Abstract: 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: inverse probability weighting, estimating equations imputation, and augmented inverse probability weighting. We also obtain the associated asymptotic theories of the proposed estimators and investigate their small sample behaviour in a simulation study. A direct plug-in method is suggested for estimating the asymptotic variances of the proposed estimators. A data application based on a HIV vaccine efficacy trial study is considered.

Key words and phrases: Accelerated failure time model, competing risks, imputation, inverse probability weighting, missing at random, monotone estimating equation, rank-based estimator, U-statistic.