Abstract
Optimal batch-sequential designs are difficult to compute, even when sufficient statistics and relatively uncomplicated loss functions simplify the calculations required. While backward induction applies, its difficulty grows exponentially in the number of stages, while a recently developed forward algorithm grows only linearly, but involves a maximization over a rather flat surface. This paper explores a hybrid algorithm, partially backward induction, partially forward, that has some of the advantages of each.
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References
Anscombe F.J. 1963. Sequential medical trials. Journal of the American Statistical Association 58: 365-383.
Berry D.A. and Ho C.H. 1988. One-sided sequential boundaries for clinical trials: Adecision-theoretic approach. Biometrics 44: 219-227.
Carlin B.P., Chaloner K., Church T., Louis T.A., and Matts J. 1993. Bayesian approaches for monitoring clinical trials with an application to toxoplasmic encephalitis prophylaxis. The Statistician 42: 355-367.
Carlin B.P., Kadane J.B., and Gelfand A.E. 1998. Approaches for opti-mal sequential decision analysis in clinical trials. Biometrics 54: 964-975.
DeGroot M.H. 1970. Optimal Statistical Decisions. McGraw Hill, New York.
Freedman L.S. and Spiegelhalter D.J. 1989. Comparison of Bayesian with group sequential methods for monitoring clinical trials. Controlled Clinical Trials 10: 357-367.
Hardwick J.P. and Stout Q.F. 1999. Using path induction to evaluate sequential allocation procedures. SIAM Journal of Scientific Computing 21: 67-87.
Jacobson M.A., Besch C.L., and Child C. 1994. Primary prophy-laxis with pyrimethamine for toxoplasmic encephalitis in patients with advanced human immunodeficiency virus disease: Results of a randomized trial. Journal of Infectious Diseases 169: 384-394.
Müller P. and Parmigiani G. 1995. Optimal design via curve fitting of Monte Carlo experiments. Journal of the American Statistical Association 90: 1322-1330.
Stallard N. 1998. Sample size determination for phase II clinical trials based on Bayesian decision theory. Biometrics 54: 279-294.
Thall P.F., Simon R., and Estey E.H. 1995. Bayesian sequential monitoring designs for single-arm clinical trials with multiple outcomes. Statistics in Medicine 14: 357-379.
Thall P.F., Simon R., and Ellenberg S.S. 1989. A two-stage design for choosing among several experimental treatments and a control in clinical trials. Biometrics 45: 537-547.
Vlachos P.K. and Gelfand A.E. 1996. Bayesian decision theoretic design for group sequential clinical trials having multivariate patient response. Department of Statistics, University of Connecticut, Technical Report.
Whitehead J. 1997. The Design and Analysis of Sequential Medical Trials. Revised 2nd edn. J. Wiley & Sons, New York.
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Kadane, J.B., Vlachos, P.K. Hybrid methods for calculating optimal few-stage sequential strategies: Data monitoring for a clinical trial. Statistics and Computing 12, 147–152 (2002). https://doi.org/10.1023/A:1014834602714
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DOI: https://doi.org/10.1023/A:1014834602714