In longitudinal observational studies, one observes a series of measurements of an outcome at various timepoints, whose patterns are often associated with the outcome of interest (eg., hospital/clinic visits by patients). The usual longitudinal models such as a mixed effect model do not account for the dependence between the longitudinal outcome and the pattern of timepoints where the outcome was measured. In this paper, we propose a joint modeling approach for this problem. The longitudinal outcome of interest and the timepoints where the outcome was measured are modeled simultaneously with a longitudinal model and a survival model, respectively. This approach takes the dependence between the outcome and the timepoints into account so the valid inference can be made. The MLEs of the parameters of interest in our model are calculated by the EM algorithm and their variances are estimated using the profile likelihood method. Our simulation studies indicate that the joint modeling approach works well for this type of problem. A real example is used to illustrate our approach.* This is joint work with Daohai Yu, Department of Biostatistics and Bioinformatics, Duke University.
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