Methods Inf Med 2011; 50(03): 237-243
DOI: 10.3414/ME09-01-0063
Original Articles
Schattauer GmbH

Sample Size Reassessment in Non-inferiority Trials

Internal Pilot Study Designs with ANCOVA
T. Friede
1   Department of Medical Statistics, University of Göttingen, Göttingen, Germany
,
M. Kieser
2   Institute of Medical Biometry and Informatics, University of Heidelberg, Heidelberg, Germany
› Institutsangaben
Weitere Informationen

Publikationsverlauf

received: 16. Juli 2009

accepted: 12. Januar 2010

Publikationsdatum:
18. Januar 2018 (online)

Summary

Objectives: Analysis of covariance (ANCOVA) is widely applied in practice and its use is recommended by regulatory guidelines. However, the required sample size for ANCOVA depends on parameters that are usually uncertain in the planning phase of a study. Sample size recalculation within the internal pilot study design allows to cope with this problem. From a regulatory viewpoint it is preferable that the treatment group allocation remains masked and that the type I error is controlled at the specified significance level. The characteristics of blinded sample size reassessment for ANCOVA in non-inferiority studies have not been investigated yet. We propose an appropriate method and evaluate its performance.

Methods: In a simulation study, the characteristics of the proposed method with respect to type I error rate, power and sample size are investigated. It is illustrated by a clinical trial example how strict control of the significance level can be achieved.

Results: A slight excess of the type I error rate beyond the nominal significance level was observed. The extent of exceedance increases with increasing non-inferiority margin and increasing correlation between outcome and covariate. The procedure assures the desired power over a wide range of scenarios even if nuisance parameters affecting the sample size are initially mis-specified.

Conclusions: The proposed blinded sample size recalculation procedure protects from insufficient sample sizes due to incorrect assumptions about nuisance parameters in the planning phase. The original procedure may lead to an elevated type I error rate, but methods are available to control the nominal significance level.

