A Joint Model for Prognostic Effect of Biomarker Variability on Outcomes: long-term intraocular pressure (IOP) fluctuation on the risk of developing primary open-angle glaucoma (POAG)

Primary open-angle glaucoma (POAG) is among the leading causes of blindness in the United States and worldwide. While numerous prospective clinical trials have convincingly shown that elevated intraocular pressure (IOP) is a leading risk factor for the development of POAG, an increasingly debated issue in recent years is the effect of IOP fluctuation on the risk of developing POAG. In many applications, this question is addressed via a "naïve" two-step approach where some sample-based estimates (e.g., standard deviation) are first obtained as surrogates for the "true" within-subject variability and then included in Cox regression models as covariates. However, estimates from two-step approach are more likely to suffer from the measurement error inherent in sample-based summary statistics. In this paper we propose a joint model to assess the question whether individuals with different levels of IOP variability have different susceptibility to POAG. In our joint model, the trajectory of IOP is described by a linear mixed model that incorporates patient-specific variance, the time to POAG is fit using a semi-parametric or parametric distribution, and the two models are linked via patient-specific random effects. Parameters in the joint model are estimated under Bayesian framework using Markov chain Monte Carlo (MCMC) methods with Gibbs sampling. The method is applied to data from the Ocular Hypertension Treatment Study (OHTS) and the European Glaucoma Prevention Study (EGPS), two large-scale multi-center randomized trials on the prevention of POAG.