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When a novel treatment has successfully passed phase I, different options to design subsequent phase II trials are available. One approach is a single-arm trial, comparing the response rate in the intervention group against a fixed proportion. Another alternative is to conduct a randomized phase II trial, comparing the new treatment with placebo or the current standard. A significant problem arises in both approaches when the investigated patient population is very heterogeneous regarding prognostic factors. For the situation that a substantial dataset of historical controls exists, we propose an approach to enhance the classic single-arm trial design by including matched control patients. The outcome of the observed study population can be adjusted based on the matched controls with a comparable distribution of known confounders. We propose an adaptive two-stage design with the options of early stopping for futility and recalculation of the sample size taking the matching rate, number of matching partners, and observed treatment effect into account. The performance of the proposed design in terms of type I error rate, power, and expected sample size is investigated via simulation studies based on a hypothetical phase II trial investigating a novel therapy for patients with acute myeloid leukemia.