The competing risks Cox model with and without auxiliary case covariates under weaker or no missing-at-random cause of failure
In the analysis of time-to-event data with multiple causes using a competing risks Cox model, often the cause of failure is unknown for some of the cases. The probability of a missing cause is typically assumed to be independent of the cause given the time of the event and covariates measured before the event occurred. In practice, however, the underlying missing-at-random assumption does not necessarily hold. Motivated by colorectal cancer subtype analysis, we develop semiparametric methods to conduct valid analysis, first when additional auxiliary variables are available for cases only. We consider a weaker missing-at-random assumption, with missing pattern depending on the observed quantities, which include the auxiliary covariates. Overlooking these covariates will potentially result in biased estimates. We use an informative likelihood approach that will yield consistent estimates even when the underlying model for missing cause of failure is misspecified. We then consider a method to conduct valid statistical analysis when there are no auxiliary covariates in the not missing-at-random scenario. The superiority of our methods in finite samples is demonstrated by simulation study results. We illustrate the use of our method in an analysis of colorectal cancer data from the Nurses' Health Study cohort, where, apparently, the traditional missing-at-random assumption fails to hold for particular molecular subtypes.