Effect of a correlated competing risk on marginal survival estimation in an accelerated failure time model

In problems with a time to event outcome, subjects may experience competing events, which censor the outcome of interest. Cox’s partial likelihood estimator treating competing events as independent censoring is commonly used to examine group differences in clinical trials but fails to adjust for omitted covariates and can bias the assessment of marginal benefit. A bivariate normal linear model generating latent data with dependent censoring is used to assess this bias. Our R-package bnc provides maximum penalized likelihood (MPL) parameter estimation using a novel EM algorithm. Using bnc, we study the properties of such MPL estimation. Simulation results for two-sample survival comparisons of time to an event of interest, with independent censoring accompanied by censoring from a correlated competing risk, are presented. Key parameters—means, hazard ratios, and correlation—are estimated. These results demonstrated that, despite ill-conditioning in models generating correlated competing risks, estimates of marginal effects are reliable. Bivariate normal models were fitted in a trial of head and neck cancer. Model fits help with clinical interpretation while also supplementing other standard methods for follow-up that are terminated by intervening risks.