EWOC Sample Clauses

EWOC. Under EWOC, the dose level and toxicity relationship is modeled as follows: P (DLT|Dose = x) = F (β0 + β1x) (1) where x is the specified dose level, F is a specified distribution function (tolerance distribution), and β0 and β1 are unknown parameters. β1 is assumed to be greater than 0 such that the probability of the DLT is a monotonic increasing function of dose level. Since the distribution function is assumed to be logistic, we can write the model as: eβ0+β1x P (DLT|Dose = x) = 1 + eβ0+β1x (2) The probability of the DLT at the minimum dose xmin is denoted by ρ0, with yi as a binary indicator for the DLT of the ith patient. Utilizing all patient data, given by Dn = {(xi, yi), i = 1, ..., n}, the likelihood function of x0, x0 given Dn is: Y n X(x0, x0|Xx) = logit−1(β0 + β1xi)yi [1 − logit−1(β0 + β1xi)]1−yi (3) i=1 Prior information is incorporated about x0, x0 through a prior probability density function h(β0, β1). Using Bayes Theorem, the joint posterior distribution of (β0, β1) given the data Dk is then: P (β0, β1|Dn ) = L(β0, β1|Dn)h(β0, β1) ∫ ∫ L(x, y|Dn)h(x, y)dxdy
Sample 1
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