the above methods use a binary assessment of toxic response, toxicity is often measured on a multinomial scale, graded according to NCI toxicity criteria, or through a variable that can be modeled as continuous (e.g., white blood cell count). This additional information can be incorporated into the trial design through an extension of the dose-toxicity model. To illustrate this in the multinomial setting, we consider a trinomial response measure Y that assumes the values 0, 1, and 2 according as each patient manifests ‘‘ mild, ’’ ‘‘ moderate, ’’ or dose limiting toxicity. The variable Y may represent a summary of all relevant adverse events by recording the highest level of toxicity observed for each patient. The dose-toxicity model can then be speciﬁed through the functions f i ð x j N Þ¼ Prob f Y ¼ i j Dose ¼ x g i ¼0 ; 1 ; 2 given by f 2 ð x j N Þ¼ F ð a 2 þ h 2 x Þ f 1 ð x j N Þ¼ F ð a 1 þ b 1 x Þ± f 2 ð x j N Þ and f0 ð x j N Þ¼ 1 ± f 2 ð x j
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