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.

翻译：针对亚分布风险Fine-Gray模型常用于估计协变量与竞争风险结局之间的关联。当给定模型包含的协变量存在缺失值时，研究者可能希望对其进行多重插补。假设研究兴趣仅在于估计其中一个竞争事件的风险，本文基于Fine-Gray模型与标准（单事件）Cox模型之间的相似性，开发了一种与实质性模型兼容的多重插补方法。在存在右删失的情况下，该方法首先对因竞争事件失效个体的潜在删失时间进行插补，随后利用先前针对无竞争风险场景下Cox模型开发的方法对缺失协变量进行插补。在一项模拟研究中，我们将所提方法与替代方法（如基于病因特异性Cox模型的兼容插补）进行了比较。当数据生成满足比例亚分布风险假设时，所提方法在亚分布对数风险比和累积发生率的估计方面均表现良好；即使在该假设不满足时，其表现亦令人满意。在模拟研究及一项关于异基因干细胞移植后竞争结局的实际数据案例中，均证明了该方法相较于完全案例分析在效率上的提升。对于个体特异性累积发生率估计，在分析阶段采用正确尺度上的比例性假设，似乎比正确指定用于插补缺失协变量的插补程序更为重要。