Proportional subdistribution hazards modeling offers a summary analysis, even if misspecified

Abstract

Competing risks model time-to-first-event and the event type. Our motivating data example is the ONKO-KISS study on the occurrence of infections in neutropenic patients after stem-cell transplantation with first-event-types 'infection' and 'end of neutropenia'. The standard approach to study the effects of covariates in competing risks is to assume each event-specific hazard (ESH) to follow a proportional hazards model. However, a summarizing probability interpretation of the different event-specific effects of one covariate can be challenging. This difficulty has led to the development of the proportional subdistribution hazards model of a competing event of interest. However, one model specification usually precludes the other. Assuming proportional ESHs, we find that the subdistribution log-hazard ratio may show a pronounced time-dependency, even changing sign. Still, the subdistribution analysis is useful by estimating the least false parameter (LFP), a time-averaged effect on the cumulative event probabilities. In examples, we find that the LFP offers a robust summary of the effects on the ESHs for different observation periods, ranging from heavy censoring to no censoring at all. In particular, if there is no effect on the competing ESH, the subdistribution log-hazard ratio is close to the event-specific log-hazard ratio of interest. We reanalyze an interpretationally challenging example from the ONKO-KISS study and conduct a simulation study, where we find that the LFP is reliably estimated by the subdistribution analysis even for moderate sample sizes.