Sequential Patient Recruitment and Allocation for Adaptive Clinical Trials
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Randomized Controlled Trials (RCTs) are the gold standard for comparing the effectiveness of a new treatment to the current one (the control). Most RCTs allocate the patients to the treatment group and the control group by repeated tosses of a fair coin. We show that this procedure can be highly sub-optimal if -- as is often the case -- patients can be recruited in cohorts (rather than all at once), the effects on each cohort can be observed before recruiting the next cohort, and the effects are heterogeneous across groups of patients. We formulate the patient allocation problem as a finite stage Markov Decision Process in which the objective is to minimize a given weighted combination of type-I and type-II errors. Because finding the exact solution to this Markov Decision Process is computationally intractable, we propose an algorithm -- Knowledge Gradient for Randomized Controlled Trials (RCT-KG) -- that yields an approximate solution. We illustrate our algorithm on a synthetic dataset with Bernoulli outcomes, showing that it is significantly more efficient than repeated fair coin tossing. For a given size of trial our method achieves significant reduction in error, and to achieve a prescribed level of confidence (in identifying whether the treatment is superior to the control), our method requires many fewer patients. Our approach uses what has been learned from the effects on previous cohorts to allocate patients in succeeding cohorts, and allocates more patients to subgroups for which the uncertainty is greater.
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