  The Fine-Gray model for the subdistribution hazard is commonly used for
estimating associations between covariates and competing risks outcomes. When
there are missing values in the covariates included in a given model,
researchers may wish to multiply impute them. Assuming interest lies in
estimating the risk of only one of the competing events, this paper develops a
substantive-model-compatible multiple imputation approach that exploits the
parallels between the Fine-Gray model and the standard (single-event) Cox
model. In the presence of right-censoring, this involves first imputing the
potential censoring times for those failing from competing events, and
thereafter imputing the missing covariates by leveraging methodology previously
developed for the Cox model in the setting without competing risks. In a
simulation study, we compared the proposed approach to alternative methods,
such as imputing compatibly with cause-specific Cox models. The proposed method
performed well (in terms of estimation of both subdistribution log hazard
ratios and cumulative incidences) when data were generated assuming
proportional subdistribution hazards, and performed satisfactorily when this
assumption was not satisfied. The gain in efficiency compared to a
complete-case analysis was demonstrated in both the simulation study and in an
applied data example on competing outcomes following an allogeneic stem cell
transplantation. For individual-specific cumulative incidence estimation,
assuming proportionality on the correct scale at the analysis phase appears to
be more important than correctly specifying the imputation procedure used to
impute the missing covariates.
