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Abstract:
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Technological advancements in the field of mobile devices and wearable sensors have helped overcome obstacles in the delivery of care, making treatment available anytime and anywhere. These treatments are often designed to have near-term impact on individuals; yet it is often unclear whether treatment effects occur and if so, when and in which context, the treatments are most effective.
We introduce the ``Stratified Micro-randomized Trial'', in which individuals are randomized among treatments 100's or 1000's of times. The randomization probabilities depend on the patient history, which includes a time-varying covariate that may be an outcome of past treatment. We develop two approaches to determining sample size. In the first approach the primary hypothesis concerns testing for a marginal treatment effect, marginal over the time-varying covariate used in stratification. The second approach concerns testing for the treatment effect conditional on the time-varying covariate. We address trade-offs between the two approaches and provide associated sample size calculators. This work is motivated by a mobile health smoking cessation study.
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