×

Bayesian optimal designs for phase I clinical trials. (English) Zbl 1210.62165

Summary: A broad approach to the design of Phase I clinical trials for the efficient estimation of the maximum tolerated dose is presented. The method is rooted in formal optimal design theory and involves the construction of constrained Bayesian c- and D-optimal designs. The imposed constraint incorporates the optimal design points and their weights and ensures that the probability that an administered dose exceeds the maximum acceptable dose is low. Results relating to these constrained designs for log doses on the real line are described and the associated equivalence theorem is given. The ideas are extended to more practical situations, specifically to those involving discrete doses. In particular, a Bayesian sequential optimal design scheme comprising a pilot study on a small number of patients followed by the allocation of patients to doses one at a time is developed and its properties explored by simulation.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62F15 Bayesian inference
62K05 Optimal statistical designs
62L05 Sequential statistical design
92C50 Medical applications (general)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Atkinson, Optimum Experimental Designs (1992)
[2] Atkinson, Optimum dose levels when males and females differ in response, Applied Statistics 44 pp 213– (1995) · Zbl 0821.62071
[3] Babb, Cancer Phase I clinical trials: Efficient dose escalation with overdose control, Statistics in Medicine 17 pp 1103– (1998)
[4] Chaloner, Bayesian design for estimating the turning point of a quadratic regression, Communications in Statistics-Theory and Methods 18 pp 1385– (1989) · Zbl 0696.62335
[5] Clyde, The equivalence of constrained and weighted designs in multiple objective problems, Journal of the American Statistical Association 91 pp 1236– (1996) · Zbl 0883.62079
[6] Durham, Statistical Decision Theory and Related Topics V pp 467– (1994) · doi:10.1007/978-1-4612-2618-5_36
[7] Durham, A random walk rule for Phase I clinical trials, Biometrics 53 pp 745– (1997) · Zbl 0877.62075
[8] Fan, mODa 6: Advances in Model-Oriented Design and Analysis pp 77– (2001) · doi:10.1007/978-3-642-57576-1_9
[9] Fedorov, Theory of Optimal Experiments (1972)
[10] Gasparini, A curve-free method for Phase I clinical trials, Biometrics 56 pp 609– (2000) · Zbl 1060.62611
[11] Haines, New Developments and Applications in Experimental Design pp 152– (1998)
[12] Karp, Clinical and biologic activity of the farnesyltransferase inhibitor R115777 in adults with refractory and relapsed acute leukemias: A Phase 1 clinical-laboratory correlative trial, Blood 97 pp 3361– (2001)
[13] Mats, New Developments and Applications in Experimental Design pp 50– (1998)
[14] O’Quigley, Continual reassessment method: A practical design for Phase I clinical trials in cancer, Biometrics 46 pp 33– (1990)
[15] Perevozskaya, I. (2001). Constrained Bayesian optimal designs for phase I clinical trials. Ph.D. thesis, University of Maryland Graduate School, Baltimore.
[16] Pshenichnyi, Necessary Conditions for an Extremum (1971) · Zbl 0764.90079
[17] Pukelsheim, Optimal Design of Experiments (1993)
[18] Rosenberger, Competing designs for Phase I clinical trials: A review, Statistics in Medicine 21 pp 2757– (2002)
[19] Rosenberger, Asymptotic normality of maximum likelihood estimators from multiparameter response-driven designs, Journal of Statistical Planning and Inference 60 pp 69– (1997) · Zbl 0900.62454
[20] Tsutakawa, Design of experiment for bioassay, Journal of the American Statistical Association 67 pp 584– (1972) · Zbl 0251.62051
[21] Tsutakawa, Selection of dose levels for estimating a percentage point of a logistic quantal response curve, Applied Statistics 29 pp 25– (1980) · Zbl 0429.62077
[22] Whitehead, Bayesian decision procedures for dose determining experiments, Statistics in Medicine 14 pp 885– (1995)
[23] Whitehead, Easy-to-implement Bayesian methods for dose-escalation studies in healthy volunteers, Biostatistics 2 pp 47– (2001) · Zbl 1017.62120
[24] Whittle, Some general points in the theory of optimal experimental design, Journal of the Royal Statistical Society, Series B 35 pp 123– (1973) · Zbl 0282.62065
[25] Zocchi, Optimum experimental designs for multinomial logistic models, Biometrics 55 pp 437– (1999) · Zbl 1059.62580
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.