Regression analysis of interval-censored competing risks data with missing causes of failure: A direct likelihood approach

Regression analysis of interval-censored competing risks data is often required and plays an important role in many areas. For the situation, in addition to competing risk and interval censoring, another feature that makes the analysis difficult is that the failure cause may be unknown or missing. Most existing methods for addressing these challenges rely on two-stage estimation procedures, which could suffer efficiency loss and high computational cost. To overcome these, we propose a direct likelihood approach based on a mixture model framework. The proposed method accounts for both competing risks and missingness of event types directly in a likelihood function and facilitates estimation through a sieve maximum likelihood estimation, simplifying the estimation procedure and thus enhancing the estimation efficiency. The consistency and asymptotic normality of the resulting estimators are established, and the idea behind the proposed approach can be extended to other competing risks model frameworks. We demonstrate the promising performance of the proposed method in a comprehensive simulation study and illustrate its practical utility with an application to an Alzheimer's disease study.