Selecting the best dose when a monotonic dose‐response relation exists

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Abstract
We propose a method for selecting the best treatment when a monotonic dose—response relationship exists. Because of side effects associated with higher doses, the highest dose may not be the optimum, particularly when a lower dose gives a similar response. Rather than assume a particular functional relationship of dose to response, we use isotonic regression techniques. We consider the case of three treatment levels, which is applicable to many clinical trials. The lowest treatment level may represent a placebo or no treatment control. While we focus primarily on Bernoulli response variables, we also discuss a model for normally distributed data. We suggest a two‐stage procedure that we have investigated via simulation.