An issue of identifying longitudinal biomarkers for competing risks data with masked causes of failure considering frailties model.

In this paper, we consider joint modeling of repeated measurements and competing risks failure time data to allow for more than one distinct failure type in the survival endpoint. Hence, we can fit a cause-specific hazards submodel to allow for competing risks, with a separate latent association between longitudinal measurements and each cause of failure. We also consider the possible masked causes of failure in joint modeling of repeated measurements and competing risks failure time data. We also derive a score test to identify longitudinal biomarkers or surrogates for a time-to-event outcome in competing risks data which contain masked causes of failure. With a carefully chosen definition of complete data, the maximum likelihood estimation of the cause-specific hazard functions and of the masking probabilities is performed via an expectation maximization algorithm. The simulations are used to explore how the number of individuals, the number of time points per individual, and the functional form of the random effects from the longitudinal biomarkers considering heterogeneous baseline hazards in individuals influence the power to detect the association of a longitudinal biomarker and the survival time.