Association between the number of visual fields and the accuracy of future prediction in eyes with retinitis pigmentosa

Introduction

Retinitis pigmentosa (RP) is a slow, progressive, hereditary retinal disease caused by the loss of photoreceptors.1 2 RP is characterised by nyctalopia and constriction of the visual field (VF), which sometimes progresses in legal blindness. Precise measurement of the VF is important in RP and can be performed using a static automated perimeter, such as the Humphrey Field Analyzer (HFA) (Carl Zeiss Meditec, Dublin, California).3 4 An assessment of central VF, such as the HFA 10–2 test, is particularly important because VF is closely related to visual disability.5 The progression of RP can be quantitatively measured using the HFA 10–2 test,6–8 in contrast to the Goldmann perimetry test. Nonetheless, a detailed investigation regarding the reliability and clinical usefulness of the trend analysis using the HFA 10–2 test in RP has not been made.

In the clinical setting, the prediction of future VFs (using HFA) is usually conducted using a linear trend analysis. Using the ordinary least square regression (OLSLR), the linear trend analysis tracks changes in VF indices over time, such as mean deviation (MD, MD trend analysis) as implemented in the Guided Progression Analysis software on the HFA or pointwise (PW) VF sensitivity. Accurate assessment of VF progression is hampered by VF variability.9 The reliability of VF measurements is inherently affected by a patient’s concentration. Furthermore, the effect of measurement noise cannot be completely avoided, even with reliable indices.10 11 Glaucoma also exhibits chronic and irreversible VF deterioration. The assessment of VF progression for glaucoma is usually carried out using a linear trend analysis of the HFA 24–2 test. We demonstrated that a considerably large number of VFs (approximately 10) are required to accurately predict future VFs, even when predicting relatively near-future VFs (between 6 months and 1.5 years into the future).12 These findings are in agreement with other previous studies.13–16 Thus, careful attention is needed when clinicians assess and predict VF progression in glaucoma based on a small number of VFs. The purpose of the current study was to investigate whether similar findings were observed when applying the linear trend analysis of the HFA 10–2 test results for predicting future VFs in RP.

As widely acknowledged, OLSLR is highly sensitive to outliers, and attempts have been made to overcome this problem. For example, in a robust model, the weight of each data point in the regression is dependent on the size of its residual. Thus, the model is more ‘robust’ to the influence of outliers.17 We investigated the usefulness of applying this approach in glaucoma, however, the improvement in the prediction accuracy was small and only marginally beneficial in the clinical setting.12 In the current study, we investigated the usefulness of a non-linear trend analysis approach (robust and quadratic regressions) in RP to predict future VFs, in comparison with OLSLR.

Method

Results

Patient demographic information is shown in table 1. The mean±SD of MD in VF₁ was −17.1±8.6 dB. The mean±SD interval between VF1 and VF12 was 8.9±2.1 years. The MD progression rate with VF_1–12 was −0.51±0.41 dB/year.

When predicting the 12th VF using OLSLR in the PW manner, the 95% CI of the absolute prediction error was 2.4 and 2.9 (first next VF prediction with VF_1–11), 2.8 and 3.8 (second next VF prediction with VF_1–10) and 3.5 and 4.6 dB (third next VF prediction with VF_1–9), respectively (figure 1A–C). The minimum number of VFs required for the mean absolute prediction error to reach this range was 5 (first and second next VF predictions) or 6 (third next VF prediction). In all comparisons, there were no significant differences between the absolute prediction errors with OLSLR and robust regression. On the other hand, the absolute prediction errors with quadratic regression were significantly larger than the prediction errors with OLSLR in most cases (p<0.05, linear mixed model with Dunnett’s test). The predictions of VF₁₃ (72 eyes) using VF_1–12, VF_1–11 and VF_1–10; VF₁₄ (59 eyes) using VF_1–13, VF_1–12 and VF_1–11; and VF₁₅ (38 eyes) using VF_1–10, VF_1–9 and VF_1–8 were conducted. The mean absolute prediction error values were within the range of the 95% CI for the VF₁₂ prediction, except for predicting VF₁₃ using VF_1–10.

