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Abstract:
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Consider a population of patients partitioned into strata based on baseline covariates, each stratum covering a proportion p, say 5%, with respect to the population's covariate distribution. We investigate the effect of a binary treatment in an adaptive trial setting in which the sampling distribution for covariates is determined by investigators. We wish to estimate the largest conditional average treatment effect within unions of m strata covering a proportion mp of the population, say 10%, while sampling from the corresponding optimal union of m strata as often as possible. The multi-armed bandit literature studies this problem in terms of regret. We study it in terms of inference. From our perspective, an optimal design should satisfy two conditions. First, the resulting estimator should have the same asymptotic variance as the semiparametric efficient estimator in a trial where one only samples from the optimal union of strata. Second, the proportion of samples belonging to the suboptimal covariate strata should decay at the optimal rate given in the multi-armed bandit literature. We present an optimal design and estimator satisfying these properties.
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