Semiparametric Estimators for the Regression Coefficients in the Linear Transformation Competing Risks Models with Missing Cause of Failure

Abstract

In many clinical studies, researchers are mainly interested in studying the effects of some prognostic factors on the hazard of failure from a specific cause while individuals may failure from multiple causes. This leads to a competing risks problem. Often, due to various reasons such as finite study duration, loss to follow-up, or withdrawal from the study, the time-to-failure is right-censored for some individuals. Although the proportional hazards model has been commonly used in analyzing survival data, there are circumstances where other models are more appropriate. Here we consider the class of linear transformation models that contains the proportional hazards model and the proportional odds model as special cases. Sometimes, patients are known to die but the cause of death is unavailable. It is well known that when cause of failure is missing, ignoring the observations with missing cause or treating them as censored may result in erroneous inferences. Under the Missing At Random assumption, we propose two methods to estimate the regression coefficients in the linear transformation models. The augmented inverse probability weighting method is highly efficient and doubly robust. In addition, it allows the possibility of using auxiliary covariates to model the missing mechanism. The multiple imputation method is very efficient, is straightforward and easy to implement and also allows for the use of auxiliary covariates. The asymptotic properties of these estimators are developed using theory of counting processes and semiparametric theory for missing data problems. Simulation studies demonstrate the relevance of the theory in finite samples. These methods are also illustrated using data from a breast cancer stage II clinical trial.