Designing Group Sequential Trials with Survival Endpoints
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0092-8615/2002 Copyright 0 2002 Drug Information Association Inc.
DESIGNING GROUP SEQUENTIAL TRIALS WITH SURVIVAL ENDPOINTS* JOHN LAWRENCE, PHD United States Food and Drug Administration, Division of Biometrics I, Rockville, Maryland
This paper discusses an algorithm to calculate information about the trial that is needed at the design stage implemented as an S-plus function. The function allows the user to specify arbitrary length of accrual, control, and treatment survival distributions; number and timing of interim analyses; stopping boundaries or an alpha-spending function; and which member of the Harrington-Fleming GP class of statistics it is. Three examples from real treatment protocols are presented. Key Words: Interim analysis; Sequential monitoring; Sample size estimation; Time-dependent rates; G-rho family
INTRODUCTION THERE ARE SEVERAL programs that are commonly used to estimate the power of a trial with time-to event endpoints with interim monitoring. In many cases, however, the software restricts the user to use a statistic, stopping boundaries, or times of interim analyses that the investigator does not intend to use or to make distributional assumptions that are not realistic. For example, the program described by Shih (1) allows much greater generality than many programs in that nonproportional hazards and loss to follow-up are permitted. In that program, the hazard function is piecewise constant. However, no interim monitoring is incorporated and the power calculations are made under the assumptions that the logrank test is used for the analysis. In the opinion of the author, it is more appropriate to design the study based on assumptions that are as close to what is believed in reality as possible. This paper discusses an algorithm implemented as an S-plus function that allows the user to specify arbitrary length of accrual, control, and treatment survival distributions; number and timing of interim analyses; stopping boundaries or an alpha-spending function; and which member of the Harrington-Fleming GP class of statistics it is (2). Three examples from real treatment protocols are presented.
DESCRIPTION OF THE ALGORITHM This function will compute the boundaries for an arbitrary alpha-spending function at an arbitrary number and times of interim analyses (or the boundaries can be directly input). *The views expressed are those of the author and not necessarily those of the United States Food and Drug Administration. Reprint address: John Lawrence, PhD, Division of Biometrics I, Food and Drug Administration, HFD-710 Room 2030, Woodmont 11, 1451 Rockville Pike, Rockville, MD 20852.
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John Lawrence
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Also, it will find the probability of crossing these boundaries at each time point for any distributions in both groups. Arbitrary accrual times (uniformly distributed) and rates of dropouts (exponentially distributed) are allowed. The test statistic is any member of the Harrington-Fleming GPclass of statistics.
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