Re-calculating the sample size in internal pilot study designs with control of the type I error rate.

When designing a clinical trial, there is usually some uncertainty about the variability of the primary outcome variable. This may lead to an unnecessarily high or inadequately low sample size. The internal pilot study approach uses data from patients recruited up to an interim stage to re-estimate the variance and to re-calculate the final sample size accordingly. Previously, simulation studies have shown that this methodology may highly improve the chance to obtain a well-powered trial. However, it also turned out that the type I error rate may be inflated by this procedure. We quantify the maximum excess of the type I error rate for normally distributed outcomes. If strict control of the alpha-level is considered to be an important issue, a method is proposed to achieve this when re-calculating the sample size in internal pilot studies. The characteristics of the power distributions are investigated for various sample size adaptation rules and implications are discussed.

[1]  C. Stein.  A Two-Sample Test for a Linear Hypothesis Whose Power is Independent of the Variance , 1945 .

[2]  Jack Moshman,et al.  A Method for Selecting the Size of the Initial Sample in Stein's Two Sample Procedure , 1958 .

[3]  J. Wittes,et al.  The role of internal pilot studies in increasing the efficiency of clinical trials. , 1990, Statistics in medicine.

[4]  A L Gould,et al.  Interim analyses for monitoring clinical trials that do not materially affect the type I error rate. , 1992, Statistics in medicine.

[5]  A. Gould,et al.  Sample size re-estimation without unblinding for normally distributed outcomes with unknown variance , 1992 .

[6]  A. Lawrence Gould,et al.  Discussion of papers of session 3: Bayes/empirical bayes , 1992 .

[7]  D. Bristol.  Sample size determination using an interim analysis , 1993 .

[8]  P. Bauer,et al.  Evaluation of experiments with adaptive interim analyses. , 1994, Biometrics.

[9]  S. Day,et al.  Internal pilot studies for estimating sample size. , 1994, Statistics in medicine.

[10]  M. Proschan,et al.  Designed extension of studies based on conditional power. , 1995 .

[11]  R. H. Browne.  On the use of a pilot sample for sample size determination. , 1995, Statistics in medicine.

[12]  J. Erikssen,et al.  A method for determining the size of internal pilot studies. , 1996, Statistics in medicine.

[13]  Meinhard Kieser,et al.  On the Use of the Upper Confidence Limit for the Variance from a Pilot Sample for Sample Size Determination , 1996 .

[14]  R A Betensky,et al.  An examination of methods for sample size recalculation during an experiment. , 1997, Statistics in medicine.

[15]  W. Lehmacher,et al.  Adaptive Sample Size Calculations in Group Sequential Trials , 1999, Biometrics.