Estimation of Regression Coefficients in the Competing Risks Model with Missing Cause of Failure

Abstract

In many clinical studies, researchers are interested in theeffects of a set of prognostic factors on the hazard of death from a specific disease even though patients may die from other competing causes. Often the time to relapse is right-censored for some individuals due to incomplete follow-up. In some circumstances, it may also be the case that patients are known to die but the cause of death is unavailable. When cause of failure is missing, excluding the missing observations from the analysis or treating them as censored may yield biased estimates and erroneous inferences. Under the assumption that cause of failure is missing at random, we propose three approaches to estimate the regression coefficients. The imputation approach isstraightforward to implement and allows for the inclusion ofauxiliary covariates, which are not of inherent interest formodeling the cause-specific hazard of interest but may be related to the missing data mechanism. The partial likelihood approach we propose is semiparametric efficient and allows for more general relationships between the two cause-specific hazards and more general missingness mechanism than the partial likelihood approach used by others. The inverse probability weighting approach isdoubly robust and highly efficient and also allows for theincorporation of auxiliary covariates. Using martingale theory and semiparametric theory for missing data problems, the asymptotic properties of these estimators are developed and the semiparametric efficiency of relevant estimators is proved. Simulation studies are carried out to assess the performance of these estimators in finite samples. The approaches are also illustrated using the data from a clinical trial in elderly women with stage II breast cancer. The inverse probability weighted doubly robust semiparametric estimator is recommended for itssimplicity, flexibility, robustness and high efficiency.