice. In short, we seek the benefit of getting more precise information of progression earlier by using proposed practice. We speculate that this gain in information, especially in identifying rapidly progressing patients sooner, will yield improved cost-effectiveness of clinical care.

Results

Probabilistic sensitivity analysis

Greater variability was observed in CEP plots for the 70-year-old cohorts than for the 50-year-old cohorts; simulated incremental costs associated with the 70-year-old cohorts were considerably higher than those associated with the 50-year-old cohorts because more older patients were simulated in the model, while incremental utilities were also significantly higher in the 70-year-old cohorts than in the 50-year-old cohorts (Figure 16). In addition, there were twice as many observations in the north-west (dominated) quadrant of the plane in the 50-year-old cohorts (M50 = 540, F50 = 578) than in the 70-year-old cohorts (M70 = 211, F70 = 219).

FIGURE 16.

Cost-effectiveness planes by cohort. (a) M50; (b) base case; (c) F50; and (d) F70.

Subsequently, CEACs were defined from these simulations (Figure 17). Willingness to pay for each QALY gained was varied from £0 to £50,000 and the proportion of simulations deemed acceptable at this level was noted. Similarly shaped CEACs were observed for the M50 and F50 cohorts, and for the M70 and F70 cohorts. At a £30,000 cost per QALY ceiling ratio, the proportion of observations deemed acceptable in the M70, F70, M50 and F50 cohorts was 57.33%, 67.78%, 73.36%, and 74.26% respectively. When the ceiling ratio was increased to £50,000 cost per QALY, the proportion of observations deemed acceptable was 81.69%, 86.35%, 84.22%, and 84.44% for the M70, F70, M50 and F50 cohorts respectively. The 50-year-old cohorts’ CEACs were observed to plateau sooner than those for the 70-year-old cohorts, with the M70 cohort CEAC consistently lower than in other cohorts in terms of probability of acceptance. The F70 cohort’s CEAC was consistently lower than those from the 50-year-old cohorts up until the £42,000 per QALY mark, at which point its ICER had an increased probability of acceptance compared with the 50-year-old cohorts.

FIGURE 17.

Cost-effectiveness acceptability curves across all cohorts.

Health state utilities

The utilities associated with health state membership were varied in 0.01-QALY increments from baselines of 0.8015, 0.7471, 0.7133 and 0.5350 for utility health states 1, 2, 3 and 4, respectively, and the impact on the ICER was assessed (Figure 18). A negative relationship between the parameters and ICERs was observed for the utility associated with health state 1 for all cohorts, although only a decrease in utility in the M70 cohort was found to push ICERs above £30,000 per QALY. Similar findings were observed for the utility associated with health state 2; however, a reduction in this utility caused an accelerated increase in ICERs for the M50 and F50 cohorts compared with the 70-year-old cohorts. When the utilities of health states 3 and 4 were examined, a positive relationship existed between the parameters and cohort ICERs. Within utility health state 3, the M70 and M50 cohorts were found to surpass the £30,000 per QALY ratio when utilities were increased; however, only the M70 cohort tipped this ratio when the utility of health state 4 was examined.

FIGURE 18.

One-way analysis of utility health states. (a) Utility health state 1, baseline = 0.8015 QALYs; (b) utility health state 2, baseline = 0.7471 QALYs; (c) utility health state 3, baseline = 0.7133 QALYs; and (d) utility health state 4, baseline = 0.5350 QALYs.

Treatment costs

Treatment costs were varied by increments and decrements of £25, in the range ± £125 from a baseline of £696.49, £784.28 and £970.40 for first-, second- and third-line treatment costs, respectively (Figure 19). For first-line treatment costs, a negative relationship was observed between this parameter and ICERs of all cohorts, but the M70 cohort was the only grouping to surpass the £30,000 per QALY mark when treatment costs were reduced to £600. For second-line treatment costs, a positive relationship was found in the M70 and F70 cohorts, while a marginal negative relationship was observed in the M50 and F50 cohorts; however, the £30,000 per QALY mark was not exceeded in any cohort. For third-line treatment costs, a slight positive relationship was observed in all cohorts; however, the £30,000 per QALY mark was not surpassed for any cohort. The nature of these relationships can be attributed to the fact that proposed practice and current practice utilises the different treatment lines to varying extents across the patient characteristic framework (for example, proposed practice implements the first line of treatment to a lesser degree than current practice, as it identifies fast progressors sooner and, thus, these patients receive more aggressive treatments lines earlier).

