Abstract:
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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. 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 before. Moreover, the approach avoids approximating the correlations and their values cover a wide range. We can also incorporate the cases of missing data, covariate adjustment, and comparison between different groups. We demonstrate properties and implementation of our proposal with a large simulation study and real data from two clinical trials of an insomnia drug.
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