Subgroup identification from randomized clinical trial data

We consider the problem of identifying a subgroup of patients who may have an enhanced treatment effect in a randomized clinical trial, and it is desirable that the subgroup be defined by a limited number of covariates. For this problem, the development of a standard, pre-determined strategy may help to avoid the well-known dangers of subgroup analysis. We present a method developed to find subgroups of enhanced treatment effect. This method, referred to as 'Virtual Twins', involves predicting response probabilities for treatment and control 'twins' for each subject. The difference in these probabilities is then used as the outcome in a classification or regression tree, which can potentially include any set of the covariates. We define a measure Q(Â) to be the difference between the treatment effect in estimated subgroup  and the marginal treatment effect. We present several methods developed to obtain an estimate of Q(Â), including estimation of Q(Â) using estimated probabilities in the original data, using estimated probabilities in newly simulated data, two cross-validation-based approaches, and a bootstrap-based bias-corrected approach. Results of a simulation study indicate that the Virtual Twins method noticeably outperforms logistic regression with forward selection when a true subgroup of enhanced treatment effect exists. Generally, large sample sizes or strong enhanced treatment effects are needed for subgroup estimation. As an illustration, we apply the proposed methods to data from a randomized clinical trial.