[生物书合集].Advances.in.Clinical.TBiostatisti

[生物书合集].Advances.in.Clinical.TBiostatisti

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corresponding to the clinicians’ prior guess for u i , and yet disperse enough to permit dose escalation in the absence of toxicity. They also discuss why alternative priors, such as the ordered Dirichlet distribution, may not be appropriate for use in cancer phase I trials designed according to the curve-free method. 2.4. Posterior Distribution Perceptions concerning the unknown model parameters change as the trial progresses and data accumulate. The appropriate adjustment of subjective opinions can be made by transforming the prior distribution h through an application of Bayes’ theorem. Thus, we obtain the posterior distribution C k which reflects our beliefs about N based on a combination of prior knowledge and the data available after k patients have been observed. The transformation from prior to posterior distribution is accom- plished through the likelihood function. If we denote the dose-toxicity model parameterized in terms of N as
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Unformatted text preview: p x j N Prob f DLT j Dose x g then the likelihood function for r = [ g N ] given the data D k is L N j D k P k i 1 p x i j N y i f 1 p x i j N g 1 y i : Bayes theorem then implies that the joint posterior distribution of ( g , N ) given the data D k is C k g ; N j D k L g ; N j D k h g ; N m L u j D k h u d u where the integral is over Q . To facilitate exposition, it will hereafter be assumed that the prior distribution h is dened on some set G V containing the parameter space Q such that g 2 G and N 2 V with prior probability 1. Whenever necessary, this will entail extending h from Q to G V by dening h to be identically equal to zero on the dierence ( G V )\ Q . This convention will simplify ensuing formulations without a loss of Copyright n 2004 by Marcel Dekker, Inc. All Rights Reserved....
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This note was uploaded on 06/13/2011 for the course PHYSICS 101 taught by Professor Shu during the Spring '11 term at FIU.

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