Simulation Study of Confounder Selection Procedures using the Hoffman’s Collapsibility Test

Hoffman et al. proposed a convenient collapsibility test in Cox regression [1]. Collapsibility tests have been considered as an effective way to select confounders to be included in multiplicative rate models [2]. However, it is not reasonable to expect that the performance of a confounder-selection procedure (CSP) using the Hoffman’s test is as shown in [2]. First, unlike multiplicative rate models, the regression coefficient of exposure in Cox regression is not collapsible even if the covariate is independent of exposure [3]. Second, impact of a CSP would be different when confounders are adjusted by propensity-score [4]. Although Hoffman et al. did not recommend applying their test to confounder selection problems, these issues should be addressed.