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When predicting the 12th VFs using OLSLR with MD values, the 95% CI of the absolute prediction error was 0.82 and 1.4 (first next VF prediction with VF_1–11), 0.92 and 2.0 (second next VF prediction with VF_1–10) and 1.2 and 2.5 dB (third next VF prediction with VF_1–9), respectively, as shown in figure 2A–C. The minimum number of VFs required for the mean absolute prediction error to reach this range was 3 (first and second next VF predictions) or 4 (third next VF prediction). In all comparisons, there were no significant differences between absolute prediction errors using OLSLR and robust regression. On the other hand, the absolute prediction errors using quadratic regression were significantly larger than the prediction errors with OLSLR in most of the cases (p<0.05, linear mixed model with Dunnett’s test). The predictions of VF₁₃ (72 eyes) using VF_1–12, VF_1–11 and VF_1–10; VF₁₄ (59 eyes) using VF_1–13, VF_1–12 and VF_1–11; and VF₁₅ (38 eyes) using VF_1–10, VF_1–9 and VF_1–8 were conducted. The mean absolute prediction error values were within the range of the 95% CI for the VF₁₂ prediction.

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Table 2 shows the association between the absolute prediction errors and the values of the MD progression rate for 12 VFs. No significant association was observed between these values in all investigations (linear mixed model with adjustment for multiple comparisons using Benjamini and Hochberg’s method,22 p>0.05).

Table 3 shows the association between the absolute prediction errors and the MD p value in the initial VF. No significant association was observed between these values in all investigations (linear mixed model with adjustment for multiple comparisons using Benjamini and Hochberg’s method,22 p>0.05), except for the prediction of VF₉ using VF_1–8.

Discussion

In this study, time series VF data were collected from the eyes of patients with RP, and the relationship between the number of VFs and the prediction accuracy of VF test results was investigated. The accurate prediction of future VFs was accomplished when at least five or six VF records were used, which is much lower than the similar prediction using the HFA 24–2 test in the eyes of patients with glaucoma (approximately 10).12 We observed no merit in using non-linear regression models (quadratic and robust regressions), similar to our previous investigation in patients with glaucoma.12

The accuracy of the prediction of VF progression is largely influenced by VF variability. As a result, the number of VF and the accuracy of prediction are in a trade-off relationship.9 In glaucoma, studies using the HFA 24–2 test suggest that clinicians should acquire 816 23 or 1012 VFs to accurately forecast future progression. In contrast, no investigation has determined the number of VFs needed to accurately forecast disease progression in patients with RP. One reason for this discrepancy may be the difficulty in collecting a long series of VFs from a large number of patients with RP. Glaucoma is the leading cause of irreversible blindness in the world, affecting >60 million people.24 On the other hand, RP affects only 1.4 million people worldwide.25 In the current study, a long series of VFs (12 VFs) were collected from a relatively large number of patients with RP (102 eyes). Using this data set, the 95% CI of the absolute prediction error when predicting the 12th VF using the prior 11 (first next VF prediction), 10 (second next VF prediction) and 9 VFs (third next VF prediction) was between 2.4 and 2.9, 2.8 and 3.8 and 3.5 and 4.6 dB, respectively, for PW VF sensitivities. The mean absolute prediction error values were between these intervals when predicting the first next VF using an initial 5–11 VFs, when predicting the second next VF using an initial 5–11 VFs, and when predicting the third next VF using an initial 6 and 11 VFs (figure 1A–C). We iterated similar analyses using subsets of eyes (between 38 and 72 eyes) with various numbers (from 13 to 15) of maximum VFs obtained. Very similar absolute prediction errors were observed in most cases, suggesting that a different finding is unlikely even if a larger data set with 15 VF records was analysed. The reasons why smaller numbers of VFs are needed to accurately predict future VF in RP with the HFA 10–2 test compared with those in predicting future glaucoma with the HFA 24–2 test (approximately 10 VFs)12 are unclear; however, one reason may be the different courses of the diseases. Intraocular pressure reduction is usually administered in glaucoma. As a result, the progression of the disease can vary according to the treatment status, even in the same eye. However, in RP, the disease usually progresses at a steady rate. In addition, differences in the areas of VF may be important; the variance in VF sensitivity in the central area of the eye is much smaller than in the sensitivity in the peripheral area.26 Future studies are needed to investigate whether similar results are shown in eyes with glaucoma using the HFA 10–2 test.