FIGURE 19.

One-way analysis of treatment costs. (a) First-line treatment costs; (b) second-line treatment costs; and (c) third-line treatment costs.

Treatment modality effects

First-line treatment effects on rate of VF progression were analysed in 0.05 dB/year decrements from 0 to –0.5 dB/year from a baseline of 0 dB/year, –0.74 dB/year and –1.22 dB/year for first-, second- and third-line treatment costs, respectively (Figure 20). It is worth noting here, again, that an improvement in treatment effects is associated with a decrease in the rate of MD progression. The second- and third-line treatment effects were varied in increments or decrements of 0.05 dB/year and the impact on the ICER was assessed in the range ± 0.25 dB/year. For first-line treatment effects, an improvement in effectiveness increased ICERs. The M70 cohort surpassed the £30,000 per QALY mark at –0.15 dB/year, while the F70 cohort exceeded this ceiling ratio at roughly –0.3 dB/year; the F50 and M50 cohorts did not surpass the £30,000 per QALY mark. When second-line treatment effects were examined, improving effectiveness increased ICERs in the M50 and F50 cohorts and decreased ICERs in the M70 and F70 cohorts. However, the £30,000 per QALY mark was only surpassed by the M70 cohort when the treatment effect was equal to approximately –0.6 dB/year. Improving effects for third-line treatment decreased ICERs for all cohorts, with no cohort surpassing the £30,000 per QALY mark.

FIGURE 20.

One-way analysis of treatment effects. (a) First-line treatment costs; (b) second-line treatment costs; and (c) third-line treatment costs.

Implementation costs, visual impairment costs and time horizons

The costs of implementing proposed practice, the costs of patients progressing into a state of visual impairment and the time horizons utilised in the model were also chosen for one-way analysis. Implementation costs were varied between £0 and £900,000 in £100,000 steps and the impact on the ICER was assessed from a baseline of £410,000. Increasing implementation increased ICERs in all cohorts; the £30,000 ceiling ratio was exceeded in the M70 cohort only when this cost was equal to roughly £800,000. Costs of visual impairment were expanded to £9000 per subject in £1000 increments from the initial baseline assumption of £0 as a result of the NHS perspective of the model. As visual impairment costs increased, ICERs decreased for all cohorts, with the total cost associated with current practice superseding that of proposed practice over the 25-year time horizon at approximately £5000 for the M70 cohort, £4000 for the F70 cohort and £2500 for the M50 and F50 cohorts. The impact of the time horizon was examined at 5-year intervals in both directions. For all 70-year-old cohorts, ICERs were observed to begin plateauing after 15-year time horizons; however, ICERs grew exponentially below 15 years. For the 50-year-old cohorts, ICERs were observed to continually shrink as time horizons expanded with reductions beginning to plateau after a horizon length of 45 years. All cohorts surpassed the £30,000 per QALY mark when the time horizon was shortened to approximately 10 years in length.

Deterministic sensitivity analysis: tornado analysis

Tornado diagrams were constructed to represent model outcomes for the limits associated with each parameter, thereby mapping how the maximum and minimum values impact on ICERs. In addition, the costs associated with progressing into visual impairment were also explored using deterministic sensitivity analysis. For all parameters, outcomes were sorted in order of ICER impact, resulting in the tornado appearance. Tornado analysis was performed on both the full simulation results (Figure 21) and individual cohorts.

FIGURE 21.

Full simulation tornado diagram.

