A fast EM algorithm for fitting joint models of a binary response and multiple longitudinal covariates subject to detection limits

Joint modeling techniques have become a popular strategy for studying the association between a response and one or more longitudinal covariates. Motivated by the GenIMS study, where it is of interest to model the event of survival using censored longitudinal biomarkers, a joint model is proposed for describing the relationship between a binary outcome and multiple longitudinal covariates subject to detection limits. A fast, approximate EM algorithm is developed that reduces the dimension of integration in the E-step of the algorithm to one, regardless of the number of random effects in the joint model. Numerical studies demonstrate that the proposed approximate EM algorithm leads to satisfactory parameter and variance estimates in situations with and without censoring on the longitudinal covariates. The approximate EM algorithm is applied to analyze the GenIMS data set.