Novel metrics for quantifying the capacity of subgroup-defining variables to yield efficient treatment rules
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A major objective of subgroup analysis in clinical trials is to explore to what extent patient characteristics can determine treatment outcomes. 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 novel, threshold-free metrics that quantify the capacity of a set of covariates towards concentrating treatment benefit. Our proposed framework is based on the concept of Improvement Upon Randomization: the extent to which a covariate-informed treatment rule can reduce the size of the treated population yet generate the same expected outcome as a naïve rule based on random treatment assignment. 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 metrics have intuitive and theoretically sound interpretations and enable comparison of arbitrary sets of covariates on scalar, scale-free metrics. They can be estimated with relative ease for a wide class of regression models and can accompany conventional metrics for subgroup analysis when reporting the results of clinical trials. Beyond the conceptual developments presented in this work, various aspects of estimation and inference for such metrics needs to be pursued in future research.
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