Multiple Imputation of Missing Covariates When Using the Fine–Gray Model

Statistics in Medicine, vol. 44, pp. e70166

Abstract

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.

Authors 8

1. Edouard F. Bonneville Aachen Department of Biomedical Data Sciences Leiden University Medical Center Leiden The Netherlands

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences Leiden University Medical Center Leiden the Netherlands

2. Jan Beyersmann

   Universität Ulm

   Affiliation as printed

   Institute of Statistics Ulm University Ulm Germany

3. Ruth H. Keogh

   London School of Hygiene & Tropical Medicine

   Affiliation as printed

   Department of Medical Statistics London School of Hygiene and Tropical Medicine London UK

4. Jonathan William Bartlett

   London School of Hygiene & Tropical Medicine

   Affiliation as printed

   Department of Medical Statistics London School of Hygiene and Tropical Medicine London UK

5. Tim Peter Morris

   MRC Clinical Trials Unit at UCL · University College London

   Affiliation as printed

   MRC Clinical Trials Unit at UCL University College London London UK

6. Nicola Polverelli

   Policlinico San Matteo Fondazione

   Affiliation as printed

   Unit of Bone Marrow Transplantation, Division of Hematology Fondazione IRCCS Policlinico San Matteo di Pavia Pavia Italy

7. Liesbeth C. de Wreede Aachen Department of Biomedical Data Sciences Leiden University Medical Center Leiden The Netherlands

   Leiden University Medical Center

   Affiliation as printed

   DKMS Clinical Trials Unit Dresden Germany

   Department of Biomedical Data Sciences Leiden University Medical Center Leiden the Netherlands

8. Hein Putter Aachen Department of Biomedical Data Sciences Leiden University Medical Center Leiden The Netherlands

   Leiden University · Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences Leiden University Medical Center Leiden the Netherlands

   Mathematical Institute Leiden University Leiden the Netherlands