Is Complete Case Analysis Appropriate for Cox Regression with Missing Covariate Data?

Abstract

Purpose: Complete case analysis of survival datasets with missing covariates in Cox proportional hazards model relies heavily on strong and usually unverifiable missing mechanism assumptions such as missing completely at random (MCAR) to produce reasonable parameter estimates. Based on the nature of survival data, missing at random (MAR) for missing covariates can be further decomposed into 1) censoring ignorable missing at random (CIMAR) and 2) failure ignorable missing at random (FIMAR). Unlike MCAR and MAR, there are procedures to assess whether missingness of covariates in survival data are consistent with CIMAR or FIMAR. In my thesis, I investigate the performances of the complete case analysis under various missing mechanisms in Cox model and demonstrate the procedures for checking consistency with CIMAR or FIMAR. Experimental design: For research involving missing data, simulation studies are especially useful while studying the performance of some estimation (e.g. complete case analysis) as all parameters are pre-specified and known. I simulate survival data with missing covariates under various missing data mechanisms including MCAR, missing at random (MAR), missing not at random (MNAR), CIMAR and FIMAR. I then perform complete case Cox regression on simulated datasets and compare results to determine which missingness mechanisms produce reasonable parameter estimates. Finally, I perform a two-step procedure to check whether covariate missingness is consistent with CIMAR or FIMAR on a real dataset as outlined by Rathouz (2006). Results: This simulation study illustrates that when covariate missingness is FIMAR but not CIMAR, complete case Cox regression produces reasonable parameter estimates similar to when missingness is MCAR. When covariate missingness is CIMAR, complete case Cox regression produces biased parameter estimates. The two-step procedure suggests covariate missingness in the Stanford heart transplant data is consistent with FIMAR. Conclusions: Survival data with missing covariates that are FIMAR are appropriate for complete case analysis in Cox models. Survival data with missing covariates that are CIMAR are not appropriate for complete case analysis in Cox models. Under independent censoring, it should be possible for researchers to check the consistency of missing covariates in survival data with FIMAR and CIMAR assumptions. If missingness is consistent with FIMAR, complete case Cox regression should produce reasonable estimates. If missingness is consistent with CIMAR or if the data is inconsistent with both CIMAR and FIMAR, complete case Cox regression may produce biased estimates and researchers should consider sensitivity analyses.