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

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

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generality. For example, the marginal posterior distribution of the MTD given the data from k patients can then be simply expressed as P k ð g Þ¼ Z X C k ð c ; u j D k Þ d u irrespective of whether or not g and N were assumed to be independent a priori. Example: 5-FU Trial (continued) The dose-toxicity relationship was modeled according to the logistic tolerance distribution given by (3) reparameterized in terms of N =[ g U 0 ], where U 0 is the probability of DLT at the starting dose x 1 = 140. As shown by Eq. (7), the prior distribution for r was taken to be the uniform on G ± V = [140, 425] ± [0, .2]. It follows that the marginal posterior probability density function of the MTD given the data D k is P k ð g Þ¼ 0 : 2 0 C k i ¼ 1 ð exp f y i f ð g ; u j x i Þg ½ 1 þ exp f f ð g ; u j x i ÞgÞ du g 140 ; 425 ² where f ð g ; u j x i Þ¼ ð g ³ x i Þ ln f u = ð 1 ³ u Þg þ ð x i ³ 140 Þ ln f u = ð 1 ³ u Þg g ³ 140 : The marginal posterior distribution P k represents a probabilistic summary of all the information about the MTD that is available after the observa-
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Unformatted text preview: tion of k patients. Figure 2 shows the marginal posterior distribution of the MTD given the data shown in Table 1. 2.5. Loss Function As each patient is accrued to the trial, a decision must be made regarding the dose level that the patient is to receive. In a strict Bayesian setting, the decisions are made by minimizing the posterior expected loss associated with each permissible choice of dose level. To accomplish this, the set S of all permissible dose levels is specified and a loss function is chosen to quantify the cost or loss arising from the administration of each permissible dose under each possible value of N . The loss may be expressed in financial terms, in terms of patient well-being, or in terms 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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