Predicting the Duration of Sequential Survival Studies
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Drug Informnrion Journal, Vol. 35, 1387-1400. 2001 Printed in the USA. All rights reserved.
Copyright 0 2001 Drug Information Association Inc.
PREDICTING THE DURATION OF SEQUENTIAL SURVIVAL STUDIES JOHN WHITEHEAD,PHD Medical and Pharmaceutical Statistics Research Unit, The University of Reading, Reading, United Kingdom
Interim analyses are a common feature of clinical trial design, especially for large trials in high mortality conditions such as cancer or cardiovascular disease in which the primary endpoint is ojien the survival time from randomization to death. A plan for a series of interim analyses in which the criteria for stopping are specified in advance is known as a sequential design, and can be constructed to prevent patients from being randomized to an evidently inferior treatment and avoid continuation of a trial that is obviously futile. In this paper; methods for predicting the final sample size and total duration of a sequential survival study are described, and the play-off between speed of recruitment and length of follow-up is examined. The use of interim analyses to review the event rate, recruitment period, and model assumptions is discussed and sofhvare f o r the implementation of the methods is described. The approach i s illustrated in the context of a trial seeking to establish noninferiority. Key Words: Interim analysis; Noninferiority; Sequential analysis; Survival analysis
INTRODUCTION SEQUENTIAL METHODS involve the conduct of a series of interim analyses of the accumulating data of a clinical trial. Survival studies involve the long-term observation of patients until death or some other primary event. In combination, this means that each interim analysis may contain both data on new patients, and new follow-up data on old patients. Jones and Whitehead (l), Sellke and Siegmund (2), and Tsiatis, Rosner and Trichtler (3) describe how sequential tests of survival data can be conducted comparing an experi-
Presented at the DIA Workshop “Statistical Methodology in Clinical R&D,” April 2-4, 2001, Vienna, Austria. Reprint address: John Whitehead, PhD, Medical and Pharmaceutical Statistics Research Unit, The University of Reading, P.O. Box 240, Earley Gate, Reading, RG6 6FN,UK. E-mail: [email protected].
mental treatment with a control in a series of interim analyses based on either the logrank test or Cox’s regression method. These methods rely for their validity on the assumption of proportional hazards, the logrank test being a special case of Cox’s regression in the absence of covariates. Descriptions of trials conducted in this way include studies in cardiovascular disease (4,5), cancer (6,7), and epilepsy (8). In this paper, the prediction of the final sample size and the consequent duration of a sequential survival study are described. These quantities, together with the number of events at the termination of the study, are random variables, and they will be characterized through their means, medians, and ninetieth percentiles. The first two quantities give an idea of the sc
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