 
  • References

  • 1 Senn S. Statistical Issues in Drug Development. Second edition. Chichester: Wiley; 2007
  • 2 Sullivan LM, D’Agostino RB. Robustness and power of analysis of covariance applied to data distorted from normality by floor effects: homogeneous regression slopes. Statistics in Medicine 1996; 15: 477-496.
  • 3 Sullivan LM, D’Agostino RB. Robustness and power of analysis of covariance applied to ordinal scaled data as arising in randomized controlled trials. Statistics in Medicine 2003; 22: 1317-1334.
  • 4 Grouin JM, Day S, Lewis J. Adjustment for baseline covariates: an introductory note. Statistics in Medicine 2004; 23: 697-699.
  • 5 Grouin JM, Lewis J. Committee for proprietary medicinal products (CPMP): points to consider on adjustment for baseline covariates. Statistics in Medicine 2004; 23: 701-709.
  • 6 Julious SA, Mullee MA. Issues with using baseline in last observation carried forward analysis. Pharmaceutical Statistics 2008; 7: 142-146.
  • 7 International Conference on Harmonisation (ICH).. ICH Harmonised Tripartite Guideline E9: Statistical Principles for Clinical Trials. Statistics in Medicine 1999; 18: 1905-1942.
  • 8 European Medicines Agency (EMEA).. Reflection paper on methodological issues in confirmatory clinical trials planned with an adaptive design. CHMP/EWP/2459/02, 2007 http://www.emea.europa.eu/pdfs/human/ewp/245902enadopted.pdf (last access November 24, 2009).
  • 9 Friede T, Kieser M. Sample size recalculation for binary data in internal pilot study designs. Pharmaceutical Statistics 2004; 3: 269-279.
  • 10 Friede T, Mitchel C, Müller-Velten G. Blinded sample size reestimation in non-inferiority trials with binary endpoints. Biometrical Journal 2007; 49: 903-916.
  • 11 Wittes J, Brittain E. The role of internal pilot studies in increasing the efficiency of clinical trials. Statistics in Medicine 1990; 9: 65-72.
  • 12 Birkett MA, Day SJ. Internal pilot studies for estimating sample size. Statistics in Medicine 1994; 13: 2455-2463.
  • 13 Wittes J, Schabenberger O, Zucker D, Brittain E, Proschan M. Internal pilot studies I: type I error rate of the naive t-test. Statistics in Medicine 1999; 18: 3481-3491.
  • 14 Denne JS, Jennison C. Estimating the sample size for a t-test using an internal pilot. Statistics in Medicine 1999; 18: 1575-1585.
  • 15 Kieser M, Friede T. Re-calculating the sample size in internal pilot study designs with control of the type I error rate. Statistics in Medicine 2000; 19: 901-911.
  • 16 Proschan MA, Wittes J. An improved double sampling procedure based on the variance. Biometrics 2000; 56: 1183-1187.
  • 17 Coffey CS, Muller KE. Controlling test size while gaining the benefits of an internal pilot design. Biometrics 2001; 57: 625-631.
  • 18 Zucker DM, Wittes JT, Schabenberger O, Brittain E. Internal pilot studies II: comparison of various procedures. Statistics in Medicine 1999; 18: 3493-3509.
  • 19 Kieser M, Friede T. Simple procedures for blinded sample size recalculation that do not affect the type I error rate. Statistics in Medicine 2003; 22: 3571-3581.
  • 20 Friede T, Kieser M. Blinded sample size reassessment in non-inferiority and equivalence trials. Statistics in Medicine 2003; 22: 995-1007.
  • 21 Friede T, Kieser M. Sample size recalculation in internal pilot study designs: a review. Biometrical Journal 2006; 48: 537-555.
  • 22 Proschan MA. Sample size re-estimation in clinical trials. Biometrical Journal 2009; 51: 348-357.
  • 23 Friede T, Kieser M. Blinded sample size recalculation for clinical trials with normal data and baseline adjusted analysis. Pharmaceutical Statistics, electronically published ahead of print, 26 Nov 2009
  • 24 Committee for Medicinal Products for Human Use (CHMP).. Guideline on the choice of the non-inferiority margin. Statistics in Medicine 2006; 25: 1628-1638.
  • 25 Fleiss JL. The Design and Analysis of Clinical Experiments. New York: Wiley; 1986
  • 26 Guenther WC. Sample size formulae for normal theory t-tests. American Statistician 1981; 35: 243-244.
  • 27 Schouten HJA. Sample size formula with a continuous outcome, for unequal group size and unequal variances. Statistics in Medicine 1999; 18: 87-91.
  • 28 Frison L, Pocock SJ. Repeated measures in clinical trials: analysis using mean summary statistics and its implications for design. Statistics in Medicine 1999; 11: 1685-1704.
  • 29 Friede T, Kieser M. A comparison of methods for adaptive sample size adjustment. Statistics in Medicine 2001; 20: 3861-3873.
  • 30 Zucker DM, Wittes JE, Schabenberger O, Brittain E. Internal pilot studies II: comparison of various procedures. Statistics in Medicine 1999; 18: 3493-3509.
  • 31 Szegedi A, Kohnen R, Dienel A, Kieser M. Acute treatment of moderate to severe depression with hypericum extract WS 5570 (St John’s wort): randomised controlled double-blind non-inferiority trial versus paroxetine. BMJ 2005; 330: 503-506.
  • 32 Hedlund JL, Viewig BW. The Hamilton rating scale for depression: a comprehensive review. Journal of Operational Psychiatry 1979; 10: 149-165.
  • 33 Glueck DH, Muller KE. Adjusting power for a baseline covariate in linear models. Statistics in Medicine 2003; 22: 2535-2551.
  • 34 Berger RL, Boos DD. P values maximized over a confidence set for the nuisance parameter. Journal of the American Statistical Association 1994; 89: 1012-1016.