A comparison of multiple imputation methods for the analysis of survival data with outcome related missing covariate values
The Cox proportional hazards model is commonly used in medical research for investigating the association between the survival time and covariates. However, it is quite common for the analysis to involve missing covariate values. A reasonable assumption is that data are censoring-ignorable MAR in the sense that missingness does not depend on censoring time but may depend on failure time. In this case, a complete cases analysis produce biased regression coefficient estimates. Through a simulation study, we compare three multiple imputation approaches for a missing covariate when missingness is survival time-dependent: (i) the method proposed by White & Royston (2009) that uses the cumulative hazard in an approximation to the imputation model, (ii) the method described by Bartlett et al. (2015) that incorporates the Cox model in the imputation process, and (iii) the CART approach, a method known to deal with skewed distributions, interaction and nonlinear relations. Simulation results show that the method of White & Royston (2009) may produce very biased estimates while the CART approach underestimates the imputation uncertainty resulting in low coverage rates. The method of Bartlett et al. (2015) had the best performance overall, with small finite sample bias and coverage rates close to nominal values. We apply the imputation approaches to a Chagas disease dataset.
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