Direct likelihood inference and sensitivity analysis for competing risks regression with missing causes of failure

Summary Competing risks arise in the analysis of failure times when there is a distinction between different causes of failure. In many studies, it is difficult to obtain complete cause of failure information for all individuals. Thus, several authors have proposed strategies for semi‐parametric modeling of competing risks when some causes of failure are missing under the missing at random (MAR) assumption. As many authors have stressed, while semi‐parametric models are convenient, fully‐parametric regression modeling of the cause‐specific hazards (CSH) and cumulative incidence functions (CIF) may be of interest for prediction and is likely to contribute towards a fuller understanding of the time‐dynamics of the competing risks mechanism. We propose a so‐called “direct likelihood” approach for fitting fully‐parametric regression models for these two functionals under MAR. The MAR assumption not being verifiable from the observed data, we propose an approach for performing sensitivity analyses to assess the robustness of inferences to departures from this assumption. The method relies on so‐called “pattern‐mixture models” from the missing data literature and was evaluated in a simulation study. This sensitivity analysis approach is applicable to various competing risks regression models (fully‐parametric or semi‐parametric, for the CSH or the CIF). We illustrate the proposed methods with the analysis of a breast cancer clinical trial, including suggestions for ad hoc graphical goodness‐of‐fit assessments under MAR.