Using the Latent Correlations to Measure the Association Between Continuous and Binary Markers With Repeated Measurements

This study was motivated by one of the important challenges in sleep research: estimating not only an overall association between objective and subjective sleep measures but at within- and between-subject levels as well. Comparing to the literature on the association between two continuous or two binary outcomes, to our knowledge, fewer works were published for the case when one outcome is continuous and the other is binary while both are measured repeatedly. We address this problem by considering a latent correlation (LC) that is the correlation between two continuous outcomes. The first is the original observed continuous outcome while the second is an underlying latent variable, dichotomization of which produces the original binary outcome. Building upon a flexible Bayesian generalized linear mixed model fitted by the MCMC, our proposal allows estimation of the total correlation, and the between- and within-subject correlations simultaneously. The goal of joint estimation of all these correlations, to our knowledge, was not fulfilled in previous proposals (either the between- or within-subject correlation needed to be fixed at zero). Moreover, the approach avoids bias of a two-step procedure and does not rely on approximation of the covariance matrix and hence the correlations. It provides accurate estimates covering a wide range of values. We can also incorporate the cases of missing data, covariate adjustment, and comparison between subgroups. Furthermore, these advantages are achieved at a low computational cost. We demonstrate properties and implementation of our proposal with a large simulation study and with real data from two clinical trials of an insomnia drug where one of the questions is how continuous biomarkers derived from the polysomnographic measurements are associated with the binary patient-reported sleep quality. Supplementary materials for this article are available online.