When analysing the full simulation data, utility health states were found to have the greatest impact on the derived ICER. In particular, utility health state 4 had the most significant impact, with findings suggesting that the variability around this parameter was sufficient to push the ICER beyond the £30,000 ceiling ratio. The projected cost of visual impairment was the next most important factor in the tornado analysis, altering the ICER by ±£12,326.98, with the lowest estimation of visual impairment costs sufficient to push the ICER beyond the £30,000 per QALY mark. Costs associated with the different treatment modalities were the next most important parameters with the variability around the cost of first-line treatment affecting the ICER most, followed by second- and, then, third-line treatments. The percentage of patients with a moderate rate of progression in the 70-year-old cohorts featured next in the diagram, followed by discount rate. All other parameters had less than a £5000 impact on the ICER from the minimum to maximum value.

When deterministic sensitivity analysis focused specifically on the M70 cohort, a greater number of parameters pushed the ICER beyond the £30,000 per QALY limit, including the utility associated with health states 1, 3 and 4, the costs of visual impairment, the costs of first- and second-line treatments, the proportion of patients with moderate or slow progression in the 70-year-old cohorts and, finally, the effects associated with second-line treatment. Within the M50 and F50 cohorts, the only parameter observed to drive the ICERs beyond the £30,000 cut-off was the cost of visual impairment. For the F70 cohort, three parameters forced ICERs beyond this ceiling ratio, namely the utility health state 4, the costs of visual impairment and the percentage of patients with moderate VF progression.

Deterministic and probabilistic sensitivity analyses combined

The DSA of VF costs, discount rates, risk distributions and costs of visual impairment was combined with PSA in order to examine how variation in this specific parameter may impact on the probability of acceptance for proposed practice at given willingness to pay (see Appendix 1, Tables 30–33).

In terms of VF costs, analysis was varied from the baseline of £56.54 and varied from a maximum of £70.45 to a minimum of £38.76. In the base-case analysis at a £30,000 willingness-to-pay threshold, an increase in the cost of a VF test reduced the probability of proposed practice being cost-effective from 57.33% to 45.63%, while the low estimation increased probability to 71.11%. Altering this cost in the other cohorts produced similar results, but with a smaller percentage change, particularly in the 50-year-old cohorts.

In terms of discount rates utilised, analysis was started from the baseline of 3.5% and varied from a maximum of 5% to a minimum of 0%. In the base-case cohort with a £30,000 willingness-to-pay threshold, the removal of discounting increased the probability of cost-effectiveness from 57.33% to 71.91%, while an increase in discounting reduced this probability to 49.13%; similar results were identified in the other cohorts. The differences in the probability of cost-effectiveness between the low discount and high discount were found to reduce as willingness to pay per QALY gained was increased.

In terms of the risk distributions assumed within the model, analysis started at the baseline of 80% low risk and 20% high risk, and this was varied from a ratio of 70% low risk : 30% high risk to 90% low risk : 10% high risk. In the base case with a £30,000 willingness-to-pay threshold, a decrease in the proportion of high-risk patients increased the probability of cost-effectiveness from 57.33% to 57.34%, while an increase resulted in a reduction of probability to 55.06%. These findings were generally reflected in the other cohorts.

Finally, in terms of the costs of visual impairment, analysis was varied from a baseline of £0 and varied from a maximum of £1758.50, the maximum degree of visual impairment costs before current practice became dominated by proposed practice. The introduction of costs of visual impairment to the base case increased the probability of proposed practice being cost-effective with visual impairment costs of £250, £500, £750, £1000 being associated with an increase in probability of 4.04%, 5.87%, 9.68%, 12.76% and 86.73%, respectively, at the £30,000 willingness-to-pay threshold.

Summary and discussion

The study described in this chapter sought to examine whether or not increased VF monitoring at the earliest stages of disease identification (i.e. six VF tests in the first 2 years after diagnosis) would be cost-effective compared with the current practice of one VF test per year. The economic evaluation results show that proposed practice is associated with higher costs, but more QALYs, than current practice. Under the full simulation, the ICER was £21,679 and 834.65 years of visual impairment were avoided with proposed practice (10,000 individuals). When the model was run for the male cohort who were 70 years old (lowest residual life expectancies relative to the other cohorts), the ICER rose to £26,531, with a probability of being cost-effective at 57.3% at £30,000 threshold value. Since the economic model was constructed from the perspective of the UK NHS, when societal gains are accounted for (the costs of visual impairment beyond the UK NHS), the cost-effectiveness of proposed practice expands.

