Clinical Trial Size: Fixed versus Group-Sequential Designs

Summary

This paper deals with the estimation of the size of clinical trials for comparing two binomial proportions in both fixed and group-sequential designs. In the fixed size approach, it focuses on 1.) equal sample size design; 2.) unequal allocation designs that either maximize the test power subject to fixed total cost or minimize the total expenditure subject to prespecified power using the simplex procedure for function minimization. Emphasis is also placed on group-sequential designs, based upon closed stopping rules, multiple testing and range of clinical equivalence. The efficiency of different allocation designs is assessed by computing the power of the exact conditional Fisher-Irwin test. Designs were applied in planning a clinical trial in which the drug Pancuronium Bromide was compared with a standard treatment to reduce intraventricular haemorrhage in preterm infants.

Diese Arbeit befaßt sich mit der Schätzung des Umfangs bei klinischen Studien, wenn zwei binomiale Anteile sowohl bei festem als auch gruppensequentiellem Stichprobenumfang verglichen werden sollen. Im Falle des festen Stichprobenumfangs konzentriert sie sich auf 1.) gleiche Stichprobenumfänge, 2.) ungleiche Zuteilungsverfahren, die entweder bei festen Gesamtkosten die Macht des Tests maximieren oder bei vorgegebener Macht unter Benutzung eines Simplexverfahrens zur Bestimmung des Minimums einer Funktion die Gesamtkosten minimieren. Besonderer Wert wird auch auf gruppensequentielle Verfahren gelegt, die auf abgeschlossenen Stoppregeln, Mehrfachtests und dem Ausmaß klinischer Äquivalenz beruhen. Die Wirksamkeit verschiedener Zuteilungsverfahren wird beurteilt durch die Berechnung der Macht des exakten konditionalen Fisher-Irwin-Tests. Das Verfahren wurde zur Planung einer klinischen Studie angewandt, bei der das Arzneimittel Pancuronium-Bromid mit einer Standardtherapie zur Reduzierung intraventrikulärer Blutungen bei Frühgeburten verglichen wurde.

Key-Words

Clinical Trial - Function Minimization - Repeated Significance Tests

Schlüssel-Wörter

Klinische Studie - Minimierung einer Funktion - wiederholte Signifikanztests

• REFERENCES

• 1 Armitage P, McPherson C. K, Rowe B. C. Repeated significance tests on accumulating data. J. roy. statist. Soc. Series A. 1969; 132: 235-244.
• 2 Bennett B. M, Hsu P. On the power function of the exact test for the 2 x 2 contingency table. Biometrika 1960; 47: 393-398.
• 3 Casagrande J. T, Pike M. C, Smith P. C. An improved approximate formula for calculating sample sizes for comparing two binomial distributions. Biometrics 1978; 34: 483-486.
• 4 Casagrande J. T, Pike M. C, Smith P. G. Algorithm As 129. The power function of the “exact” test for comparing two binomial distributions. Appl. Statist 1978; 27: 212-219.
• 5 DeMets D. L, Ware J. H. Group sequential methods for clinical trials with a one-sided hypothesis. Biometrika. 1980; 67: 651-660.
• 6 Diegert C, Diegert K. V. Note on inversion of Casagrande-Pike-Smith approximate sample-size formula for Fisher-Irwin test on 2 x 2 tables (Letter to the editor). Biometrics 1981; 37: 595
• 7 Donner A. Approaches to sample size estimation in the design of clinical trials -A review. Statist. in Med 1984; 3: 199-214.
• 8 Fleiss J. L, Tytun A, Ury H. K. A simple approximation for calculating sample sizes for comparing independent proportions. Biometrics 1980; 36: 343-346.
• 9 Freedman L. S, Lowe D, Macaskill P. Stopping rules for clinical trials. Statist. in Med 1983; 2: 167-174.
• 10 Freedman L. S, Lowe D, Macaskill P. Stopping rules for clinical trials incorporating clinical opinion. Biometrics 1984; 40: 575-586.
• 11 Freiman J. A, Chalmers T. C, Smith H, Kuebler R. R. The importance of beta, the type II error and sample size in the design and interpretation of the randomized control trials. New Engl. J. Med 1978; 299: 690-694.
• 12 Jennison C, Turnbull B. W. Repeated confidence intervals for group sequential clinical trial. Contr. clin. Trials 1984; 5: 33-45.
• 13 McPherson C. K, Armitage P. Repeated significance tests on accumulating data when the null hypothesis is not true. J. roy. statist. Soc, Series A 1971; 134: 15-25.
• 14 Moussa M. A. A. Planning a clinical trial with allowance for cost and patient recruitment rate. Comp. Progr. Biomed 1984; 18: 173-180.
• 15 Moussa M. A. A. Planning a cohort or case-control study with allowance for cost and test power. Comput. Meth. Progr. Biomed 1985; 20: 225-231.
• 16 Moussa M. A. A. Allocation designs in cohort and case-control studies. Statist. in Med. (In press).
• 17 Neider J. A, Mead R. A simplex method for function minimization. Computer J 1965; 7: 308-313.
• 18 O’Brien P. C, Fleming T. R. A multiple testing procedure for clinical trials. Biometrics 1979; 35: 549-556.
• 19 Olsson D. M. A sequential simplex program for solving minimization problems. J. Qual. Technol 1974; 6: 53-57.
• 20 Pocock S. J. Group sequential methods in the design and analysis of clinical trials. Biometrika 1977; 64: 191-199.
• 21 Spiegelhalter D. J, Freedman L. S. A predictive approach to selecting the size of a clinical trial, based on subjective clinical opinion. Statist. in Med 1986; 5: 1-13.
• 22 Wald A. Sequential analysis. New York: Wiley; 1947