An adaptive hierarchical test procedure for selecting safe and efficient treatments.

We consider the situation where during a multiple treatment (dose) control comparison high doses are truncated because of lack of safety and low doses are truncated because of lack of efficacy, e.g., by decisions of a data safety monitoring committee in multiple interim looks. We investigate the properties of a hierarchical test procedure for the efficacy outcome in the set of doses carried on until the end of the trial, starting with the highest selected dose group to be compared with the placebo at the full level alpha. Left truncation, i.e., dropping doses in a sequence starting with the lowest dose, does not inflate the type I error rate. It is shown that right truncation does not inflate the type I error if efficacy and toxicity are positively related and dose selection is based on monotone functions of the safety data. A positive relation is given e.g. in the case where the efficacy and toxicity data are normally distributed with a positive pairwise correlation. A positive relation also applies if the probability for an adverse event is increasing with a normally distributed efficacy outcome. The properties of such truncation procedures are investigated by simulations. There is a conflict between achieving a small number of unsafely treated patients and a high power to detect safe and efficient doses. We also investigated a procedure to increase power where a reallocation of the sample size to the truncated treatments and the control remaining at the following stages is performed.