If there is some biological evidence that a new drug has potential to be effective only in a patient subpopulation, the primary analysis of clinical trial is often to test treatment efficacy across the overall population and subpopulation with some adjustment for multiplicity. One approach is a fallback analysis which tests an overall effect, followed by a test of a subgroup effect if the first test is not significant. However, because of the data-driven structured analysis, the subgroup effect may have some bias on the condition that it is reported when the overall effect is not significant. The difficulty in bias correction is that we make inference on the subgroup effect in an unbound parameter space that is actually bounded on the basis of the rejection region on the overall test. To address this problem, we propose bias-corrected point and interval estimations of the subgroup effect based on randomized test with smoothing rejection functions. Numerical evaluations, including simulations and application to real clinical trials, will be provided.