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A flexible B-spline model for multiple longitudinal biomarkers and survival
Authors:Brown Elizabeth R  Ibrahim Joseph G  DeGruttola Victor
Institution:Department of Biostatistics, University of Washington, Campus Mail Stop 357232, Seattle, Washington 98195-7232, USA. elizab@u.washington.edu
Abstract:Often when jointly modeling longitudinal and survival data, we are interested in a multivariate longitudinal measure that may not fit well by linear models. To overcome this problem, we propose a joint longitudinal and survival model that has a nonparametric model for the longitudinal markers. We use cubic B-splines to specify the longitudinal model and a proportional hazards model to link the longitudinal measures to the hazard. To fit the model, we use a Markov chain Monte Carlo algorithm. We select the number of knots for the cubic B-spline model using the Conditional Predictive Ordinate (CPO) and the Deviance Information Criterion (DIC). The method and model selection approach are validated in a simulation. We apply this method to examine the link between viral load, CD4 count, and time to event in data from an AIDS clinical trial. The cubic B-spline model provides a good fit to the longitudinal data that could not be obtained with simple parametric models.
Keywords:Bayesian methods  Cubic B-splines  Joint longitudinal and survival model  Model assessment
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