Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 3, pp. 492-506

BAYESIAN DESIGN FOR CLINICAL TRIALS WITH A CONSTRAINT ON THE TOTAL AVAILABLE DOSE

By

MEI-MEI ZEN, Cheng-Kung University
and
ANIRBAN DASGUPTA, Purdue University

SUMMARY. Bayesian optimal design of a dose response trial is considered when the response admits a linear regression relationship with the amount of dose applied. The important aspects of the results are that we allow the variance of the response to depend on the mean, the number of patients to be used is itself part of the design, and in addition to a lower and an upper bound on the applicable dose, there is also a constraint on the total amount of the medication available. This last restriction is important in cases where an additional supply is not feasible due to logistic, financial, or other factors. We also avoid making any assumptions whatsoever about the form of the likelihood function by using the linear Bayes estimate of the response rate. The closed form results are illustrated on some examples by numerical computations.

AMS (1991) subject classification. 62K05, 62J05, 62F15.

Key words and phrases. Bayesian optimal design, dose response trial, regression.

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