Understanding the implications of a complete case analysis for regression models with a right-censored covariate

Despite its drawbacks, the complete case analysis is commonly used in regression models with incomplete covariates. Understanding when the complete case analysis will lead to consistent parameter estimation is vital before use. Our aim here is to demonstrate when a complete case analysis is consistent for randomly right-censored covariates and to discuss the implications of its use even when consistent. Across the censored covariate literature, different assumptions are made to ensure a complete case analysis produces a consistent estimator, which leads to confusion in practice. We make several contributions to dispel this confusion. First, we summarize the language surrounding the assumptions that lead to a consistent complete case estimator. Then, we show a unidirectional hierarchical relationship between these assumptions, which leads us to one sufficient assumption to consider before using a complete case analysis. Lastly, we conduct a simulation study to illustrate the performance of a complete case analysis with a right-censored covariate under different censoring mechanism assumptions, and we demonstrate its use with a Huntington disease data example.