Comprehensive DSA and PSA were performed. DSA identified that the ICERs were most sensitive to the uncertainty surrounding the parameters utilised for utility health states, particularly for utility health state 4, while the uncertainty associated with the costs of the different treatment lines was also found to impact on the derivation of the ICER.

It should be noted that the decision nodes informing the framework behind our model impact considerably on the differentials between proposed and current practice. While the clinical review panel was consulted during the formulation of the nodes, other glaucoma subspecialists may disagree with the step increases in treatment lines used. In particular, some clinicians may not subscribe to the view that the information gained from increased VF monitoring forms such a vital component in decision-making. Nevertheless, VF testing remains the only direct method for measuring patients’ visual function and, therefore, to gauge if a treatment is effective in avoiding future impairment.

Conclusion

In conclusion, this study supports the recommendation by NICE for a randomised comparative trial (RCT) to assess the real-world implications of increased monitoring at the earliest stage of glaucoma identification. In particular, the health economic model that we have described in this chapter has demonstrated that this proposed practice is likely to be cost-effective – the analyses revealed little evidence to suggest that the strategy would not be cost-effective. Further studies of the impact of the glaucoma on the quality of life of those with the condition are required to further the understanding of the cost-effectiveness of proposed practice, as sensitivity analysis suggested that health state utilities have a considerable influence on ICER results. In addition, the impact of diagnosis of glaucoma and subsequent ‘adjustment’ to the condition124,125 needs to be considered, as this may negatively bias patients’ perceptions of quality of life with glaucoma and, therefore, quantification of utility.

Contributions of authors

David P Crabb (Professor, statistics and vision research) conceived and designed the research studies and provided methodological inputs for the whole project as well as assisting in writing all chapters.

Richard A Russell (postdoctoral research fellow, statistics) conducted the statistical analysis reported in Chapter 1, assisted in the analyses and data collection reported in Chapter 2, developed the computer model of VF tests reported in Chapter 4, assisted the development of the health economic model described in Chapter 5, led the writing of Chapter 4, assisted in writing Chapters 1, 2 and 5, drafted the main findings and summary sections and took a leading role in co-ordinating the entire study.

Rizwan Malik (clinical lecturer, ophthalmic translational research) assisted the design of the research presented in Chapters 1 and 2, conducted the analysis reported in Chapter 2, assisted in the analysis reported in Chapters 1, 4 and 5, led the writing of Chapter 2, assisted in writing Chapter 1 and took a leading role in co-ordinating the entire study.

Nitin Anand (glaucoma consultant) assisted VF data collection and assisted in the design of the research presented in Chapter 4.

Helen Baker (postdoctoral research assistant, Qualitative social research in glaucoma) assisted in the analyses and data collection reported in Chapter 2, assisted the design, led data collection and conducted analysis of research presented in Chapter 3, assisted in writing Chapter 2 and co-led writing Chapter 3.

Trishal Boodhna (PhD student, health economics) developed the health economic model described in Chapter 5 and led the writing of Chapter 5.

Carol Bronze (editorial and creative director, Publicis-Blueprint magazines London) is a glaucoma patient at Moorfields Eye Hospital who contributed to the initial study design from a patient perspective, helped pilot the study described in Chapter 3 and assisted in writing the scientific summary and plain English summary.

Simon SM Fung (specialty registrar in ophthalmology) conducted the analysis of research reported in Chapter 1 and led the writing of Chapter 1.

David F Garway-Heath assisted the design of the research presented in Chapter 4, assisted in writing Chapter 4 and supported the initial design of the overall study.

Fiona C Glen (postdoctoral research assistant, psychology and vision research) conducted the analysis of research presented in Chapter 3, assisted in writing Chapters 1 and 2, co-led the writing of Chapter 3 and edited the final draft of the report.

Rodolfo Hernández (research fellow, health economics) assisted the development of the computer model of VF tests in Chapter 4, assisted the development of the health economic model described in Chapter 5 and assisted in writing Chapter 5.

