Identification of potential longitudinal biomarkers under the accelerated failure time model in multivariate survival data

In recent years, joint analysis of longitudinal measurements and survival data has received much attention. However, previous work has primarily focused on a single failure type for the event time. In this paper, we consider joint modeling of repeated measurements and multivariate failure time data. The accelerated failure time (AFT) model is also used to deal with multivariate survival data when the proportionality assumption fails to capture the relationship between the survival time and covariates. A proposed method based on the frailty AFT model is used to identify longitudinal biomarkers or surrogates for a multivariate survival. With a carefully chosen definition of complete data, the maximum likelihood estimation is performed via an Expectation-Maximization (EM) algorithm. We use simulations to explore how the number of individuals, the number of time points per individual, and the functional form of the random effects from the longitudianl biomarkers influence the power to detect the association of a longitudinal biomarker and the multivariate survival time. The proposed method is illustrated by using the gastric cancer data.