A Unified Parametric Approach to the Estimation of Dependence and Marginal Distributions in Bivariate Competing Risks Survival Data

Abstract

In bivariate competing risks survival data where only the minimum of the time-to-events is observed and never both, dependence between the survival endpoints is known to be non-identifiable. If dependence or correlation exists between the time-to-events, cause-specific hazards analysis under independent censoring or inference under incorrectly assumed correlations become biased. Arguably, the most important parameter for estimation when dependence exists is the correlation between the time-to-events. However, maximum likelihood estimation (MLE) is known to be biased with large variance, and no practical methods to estimate the correlation exist. Using the fact that bivariate normally (BVN) distributed competing risks data is identifiable, we propose a unified parametric approach where the bivariate central limit theorem provides a connection between a given bivariate competing risks data and the identifiable BVN distribution. We demonstrate that the correlation in the given data is estimable by finding a BVN distribution that produces the same sample mean information as that of the given data. Estimating the correlation subsequently enables an unbiased estimation of the marginal survival or hazard functions of the event of interest. Simulations showed that the proposed method works well over various marginal distributions, copulas, and sizes of the correlation. Our study provides a potential contribution to the existing literature in that the proposed method is applicable to any parametric bivariate competing risks data, requires no covariate information to estimate the correlation, and shows accurate and precise results where the conventional MLE fails to do so. We expect the current study to have further applications in biomedical time-to-event analyses where dependence between the survival endpoints exist such as disease etiology research or RCTs of drug efficacy.