2.1. Motivating example: estimating structure-function relationships in RP

The FIGHT-RP study was a Phase 1 clinical trial to test the safety, tolerability, and efficacy of oral N-acetylcysteine in patients with RP⁷. The trial enrolled 30 RP patients aged 18 years and older (59 study eyes). The trial adhered to the guidelines of the Declaration of Helsinki and was approved by the Institutional Review Board of the Johns Hopkins School of Medicine. This current study used baseline data to assess relationships between ocular structure and visual function. The ocular structural parameter was the width of the ellipsoid zone (EZ) measured on a horizontal foveal optical coherence tomography (OCT) scan. There were two continuous visual function outcome measures: the best-corrected visual acuity (BCVA) and the mean macular sensitivity (MMS) obtained from microperimetry.

The inter-eye correlation was high for all the measures (e.g., The Pearson correlation coefficients were 0.91, 0.79 and 0.94 for BCVA MMS, and EZ width, respectively)(Table S2)⁸. We used LMEM and GEE models to evaluate the marginal association between each of the outcome variables (i.e., BCVA or MMS) and the exposure variable EZ width, accounting for the inter-eye correlation. Figure 1 shows the scatter plots of EZ width with BCVA and MMS and the coefficient estimates from different models. For models with MMS as the outcome, the estimates and confidence intervals (CIs) of the coefficient are similar between different models and software; but for models with BCVA as the outcome, differences in the coefficient estimates are noticeable.

The distribution of BCVA and MMS, and the estimation results of the coefficient for EZ width from GEE and LMEM models in the FIGHT-RP study. GEE independent, GEE with independent working correlation structure; GEE exchangeable, GEE with exchangeable working correlation structure; LMEM, linear mixed-effects model; BCVA, best-corrected visual acuity; MMS, mean macular sensitivity; EZ width, the width of the ellipsoid zone.

(a) shows the association between BCVA (in letters) and EZ width (in μm). The left panel shows the scatter plot of BCVA with EZ width in the RP study, with the fitted line of expected BCVA from GEE with exchangeable correlation structure in R; The right panel presents the forest plot of results from GEE and LMEM, estimating the increase in BCVA per 100 μm increase in the exposure EZ width.

(b) shows the association between MMS (in decibels) and EZ width. The left panel shows the scatter plot of MMS with EZ width in the RP study, with the fitted line of expected MMS from GEE with exchangeable correlation structure in R; The right panel presents the forest plot of results from GEE and LMEM, estimating the increase in MMS per 100 μm increase in the exposure EZ width; Note that the results from GEE with unstructured correlation were not presented because it presented the same results as those for the GEE exchangeable model in SAS. For the LMEM with both random slope and intercept terms, the variance estimate for the random slope was very small: 1.90e-12 for BCVA and 2.85e-05 for MMS in R, and 0 and 2.11e-6 in SAS; For forest plots, the squares indicate the point estimates of slopes, and the horizontal lines give the 95% confidence interval (CI) of slopes. Estimated coefficients, 95% CIs and p values are provided at the right side of the plot.