Stratification of randomization is not required for a pre-specified subgroup analysis

Published literature and regulatory agency guidance documents provide conflicting recommendations as to whether a pre-specified subgroup analysis also requires for its validity that the study employ randomization that is stratified on subgroup membership. This is an important issue, as subgroup analyses are often required to demonstrate efficacy in the development of drugs with a companion diagnostic. Here, it is shown, for typical randomization methods, that the fraction of patients in the subgroup given experimental treatment matches, on average, the target fraction in the entire study. Also, mean covariate values are balanced, on average, between treatment arms in the subgroup, and it is argued that the variance in covariate imbalance between treatment arms in the subgroup is at worst only slightly increased versus a subgroup-stratified randomization method. Finally, in an analysis of variance setting, a least-squares treatment effect estimator within the subgroup is shown to be unbiased whether or not the randomization is stratified on subgroup membership. Thus, a requirement that a study be stratified on subgroup membership would place an artificial roadblock to innovation and the goals of personalized healthcare.