Articles |
Supremum weighted log-rank test and sample size for comparing two-stage adaptive treatment strategies
Department of Biostatistics, University of Pittsburgh Graduate School of Public Health, Pittsburgh, Pennsylvania 15261, U.S.A. wentao.feng{at}novartis.com wahed{at}pitt.edu
Received for publication 1 November 2007.
Revision received 1 January 2008.
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Abstract |
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In two-stage adaptive treatment strategies, patients receive an induction treatment followed by a maintenance therapy, given that the patient responded to the induction treatment they received. To test for a difference in the effects of different induction and maintenance treatment combinations, a modified supremum weighted log-rank test is proposed. The test is applied to a dataset from a two-stage randomized trial and the results are compared to those obtained using a standard weighted log-rank test. A sample-size formula is proposed based on the limiting distribution of the supremum weighted log-rank statistic. The sample-size formula reduces to Eng and Kosorok's sample-size formula for a two-sample supremum log-rank test when there is no second randomization. Monte Carlo studies show that the proposed test provides sample sizes that are close to those obtained by standard weighted log-rank test under a proportional hazards alternative. However, the proposed test is more powerful than the standard weighted log-rank test under non-proportional hazards alternatives.
Key Words: Adaptive treatment strategy • Brownian motion • Censoring distribution • Counting process • Proportional hazard • Sample-size formula • Supremum log-rank statistic • Survival function • Two-stage design