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_Homework_homework2 - Homework 2 Due Monday 1 May 1 The...

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Homework 2. Due Monday 1 May. 1. The classic Storer design says that you treat 3 patients at dose i . If none have dose-limiting toxicities (DLT), you escalate to dose i + 1. If 2 or 3 have DLT, you stop and declare dose i - 1 to be the maximum tolerated dose (MTD). If 1 has a DLT, you give 3 more patients dose i . If none of those have DLT, you escalate, but if 1 or more have DLT, you declare dose i - 1 to be the MTD. We worked out in class and you can find in Piantadosi the probability that you escalate to dose i + 1. (That is, escalate past dose i .) Consider the modified Storer design used in the trial UCD171, where we require six patients to have been tested before we will declare a dose to be safe. Recall we declare dose i not to be safe if we have 2 or more DLT observed in either 3 or 6 patients at that dose. The modification is that if we have not already seen 6 patients at dose i - 1, we would have to treat 3 more at that dose before declaring it to be safe. Derive a formula for the probability of stopping at dose i
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