Two-sample post-stratified or subgroup analysis with restricted randomization rules

In a clinical trial to compare two treatments, subjects may be allocated sequentially to treatment groups by a restricted randomization rule. Suppose that at the end of the trial, the investigator is interested in a post-stratified or subgroup analysis with respect to a particular demographic or clinical factor which was not selected prior to the trial for stratified randomization. Under a randomization model, large sample theory of two-sample post-stratified permutational tests is developed with a broad class of restricted randomization treatment allocation rules. The test procedures proposed here are illustrated with a real-life example. The results of this example indicate that it is not always possible to ignore the treatment rule used in the trial in the design-based analysis.