**Purpose**:
It has been recommended that multiple visual field examinations be performed in the first 2 years after glaucoma diagnosis so that rapid visual field progression (≤−2 dB/year, using ordinary least squares regression over time of the summary index mean deviation [MD]) can be detected. Here I investigate how predictive a statistically significant regression slope is of truly rapid visual field progression.

**Methods**:
I simulated visual field series (*N* = 100,000) spaced at 4 monthly intervals for the first 2 years. MD values had a standard deviation of 1 dB. The true underlying rates of progression were selected from a modified hyperbolic secant with parameters averaged from fits to large data sets from Canada, Sweden, and the United States.

**Results**:
The positive predictive value (PPV) for rapid progression was 0.10 after 2 years, whereas the negative predictive value (NPV) was > 0.99. When using the criterion that a significant regression also had to have a slope of ≤ −2 dB/year, the PPV for rapid progression increased to 0.18 but the NPV was essentially unchanged (NPV >0.99).

**Conclusion**:
Although performing multiple visual fields in the first 2 years provides appropriate power to detect rapid progression, a significant regression slope in the first 2 years is not highly predictive of rapid progression, particularly so if slopes ≤ −2 dB/year are considered only.

**Translational Relevance**:
Statistically significant visual field progression in a short period after diagnosis may not necessarily indicate the presence of rapid progression, and so confirmatory signs of rapid progression should be sought before implementing treatment changes.

^{1}Many patients show progressive visual field loss in the absence of clear structural changes to the optic nerve head,

^{1}and newer ocular imaging methods—despite their increasing use as diagnostic adjuncts—are not substitutes for visual field testing.

^{2}

^{3}This recommendation is based on achieving a sufficient power to detect a significant rate of decline in MD when progression is rapid,

^{3}and has been influential in shaping glaucoma management guidelines.

^{4}However, it has been noted that whilst the

*statistical significance*of the rate might be established after 2 years (i.e., the slope is significantly different from zero), the

*rate*itself is poorly defined.

^{5}For example, assuming moderately variable fields and a true rate of progression of −2 dB/year, slope estimates after six visual fields ranged from −0.8 to −3.2 dB/year (95% limits).

^{5}Correspondingly, variability can produce rate estimates < −2 dB/year after six visual fields in people who do not have rapid visual field progression.

^{5}Given a series of visual fields on a particular patient that shows a significant rate of loss and an estimated slope of −2 dB/year, what is the likelihood that the patient indeed has rapid visual field progression? Examining the distribution of estimated visual field progression rates in several large population studies shows that visual field progression rates ≤ −2 dB/year are relatively uncommon.

^{6}Because of this, a significant slope estimate less than −2 dB/year may in fact be poorly predictive of rapid progression (i.e., the

*positive predictive value*[PPV] may be low). This may be the case despite the power to detect rapid progression having been shown to be good,

^{3}as power calculations do not consider the prevalence of rapid progression. The presumed presence of rapid progression may be a trigger for more aggressive treatments such as surgery, and surgical treatments for glaucoma have nontrivial risks of vision loss

^{7}and postoperative complications.

^{8}Therefore, numerically estimating the PPV for a rapidly progressing series of fields is of importance in determining how frequently rapid visual field progression is overcalled.

^{3,5}Linear regression can, however, return a significant value for slope after as few as three visual fields. Clinicians will examine the series of visual fields after every visit, meaning that there are several opportunities for a visual field series to be flagged as significantly progressing prior to reaching six visual fields. As such, a clinician may decide prior to 2 years that significant rapid progression has occurred and that a change in a patient's treatment may be warranted. Given such multiple assessments, might the potential to overcall rapid visual field progression increase? Nominally, this should be amenable to a simple calculation based on a multiplication of the false positive probability at each assessment. Such errors are not independent, however, and so are not simply predicted by the

*P*value for significance in the linear regression analysis. For example, the likelihood of a false positive error after six visual fields will be increased if a false positive error has already occurred after five fields.

^{9}might improve the PPV for detecting rapid visual field loss in glaucoma.

^{6}Although the distribution of true, underlying rates can never be truly known, previous works suggest that empirical estimates of distribution parameters are reasonably well defined provided the number of participants sampled is large and that there is an extended series of visual fields available for each.

^{10}The modified hyperbolic secant distribution was sampled at 0.1 dB/year resolution and used previously reported average parameters from fits to large data sets from Canada, Sweden, and the United States (

*n*= 2324, 583, and 587, respectively).

^{6}For each field, the MD value was jittered from its nominal value (predicted from the time in the series multiplied by the underlying progression rate) using a normal distribution. Only the rate of progression was considered, and so the absolute value for the first MD in the series had no influence on the current simulation. The standard deviation of the jitter was 1.0 dB (moderate variability).

^{3,5,11}Ordinary least squares linear regression was then applied to these jittered values to determine the visual field progression rate for the series of fields, in dB/year, along with a

*P*value for this rate provided it was negative (i.e., visual field deterioration). The criterion for significance was

*P*< 0.05. Although MD variability increases as damage in the visual field increases,

^{12,13}this was not modelled as changes are typically small for the rates of change and length of visual field series investigated here (a change in standard deviation of ∼0.04 dB for every decibel of decrease in MD).

