Extension of the Gradient Boosting Algorithm for Joint Modeling of Longitudinal and Time-to-Event data.

In various data situations joint models are an efficient tool to analyze relationships between time dependent covariates and event times or to correct for event-dependent dropout occurring in regression analysis. Joint modeling connects a longitudinal and a survival submodel within a single joint likelihood which then can be maximized by standard optimization methods. Main burdens of these conventional methods are that the computational effort increases rapidly in higher dimensions and they do not offer special tools for proper variable selection. Gradient boosting techniques are well known among statisticians for addressing exactly these problems, hence an initial boosting algorithm to fit a basic joint model based on functional gradient descent methods has been proposed. Aim of this work is to extend this algorithm in order to fit a model incorporating baseline covariates affecting solely the survival part of the model. The extended algorithm is evaluated based on low and high dimensional simulation runs as well as a data set on AIDS patients, where the longitudinal submodel models the underlying profile of the CD4 cell count which then gets included alongside several baseline covariates in the survival submodel.