A copula-based approach for dynamic prediction of survival with a binary time-dependent covariate

Dynamic prediction methods incorporate longitudinal biomarker information to produce updated, more accurate predictions of conditional survival probability. There are two approaches for obtaining dynamic predictions: (1) a joint model of the longitudinal marker and survival process, and (2) an approximate approach that specifies a model for a specific component of the joint distribution. In the case of a binary marker, an illness-death model is an example of a joint modeling approach that is unified and produces consistent predictions. However, previous literature has shown that approximate approaches, such as landmarking, with additional flexibility can have good predictive performance. One such approach proposes using a Gaussian copula to model the joint distribution of conditional continuous marker and survival distributions. It has the advantage of specifying established, flexible models for the marginals for which goodness-of-fit can be assessed, and has easy estimation that can be implemented in standard software. In this article, we provide a Gaussian copula approach for dynamic prediction to accommodate a binary marker using a continuous latent variable formulation. We compare the predictive performance of this approach to joint modeling and landmarking using simulations and demonstrate its use for obtaining dynamic predictions in an application to a prostate cancer study.