New C‐indices for assessing importance of longitudinal biomarkers in fitting competing risks survival data in the presence of partially masked causes

Abstract

Competing risks survival data in the presence of partially masked causes are frequently encountered in medical research or clinical trials. When longitudinal biomarkers are also available, it is of great clinical importance to examine associations between the longitudinal biomarkers and the cause‐specific survival outcomes. In this article, we propose a cause‐specific C‐index for joint models of longitudinal and competing risks survival data accounting for masked causes. We also develop a posterior predictive algorithm for computing the out‐of‐sample cause‐specific C‐index using Markov chain Monte Carlo samples from the joint posterior of the in‐sample longitudinal and competing risks survival data. We further construct the C‐index to quantify the strength of association between the longitudinal and cause‐specific survival data, or between the out‐of‐sample longitudinal and survival data. Empirical performance of the proposed assessment criteria is examined through an extensive simulation study. An in‐depth analysis of the real data from large cancer prevention trials is carried out to demonstrate the usefulness of the proposed methodology.