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Abstract:
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Many prospective biomedical studies collect data on longitudinal variables that are predictive of a binary outcome and oftentimes, primary interest lies in the association between the outcome and the values of the longitudinal measurements at a specific time point. Common problems in these data are 1) inconsistency in timing of measurements and 2) mixed scale issue of the longitudinal measurements due to the lack of distribution that is capable of accommodating variables of mixed scale simultaneously. Motivated by a cancer survivor cohort study, a new class of joint models for a binary outcome and longitudinal predictors of different scale are proposed as the solution for these challenges. The longitudinal model uses a latent normal random variable construction with regression splines to model time-dependent trends in mean with a Dirichlet Process prior assigned to random effects to decrease distribution assumptions. Also, a binary outcome is related to augmented predictor values at a set time point, thereby standardizing timing of predictors. The proposed model will be evaluated via simulation studies to demonstrate its performance in comparison with other competing models.
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