Smoothed Rank Regression for the Accelerated Failure Time Competing Risks Model with Missing Cause of Failure

This paper examines the accelerated failure time competing risks model with missing cause of failure using the monotone class rank-based estimating equations approach. We handle the non-smoothness of the rank-based estimating equations using a kernel smoothed estimation method, and estimate the unknown selection probability and the conditional expectation by non-parametric techniques. Under this setup, we propose three methods for estimating the unknown regression parameters based on 1) inverse probability weighting, 2) estimating equations imputation and 3) augmented inverse probability weighting. We also obtain the associated asymptotic theories of the proposed estimators and investigate the estimators' small sample behaviour in a simulation study. A direct plug-in method is suggested for estimating the asymptotic variances of the proposed estimators. A real data application based on a HIV vaccine efficacy trial study is considered.