In contrast to PW analysis, the analyses using MD values resulted in 95% CI for the absolute prediction error when predicting 12th VF using the prior 11 (first next VF prediction), 10 (second next VF prediction) and 9 VFs (third next VF prediction) between 0.82 and 1.4 (first next VF prediction with VF_1–11), 0.92 and 2.0 (second next VF prediction with VF_1–10) and 1.2 and 2.5 dB (third next VF prediction with VF_1–9). The mean absolute prediction error values were between these intervals when predicting the first next VF using initial VFs of 3–11, when predicting the second next VF using VFs of 3–11, and when predicting the third next VF using VFs of 4–11 (figure 2A–C). The prediction errors were within the 95% CI range when subsets of eyes (between 38 and 72 eyes) with various numbers (from 13 to 15) of maximum VFs were used. Thus, fewer VFs were required in the analyses with MD, compared with those in PW analyses. The MD is the averaged VF sensitivity in the whole field. As a result, the MD fluctuates less compared with PW VF sensitivities. Similar to the PW analyses, these values were smaller than those in our previous study (between 5 and 7) in the eyes of patients with glaucoma.12

To date, there are limited treatment options for RP. The importance of accurately assessing VF progression cannot be overstated for the establishment of future treatment. The crucial need for an accurate assessment of VF was demonstrated when vitamin A was considered as a potential treatment for RP, for instance. In a recent meta-analysis, the effectiveness of vitamin A was uncertain because the treatment outcomes varied widely across studies.27–34 One reason for the contradicting results was the different visual function assessments across the studies.34 Even visual acuity was often used for the assessment of visual function. However, visual acuity mainly reflects the retinal function around the fovea and tends to be insensitive to the disease severity.35 In contrast, we recently showed that the structural damage in RP, such as fundus autofluorescence, was more accurately measured by VF sensitivity34 35 using the HFA 10–2 test.36 The current results will be useful when assessing the effects of any candidate treatment on the progression of VF with the HFA 10–2 test. In addition, as suggested in a previous study, visual disability is closely associated with HFA 10–2 test results,5 and the current results will be useful when predicting patients’ future daily lives using the HFA 10–2 test.

The absolute prediction error was not significantly improved using the quadratic regression or the robust regression compared with the OLSLR. This is in agreement with our previous study in patients with glaucoma using the HFA 24–2 test, which found no merit in using the non-linear regression models at the clinical level.12 In the current study, only reliable VFs were investigated (determined as fixation losses of <20% and false-positive responses of <15%). A further study would be needed to assess the usefulness of non-linear regressions in VF series with unreliable VF measurements. However, the merit may only be marginal. All regression models assume that the distribution of VF errors is normally distributed. However, unreliable VFs may not be normally distributed.

The variability of VF tests may be high when VF damage is advanced.37 However, almost no association was observed between the prediction accuracy and disease stage in the initial VF (table 3) and also the rate of VF progression (table 2).

One of the limitations of the present study is that genetic information was not considered. RP is genetically heterogeneous, and genetic testing can direct prognosis and clinical management. For instance, variants in many genes, including ABCA4,38 PRPH239 40 and PROM141 genes, are associated with various phenotypes. A better understanding of the influence of genetics on the VF progression rate would be beneficial. This is particularly important in identifying individuals who could benefit from retinal gene therapy.42 In addition, we did not investigate the effect of macula oedema in the current study, which should be analysed in a future study.

In conclusion, the minimum number of VFs required to obtain accurate predictions of future VF test results in a PW manner was 5 or 6. The prediction error cannot be significantly improved by using other non-linear regression methods.