Interim monitoring of clinical trials: Decision theory, dynamic programming and optimal stopping
Keywords:
Clinical trial, group sequential test, Bayes decision problem, dynamic programming, optimal stoppingAbstract
It is standard practice to monitor clinical trials with a view to stopping early if results are sufficiently compelling. We explain how the properties of stopping boundaries can be calculated numerically and how to optimise boundaries to minimise expected sample size while controlling type I and II error probabilities. Our optimisation method involves the use of dynamic programming to solve Bayes decision problems with no constraint on error rates. This conversion to an unconstrained problem is equivalent to using Lagrange multipliers. Applications of these methods in clinical trial design include the derivation of optimal adaptive designs in which future group sizes are allowed to depend on previously observed responses; designs which test both for superiority and non-inferiority; and group sequential tests which allow for a delay between treatment and response.
References
Armitage, P., McPherson, C. K. Rowe, B.C. 1969. Repeated significance tests on accumulating data. Journal of the Royal Statistical Society, Series A 132: 235-244.
Barber, S. Jennison, C. 2002. Optimal asymmetric one-sided group sequential tests. Biometrika 89: 49-60.
Cui, L., Hung, H. M. J. Wang, S-J. 1999. Modification of sample size in group sequential clinical trials. Biometrics 55: 853-857.
DeMets, D. L., Hardy, R., Friedman, L. M. Lan, K. K. G. 1984. Statistical aspects of early termination in the Beta-Blocker Heart Attack Trial. Controlled Clinical Trials 5: 362-372.
Eales, J. D. Jennison, C. 1992. An improved method for deriving optimal one-sided group sequential tests. Biometrika 79: 13-24.
Hampson, L. V. 2009. Group Sequential Tests for Delayed Responses. Ph.D. thesis, University of Bath, Bath, UK.
Hampson, L. V. Jennison, C. 2013. Group sequential tests for delayed responses (with discussion). Journal of the Royal Statistical Society, Series B 75: 3-54.
Jennison, C. Turnbull, B. W. 1997. Group sequential analysis incorporating covariate information. Journal of the American Statistical Association 92: 1330-1341.
Jennison, C. Turnbull, B. W. 2000. Group Sequential Methods with Applications to Clinical Trials. Chapman Hall/CRC: Boca Raton.
Jennison, C. Turnbull, B. W. 2006a. Adaptive and nonadaptive group sequential tests. Biometrika 93: 1-21.
Jennison, C. Turnbull, B. W. 2006b. Efficient group sequential designs when there are several effect sizes under consideration. Statistics in Medicine 25: 917-932.
O'Brien, P. C. Fleming, T. R. 1979. A multiple testing procedure for clinical trials. Biometrics 35: 549-556.
غhrn, F. Jennison, C. 2010. Optimal group sequential designs for simultaneous testing of superiority and non-inferiority. Statistics in Medicine 29: 743-759.
Pocock, S. J. 1977. Group sequential methods in the design and analysis of clinical trials. Biometrika 64: 191-199.
Rosner, G. L. Tsiatis, A. A. 1989. The impact that group sequential tests would have made on ECOG clinical trials. Statistics in Medicine 8: 505--516.
Scharfstein, D. O., Tsiatis, A. A. Robins, J.M. 1977. Semiparametric efficiency and its implication on the design and analysis of group-sequential studies. Journal of the American Statistical Association 92: 1342-1350.
Schmitz, N. 1993. Optimal Sequentially Planned Decision Procedures. Lecture Notes in Statistics, 79, Springer-Verlag: New York.
Wang, S. J., Hung, H. M. J., Tsong Y. Cui, L. 2001. Group sequential test strategies for superiority and non-inferiority hypotheses in active controlled clinical trials. Statistics in Medicine 20: 1903-1912.
