It has become standard in medical treatment to base dosage on evidence in randomized trials. Yet it has been rare to study how outcomes vary with dosage. In trials to obtain drug approval, the norm has been to compare some dose of a new drug with an established therapy or placebo. Standard trial analysis views each trial arm as qualitatively different, but it may be credible to assume that efficacy and adverse effects weakly increase with dosage. Optimization of patient care requires joint attention to both, as well as to treatment cost. This article develops a methodology to use limited trial evidence to choose dosage when efficacy and adverse effects weakly increase with dose. I suppose that dosage is an integer t ∊ (0,1,..., T ), T being a specified maximum dose. I study dosage choice when trial evidence on outcomes is available for only K dose levels, where K <
T + 1. Then the population distribution of dose response is partially identified. I show that the identification region is a convex polygon. I characterize clinical and population decision-making using the minimax regret criterion. A simple analytical solution exists when T = 2. Computation is tractable when T is larger.