Proposals for Sample Size Calculation Programs

Summary

Objectives : Numerous sample size calculation programs are available nowadays. They include both commercial products as well as public domain and open source applications. We propose modifications for these programs in order to even better support statistical consultation during the planning stage of a two-armed clinical trial.

Methods : Directional two-sided tests are commonly used for two-armed clinical trials. This may lead to a non-negligible Type III error risk in a severely underpowered study. In the case of a reasonably sized study the question for the so-called auxiliary alternative may evolve.

Results : We propose that sample size calculation programs should be able to compute i) Type III errors and the so-called (q-values, ii) minimum sample sizes required to keep the (q-values below pre-specified levels, and iii) detectable effect sizes of the so-called auxiliary alternatives.

Conclusions : Proposals iand ii are intended to help prevent irresponsibly underpowered clinical trials, whereas the proposal iii is meant as additional assistance for the planning of reasonably sized clinical trials.

Keywords

Directional two-sided hypothesis test - Type III error - sample size calculation - irresponsibly underpowered study - auxiliary alternative hypothesis

• References

• 1. Bock J. Bestimmung des Stichprobenumfangs für biologische Experimente und kontrollierte klinische Studien. München: R. Oldenbourg Verlag; 1998
• 2. Brown BW, Brauner C, Chan A, Gutierrez D, Herson J, Lovato J, Polsley J, Venier J. DSTPLAN Version 4.2: Calculations for Sample Sizes and Related Problems. The University of Texas MD Anderson Cancer Center: Houston, TX, 2000
• 3. Chow SC, Liu JP. Design and analysis of clinical trials. Concepts and methodologies. Second edition. Hoboken, New Jersey: Wiley; 2004
• 4. Chow SC, Shao J, Wang H. Sample size calculations in clinical research. Boca Raton, Florida: CRC Press - Taylor & Francis Group; 2003
• 5. Dahmen G, Rochon J, König IR, Ziegler A. Sample size calculations for controlled clinical trials using generalized estimating equations (GEE). Methods Inf Med 2004; 43 (05) 451-456.
• 6. Dahmen G, Ziegler A. Independence estimating equations for controlled clinical trials with small sample sizes - interval estimation. Methods Inf Med 2006; 45 (04) 430-434.
• 7. Draxler W, Mittlböck M. Basic principles in the planning of clinical trials in surgical oncology. European Surgery 2006; 38 (01) 27-32.
• 8. Emerson JD, Tritchler D. The three-decision problem in medical decision making. Statistics in Medicine 1987; 6 (02) 101-112.
• 9. Finner H. Stepwise multiple test procedures and control of directional errors. The Annals of Statistics 1999; 27 (01) 274-289.
• 10. Hasselblad V, Allen AS. Power calculations for large multi-arm placebo-controlled studies of dichotomous outcomes. Statistics in Medicine 2003; 22 (12) 1943-1954.
• 11. Hauschke D. Steinijans VW Directional decision for a two-tailed alternative. Letter to the editor. Journal of Biopharmaceutical Statistics 1996; 6 (02) 211-213.
• 12. Hintze J. NCSS and PASS. Number Cruncher Statistical Systems. Kaysville, Utah, 2001
• 13. ICH. Guideline E9 on Statistical Principles for Clinical Trials. International Conference on Harmonisation. 1998 http://www.ich.org
• 14. Julious SA. Sample sizes for clinical trials with normal data. Tutorial in biostatistics. Statistics in Medicine 2004; 23 (12) 1921-1986.
• 15. Len T, Krebs CJ. A review of statistical power analysis software. Bulletin of the Ecological Society of America 1997; 78 (02) 126-139 http://www.zoology.ubc.ca/~krebs/power.html
• 16. Leventhal L, Huynh C-L. Directional decisions for two-tailed tests: power, error rates, and sample size. Psychological Methods 1996; 1 (03) 278-292.
• 17. Mace AE. Sample-Size Determination. Huntington, New York: Robert E. Drieger Publishing Company; 1974
• 18. Machin D, Campbell MJ, Fayers PM. Pinol APY Sample Size Tables for Clinical Studies. Second Edition. Blackwell Science Ltd.: Oxford; 1997
• 19. Moher D, Schulz KF, Altman DG. for the CONSORT Group. The CONSORT statement: revised recommendations for improving the quality of reports of parallel-group randomised trials. The Lancet 2001; 357 9263 1191-1194.
• 20. Neuhauser M. The Choice of [alpha] for OneSided Tests. Drug Information Journal 2004; 38: 57-60.
• 21. Parker RA, Berman NG. Sample size: more than calculations. The American Statistician 2003; 57 (03) 166-170.
• 22. Piantadosi S. Clinical Trials: A Methodologic Perspective. Second Edition. John Wiley & Sons Ltd.: New York; 2005
• 23. Rippin G. Design issues and sample size when exposure measurement is inaccurate. Methods Inf Med 2001; 40 (02) 137-140.
• 24. Schwartz D, Flamant R, Lellouch J. Clinical Trials. Translated by MJR Healy. London: Academic Press; 1980
• 25. Senn S. Statistical Issues in Drug Development. Chichester: John Wiley & Sons Ltd.; 1997
• 26. Sonnemann E. Allgemeine Lösungen multipler Testprobleme. EDV in Medizin und Biologie 1982; 13 (04) 120-128.
• 27. Stürmer T, Gefeller O, Brenner H. A computer program to estimate power and relative efficiency of flexibly matched case-control studies. Methods InfMed 2005; 44 (05) 693-696.
• 28. Victor N. On clinically relevant differences and shifted nullhypotheses. Methods Inf Med 1987; 26 (03) 109-116.