A pseudo-response approach to constructing confidence intervals for the subset of patients expected to benefit from a new treatment

In precision medicine, there is much interest in estimating the expected-to-benefit (EB) subset, i.e. the subset of patients who are expected to benefit from a new treatment based on a collection of baseline characteristics. There are many statistical methods for estimating the EB subset, most of which produce a 'point estimate' without a confidence statement to address uncertainty. Confidence intervals for the EB subset have been defined only recently, and their construction is a new area for methodological research. This article proposes a pseudo-response approach to EB subset estimation and confidence interval construction. Compared to existing methods, the pseudo-response approach allows us to focus on modelling a conditional treatment effect function (as opposed to the conditional mean outcome given treatment and baseline covariates) and is able to incorporate information from baseline covariates that are not involved in defining the EB subset. Simulation results show that incorporating such covariates can improve estimation efficiency and reduce the size of the confidence interval for the EB subset. The methodology is applied to a randomized clinical trial comparing two drugs for treating HIV infection.