Internal Pilot Studies for Determining the Sample Size without Unblinding
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35, pp. 399-405, 2001 Printed i n the USA. All rights reserved. Drug Informorion Joirrnrrl, Vol.
Copyright 0 2001 Drug Information Association Inc.
INTERNAL PILOT STUDIES FOR DETERMINING THE SAMPLE SIZE WITHOUT UNBLINDING DIETMAR ZELLNER,PHD Division of Nephrology. Medical Department, University of Ulm, Ulrn, Germany
GUNTERE. ZELLNER, MD Clinic for Surgery, Spital Zofingen. Zofingen, Switzerland
THOMASFRANKEWITSCH, MD Institute for Medical Informatics and Biomathematics, University of Miinster, Miinster, Germany
FRIEDER KELLER,MD Division of Nephrology. Medical Department. University of Ulm, Ulm, Germany
If no reliable itlformation about the variance of the key response is available at beginning of a clinical trial, the use of data from the first few patients entered in the trial ('internal pilot') may be appropriate to estimate the variance and thus to recalculate the required sample size. We investigate the influence on existing methods of variance estimation via the Expectation-Maximization (EM) algorithm without unveiling of the treatment status. In addition, "e investigate the use of a formula derived by Guenther to estimate the preplanned sample size. This simple modification could improve somewhat the existing methods for the same problem. There is no effect of the EM algorithm on the type I error rate of the e-xisting procedures, and the effect on the type I I error rate is negligible as long as the number of patients in the internal pilot is not too small. Thus, to recalculate the sample size it is not necessaty to unveil the treatment status in an internal pilot with a moderate number of patients. Key Words: Sample size: Unblinding; Internal pilot
INTRODUCTION THE SAMPLE SIZE FOR a clinical trial depends on the type I and type I1 error rates, the minimum relevant clinical difference, and the value of a measure of variation for the key response. When planning a clinical trial the required value of the variability measure for this main efficacy variable generally
Reprint address: Dietmar Zellner, Im Pfarrgarten 4, 88457 Kirchdorfnller, Germany. E-mail: DZellner@ T-Online.de.
is unknown. A prior estimate of variance is usually obtained from a small pilot study taken from previous trials or estimated. However, a variance estimate obtained from a small pilot trial can be subject to substantial sampling error; an estimate based on data from previous trials may not be representative of the trial being designed, for example, different patient types, different treatment __ duration, different circumstances, and so on. Overstating the variability unnecessarily infhteS the Sample size, the cost of the trial, the number of patients exposed to the risk
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D. Zellner, G.E. Zellner, T. Frankewitsch. arid F. Keller
of treatment, and the time required to obtain the data for a definitive conclusion. Understating the variability leads to an inadequate sample size and an underpowered trial in which considerable resources can be expended without reaching a conclusion ( I ) . ‘Internal pilot studies’ were re
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