Flexible Two-Stage Designs: An Overview

Abstract

In this overview we introduce the basic ideas behind a new flexible approach in sequential designs. The different concepts based on two-stage combination tests and conditional error functions are brought together. We sketch the construction of p-values, confidence intervals, and median unbiased estimates. Finally, recursive combination tests are introduced which extend the flexibility to the choice of the number of interim analyses.

Keywords

Adaptive Design - Midtrial Design Modification - Two-stage Combination Test - Conditional Error Function - Confidence Interval - Recursive Combination Test

• References

• 1 Stein C. A two-sample test for a linear hypothesis whose power is independent of the variance. Annals of Mathematical Statistics 1945; 16: 234-58.
• 2 Wittes J, Brittain E. The role of internal pilot studies in increasing the efficiency of clinical trials. Stat Med 1990; 9: 65-72.
• 3 Birkett MA, Day SJ. Internal pilot studies for estimating sample size. Stat Med 1994; 13: 2455-63.
• 4 Coffey CS, Muller KE. Exact test size and power of a Gaussian error linear model for an internal pilot study. Stat Med 1999; 18: 1199-214.
• 5 Wittes JT, Schabenberger O, Zucker DM, Brittain E, Proschan M. Internal pilot studies I: Type I error rate of the naive t-test. Stat Med. 1999: 3481-91.
• 6 Zucker DM, Wittes JT, Schabenberger O, Brittain E. Internal pilot studies II: Comparison of various procedures. Stat Med 1999; 18: 3493-509.
• 7 Kieser M, Friede T. Re-calculating the sample size of clinical trials in internal pilot studies with control of the type error rate. Stat Med 2000; 19: 901-12.
• 8 Gould AL, Shih WJ. Sample size re-estimation without unblinding for normally distributed outcomes with unknown variance. Communications in Statistics-Theory and Methods 1992; 21: 2833-53.
• 9 Proschan MA, Hunsberger A. Designed extension of studies based on conditional power. Biometrics 1995; 51: 1315-24.
• 10 Lan KKG, Wittes J. The B-value: A tool for monitoring data. Biometrics 1988; 44: 579-85.
• 11 Lan KKG, Simon R, Halperin M. Stochastically curtailed tests in long-term clinical trials. Communications in Statistics 1982; C1: 207-19.
• 12 Bauer P. Multistage testing with adaptive designs. Biometrie und Informatik in Medizin und Biologie. 1989; 4: 130-48.
• 13 Bauer P, Köhne K. Evaluation of experiments with adaptive interim analyses. Biometrics 1994; 50: 1029-41. Correction in Biometrics 1996; 52: 380.
• 14 Posch M, Bauer P. Adaptive two stage designs and the conditional error function. Biometrical Journal 1999; 41: 689-96.
• 15 Wassmer G. Statistische Testverfahren für gruppensequentielle und adaptive Pläne in klinischen Studien. Köln: Alexander Mönch; 1999
• 16 Liu Q, Chi GYH. On sample size and inference for two-stage adaptive designs. Bio-metrics. 2001: 57 to appear.
• 17 Mosteller F, Bush R. Selected quantitative techniques. In Lindzey G. editor Handbook of Social Psychology. Cambridge: Addison-Wesley; 1954: 289-334.
• 18 Lehmacher W, Wassmer G. Adaptive sample size calculations in group sequential trials. Biometrics 1999; 55: 1286-90.
• 19 Brannath W, Posch M, Bauer P. Recursive combination tests, IMS Online Working Paper 99-03,. Department of Medical Statistics, University of Vienna.;
• 20 Cui L, Hung HMJ, Wang S. Modification of sample size in group sequential clinical trials. Biometrics 1999; 55: 321-4.
• 21 Fisher LD. Self-designing clinical trials. Stat Med 1998; 17: 1551-62.
• 22 Shen Y, Fisher LD. Statistical inference for self-designing clinical trials with a one-sided hypothesis. Biometrics 1999; 55: 190-7.
• 23 Banik N, Köhne K, Bauer P. On the power of Fisher’s combination test for two stage sampling in the presence of nuisance parameters. Biometrical Journal 1996; 38: 25-37.
• 24 Chase GR, Hewett JE. Double sample tests – a distribution free procedure. Journal of Statistical Computation and Simulation 1976; 4: 247-57.
• 25 Wassmer G. A comparison of two methods for adaptive interim analyses in clinical trials. Biometrics 1998; 54: 696-705.
• 26 Bauer M, Bauer P, Budde M. A simulation program for adaptive two stage designs. Computational Statistics & Data Analysis 1994; 26: 351-71.
• 27 Bauer P, Kieser M. Combining different phases in the development of medical treatments within a single trial. Stat Med 1999; 18: 1833-48.
• 28 Kieser M, Bauer P, Lehmacher W. Inference on multiple endpoints in clinical trials with adaptive interim analyses. Biometrical Journal 1999; 41: 261-77.
• 29 Lang T, Auterith A, Bauer P. Trend tests with adaptive scoring. Biometrical Journal 2000; 42: 1007-20.
• 30 Hommel G. Adaptive modifications of hypotheses after an interim analysis. Biometrical Journal. 2001: 43 to appear.
• 31 Posch M, Bauer P. Interim analysis and sample size reassessment. Biometrics 2000; 56: 1170-6.
• 32 Tsiatis AA, Rosner GL, Metha CR. Exact confidence intervals following a group sequential test. Biometrics 1984; 40: 797-803.
• 33 Wassmer G. Multistage adaptive test procedures based on Fisher’s product criterion. Biometrical Journal 1999; 41: 279-93.
• 34 Müller H, Schäfer H. Adaptive group sequential designs for clinical trials: Combining the advantages of adaptive and of classical group sequential approaches. Biometrics. 2001: 57 to appear.