^{13}Visual field series from 100,000 patients were simulated for each condition tested.

^{14}

^{3}Checking for progression at the particular time only (closed circles) returned a lower power than when progression was assessed at the time and at all times preceding it (open circles). The differences were small, however, being a maximum of 0.05 at 1.3 years and reducing to 0.02 at 2 years. Re-running both simulations resulted in alterations in power of 0.015 or less.

^{3}and between study cohorts

^{6}(see also the current results from the Rotterdam Eye study, below), and is increased in patients with greater levels of field loss.

^{13}It may also be decreased by the use of regression methods other than ordinary least squares regression.

^{15}The influence of such variability changes is shown in Figure 3. Changing visual field variability alters where the peak PPV for rapid progression occurs, with the peak shifting to shorter times as variability reduces (Fig. 3, upper panel). Because of this, the PPV for rapid progression actually declines slightly at 2 years when visual fields are very reliable (Fig. 3, upper panel, open squares), reflecting that more visual field series with slower progression rates are able to reach significance when variability is low. As NPVs are already very high at 2 years, changing visual field variability has little effect (Fig. 3, lower panel). Figure 4 shows the influence of varying the glaucomatous population on which the simulation is run. The Canadian population (open symbols) included both frank glaucoma and glaucoma suspects, and so had a substantial proportion showing no progression and comparatively few rapid progressors.

^{6,16}In contrast, the Swedish population

^{6,17}(closed symbols) included a large proportion of pseudoexfoliation glaucoma patients, a disease characterized by rapid visual field progression.

^{18}At 2 years, the PPV and NPV for rapid progression (squares) differed little. In contrast, the NPV for ruling out any progression (≤−0.1 dB/year; lower panels, circles) changed substantially. This difference in NPV reflects that the Swedish population had a much smaller proportion of nonprogressing patients (progression rate ≥0.0 dB/year) overall.

^{6}This suggests that visual field in this study may be more variable than in other studies. Consistent with this idea, the distribution of progression rates appears broader and more symmetric than other studies.

^{10}Running a simulation using an increased visual field variability (standard deviation = 2 dB/year) produced a probability figure (dashed line, lower panel) broadly similar to that from the empirical function.

^{3}However, knowing the power of the test alone does not allow us to assess how likely rapid progression is when a significant regression slope is found. The current study finds that the PPV at 2 years is moderate (Fig. 2), and that only approximately a half of those with statistically significant regression slopes by 2 years will have rapid visual field progression. Requiring the slope of the regression to also be ≤ −2 dB/year substantially decreased this predictive value. In contrast, other factors such as the presumed distribution of visual field progression rates (Fig. 4) and the variability of the visual fields (Fig. 3) only modestly affected the PPV.

^{5}Because of this, it might be thought that an additional criterion that a steep slope (≤−2 dB/year) is present would be of increasing benefit when a large amount of visual field data is present (e.g., several years). A simulation using this criterion suggests this is not the case, however (Fig. 5, squares); the PPV remains low when a slope criterion is included, even if several years of data are obtained. This reflects the cumulative increase in false positive calls of rapid progression as the length of visual field series increases. Using a slope criterion and checking for progression at the particular time only (Fig. 5, triangles) avoids such a cumulative increase in false positive calls on rapid progression. Consequently, the PPV increases for long visual field series. Such a scenario—where for many years no regression is performed, or the regression result is not acted on—is likely not clinically realistic, however. Furthermore, at the critical 2-year mark, the PPV is still 0.1 less than if when a slope criterion is not used (Fig. 2).

^{19}increased intraocular pressure,

^{20}the presence of optic nerve head changes,

^{21}optic nerve haemorrhages,

^{22}

*β-*zone parapapillary atrophy,

^{20}bilateral visual field loss,

^{23}and pseudoexfoliation.

^{18}The PPV should increase for patients with such risk factors, as the prevalence of rapid progression is increased for such patients. Finally, the summary index MD quantifies only the average level of visual field depression, and so also seeking spatial signs that a visual field is worsening in the way expected in progressing glaucoma would help reduce false alarms due to random noise. For example, glaucomatous visual field progression appears to occur through either the deepening of an existing scotoma or an increase in its spatial extent, rather than through the appearance of new scotomata.

^{24}

^{12}and so it may be expected that the VFI would show similar performance to that demonstrated in the current simulations for MD. Based on this linear relationship, the rapid progression criterion of ≤ −2 dB/year corresponds to ≤ −7.3%/year in terms of the VFI. However, the index is subject to a ceiling effect where early glaucomatous visual field damage returns a VFI equal or near to 100%.

^{12}Because of this, the VFI may underestimate the rate of progression in very early loss, and so the use of MD might be preferred in such circumstances.

^{12,25}

^{7,8}To maximize the PPV, regression analysis should be avoided until around 16 months, assuming a 4 monthly test schedule, and criteria based on regression slope magnitude should be avoided. If a significant regression is not found within the first 2 years, however, the likelihood that rapid progression is present is low and so can effectively be ruled out.

**A.J. Anderson**None

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