A method to estimate treatment efficacy among latent subgroups of a randomized clinical trial

Subgroup analysis arises in clinical trials research when we wish to estimate a treatment effect on a specific subgroup of the population distinguished by baseline characteristics. Many trial designs induce latent subgroups such that subgroup membership is observable in one arm of the trial and unidentified in the other. This occurs, for example, in oncology trials when a biopsy or dissection is performed only on subjects randomized to active treatment. We discuss a general framework to estimate a biological treatment effect on the latent subgroup of interest when the survival outcome is right-censored and can be appropriately modelled as a parametric function of covariate effects. Our framework builds on the application of instrumental variables methods to all-or-none treatment noncompliance. We derive a computational method to estimate model parameters via the EM algorithm and provide guidance on its implementation in standard software packages. The research is illustrated through an analysis of a seminal melanoma trial that proposed a new standard of care for the disease and involved a biopsy that is available only on patients in the treatment arm.