Treatment comparisons based on two-dimensional safety and efficacy alternatives in oncology trials

In addition to their desired anticancer effects, most cancer treatments may also cause transient toxicity, permanent organ damage, or death. A critical question in comparing an experimental treatment to a standard is how much increase in an adverse event rate is an acceptable trade-off for achieving a targeted improvement in efficacy, or vice versa. We consider settings where one may characterize patient outcome as a bivariate (efficacy, safety) variable and quantify treatment effect as a corresponding two- dimensional parameter. A set of target parameters, each representing a clinically meaningful improvement over the standard, are elicited from the physician. Each target is a two-dimensional generalization of the usual one- dimensional shift parameter. We define the alternative hypothesis in the two- dimensional effect space as the convex hull of the sets of parameters that are at least as desirable as each target point. The rejection region is obtained by shifting the alternative toward (0,0) to achieve a given type I error, with sample size computed to achieve a given power at the targets. The method is illustrated by application to two cancer chemotherapy trials.