James F Kirwan (glaucoma consultant) assisted in VF data collection, helped facilitate the study described in Chapter 3 and assisted in the design of the research presented in Chapter 4.

Claire Lemer (operations manager for ophthalmology) assisted the design of and conducted the analysis of research reported in Chapter 1 and assisted writing Chapter 1.

Andrew I McNaught (glaucoma consultant) assisted in VF data collection and in the design of the research presented in Chapter 4.

Ananth C Viswanathan (glaucoma consultant) assisted in VF data collection and provided clinical advice on the health economic model described in Chapter 5.

All authors commented on the draft report.

Publications

Russell, RA, Garway-Heath, DF, Crabb, DP. New insights into measurement variability in glaucomatous visual fields from computer modelling, PLOS ONE 2013;8:e83595.

Malik, R, Baker, H, Russell, RA, Crabb, DP. A survey of attitudes of glaucoma subspecialists in England and Wales to visual field test intervals in relation to NICE guidelines, BMJ Open 2013;3:e002067.

Fung, SS, Lemer, C, Russell, RA, Malik, R., Crabb, DP. Are practical recommendations practiced? A national multicentre cross-sectional study on frequency of visual field testing in glaucoma, Br J Ophthalmol 2013;97:843–7.

Russell, RA, Crabb, DP, Malik, R, Garway-Heath, DF. The relationship between variability and sensitivity in large-scale longitudinal visual field data, Invest Ophthalmol Vis Sci 2012;53:5985–90.

Crabb, DP, Garway-Heath, DF. Intervals between visual field tests when monitoring the glaucomatous patient: wait-and-see approach, Invest Ophthalmol Vis Sci 2012;53:2770–6.

Patient and public involvement

The study in Chapter 3 involved patient focus groups to determine patient views of glaucoma follow-up care, particularly with regards to the type and frequency of VF testing. A total of 30 patients with glaucoma took part across one pilot exercise and six focus groups. Please refer to Chapter 3 for more detailed information regarding the study and the nature of patient involvement.

One of the co-applicants of this project is Carol Bronze, a glaucoma patient who has been attending clinics at Moorfields Eye Hospital for around 20 years. Carol advised on the design of the study and assisted with writing the scientific summary and plain English summary of this report. She insists that this contribution is voluntary and we are most grateful for her contribution.

Disclaimers

This report presents independent research funded by the National Institute for Health Research (NIHR). The views and opinions expressed by authors in this publication are those of the authors and do not necessarily reflect those of the NHS, the NIHR, NETSCC, the HS&DR programme or the Department of Health. If there are verbatim quotations included in this publication the views and opinions expressed by the interviewees are those of the interviewees and do not necessarily reflect those of the authors, those of the NHS, the NIHR, NETSCC, the HS&DR programme or the Department of Health.

Treatment effects

Tables 24 and 25 present a collection of sources that inform the treatment effects in the model associated with each modality. The mean value represents the treatment effect while the highest and lowest MD reduction values represent the highest and lowest estimations used in sensitivity analysis.

Transition probabilities

Tables 26–29 indicate how the probability of transitioning through the model was derived. Once the number of years until transition to the next threshold was identified, the probability of transition was identified by dividing 1 by this figure.

One-way analysis

Figures 22–24 present one-way deterministic sensitivity analysis of individual parameters and how their marginal variations impact on the resultant ICERs. Implementation costs, cost of visual impairment and time horizons were all examined by each cohort.

FIGURE 22.

One-way analysis of implementation costs.

FIGURE 23.

One-way analysis of costs of visual impairment.

FIGURE 24.

One-way analysis of time horizons.

Tornado diagrams

A one-way tornado analysis of the parameters that derive the ICER is presented by cohort in Figure 25. Maximum and minimum parameter values were identified and the impact on the ICER for each cohort was identified, with parameters ordered by importance.

FIGURE 25.

Cohort tornado diagrams.

Combined probabilistic and deterministic sensitivity analysis

The analysis of the probability of acceptance at varying willingness to pay given baseline, maximum and minimum assumptions around influential parameters is presented in Tables 30–33. Cost per VF performed, discount rate, risk distributions and costs of visual impairment were all selected for analysis.