Component over Composite: Mitigating Type I Error Inflation when Imputing "Days Alive and at Home"

Abstract

Background: Days Alive and at Home (DAH) over a pre-defined follow-up period is a novel post-intervention composite outcome that combines data from at least three components: (i) initial length of hospital stay, (ii) length of total readmissions or other post-discharge care and (iii) mortality. Missing values bring unique challenges to the analysis of trials with the DAH outcome as the three components may have different rates of missingness caused by distinct missing data mechanisms. Current approaches define DAH as missing if any of the components are missing, and proceed with complete cases or Multiple Imputation (MI) of the composite. Methods: Through a simulation study motivated by the NOTACS trial, we compare several methods of handling missing data, including complete case analysis, MI of the composite, and MI of the components when the primary analysis is a Mann-Whitney-Wilcoxon test. Results: MI on the component level has good properties in terms of type I error control and power. We caution against the use of MI on the composite level with Predictive Mean Matching, which can lead to type I error inflation. Conclusions: Given the complex distributional characteristics of DAH, naive approaches such as defining missingness on the composite level and directly imputing the composite with Predictive Mean Matching, can lead to type I error inflation. Imputing on the component level is recommended, suggested future work included imputation approaches that are compatible with more complex definitions of DAH, as well as recommendations for sensitivity analyses to the Missing at Random assumption.