  The focus of this paper is on quantifying the capacity of covariates in
devising efficient treatment rules when data from a randomized trial are
available. Conventional one-variable-at-a-time subgroup analysis based on
statistical hypothesis testing of covariate-by-treatment interaction is
ill-suited for this purpose. The application of decision theory results in
treatment rules that compare the expected benefit of treatment given the
patient's covariates against a treatment threshold. However, determining
treatment threshold is often context-specific, and any given threshold might
seem arbitrary at the reporting stages of a clinical trial. We propose a
threshold-free metric that quantifies the capacity of a set of covariates
towards finding individuals who will benefit the most from treatment. The
construct of the proposed metric is comparing the expected outcomes with and
without knowledge of covariates when one of a two randomly selected patients
are to be treated. We show that the resulting index can also be expressed in
terms of integrated treatment benefit as a function of covariates over the
entire range of treatment thresholds. We also propose a semi-parametric
estimation method suitable for out-of-sample validation and adjustment for
optimism. We use data from a clinical trial of preventive antibiotic therapy
for reducing exacerbation rate in Chronic Obstructive Pulmonary Disease to
demonstrate the calculations in a step-by-step fashion. The proposed index has
intuitive and theoretically sound interpretation and can be estimated with
relative ease for a wide class of regression models. Beyond the conceptual
developments presented in this work, various aspects of estimation and
inference for such metrics need to be pursued in future research.
