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Yun Ling, Richard Anthony Bilonick, Gadi Wollstein, Hiroshi Ishikawa, Larry Kagemann, Igor I Bussel, Xuejiao Yang, Joel S Schuman; A Multivariate Mixed Effects Model for Visual Field and RNFL Thickness Measurements. Invest. Ophthalmol. Vis. Sci. 2014;55(13):4304.
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© ARVO (1962-2015); The Authors (2016-present)
Simultaneously model multiple repeatedly measured values such as visual field mean deviation (MD), pattern standard deviation (PSD), visual field index (VFI), and optical coherence tomography RNFL in order to study the joint relationships between the parameters at one time point and the relationships between their rates of change.
The model was applied on a longitudinal cohort to evaluate age-related changes. Total 1046 observations on 174 eyes (87 subjects) were analyzed. We simultaneously modeled MD, PSD, VFI, and overall RNFL as a function of follow-up (years, FY), adjusted for signal strength (SS) and baseline age (BLAGE). Multivariate linear mixed effect (MLME) model was used. Random effects and residuals are each assumed to follow a multivariate normal distribution with mean 0 and a 4x4 covariance matrix. For comparison, we also modeled MD, PSD, VFI and RNFL individually. Parameter estimates of both models are shown in Table 1. SAS PROC MIXED was used to fit the model.
Estimates of the most important and relevant functions of the model parameters are shown in Table 1. Standard errors (SE) for the parameter estimates from joint model are smaller than those from individual models. Covariance and correlation matrices are shown in Table 2 (random effects) and 3 (residuals). The joint model was: MD =-0.6341-0.00237*BLAGE+0.08406*SS+0.003167*FY PSD =1.2106+0.003743*BLAGE+0.04136*SS+0.02180*FY VFI = 99.5545-0.00574*BLAGE+0.03657*SS-0.04457*FY RNFL=95.2683-0.2495*BLAGE+2.2271*SS+0.1097*FY
The joint modeling approach had the following results. We 1) Obtained the correlations among different outcomes at same measurement time (Table 2). MD and VFI values at same time point were moderately correlated, while PSD and VFI were more strongly negatively correlated. RNFL was almost not correlated with MD, PSD and VFI. 2) Obtained the correlation among the rates of change (slope) between different outcomes (Table 3). The slope of MD and VFI was moderately positively correlated, i.e., the higher the MD slope, the higher VFI slope. The slope of PSD and VFI were highly negatively correlated, i.e., changing in opposite directions. 3) Obtained smaller SE’s (and thus higher test power) for the parameter estimates compared to the univariate models. 4) Obtained a more realistic appraisal of the diverse impacts of the predictors since we took into account the correlation between the outcomes.
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