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In medical treatment and elsewhere, it has become standard to base treatmentintensity (dosage) on evidence in randomized trials. Yet it has been rare tostudy how outcomes vary with dosage. In trials to obtain drug approval, thenorm has been to specify some dose of a new drug and compare it with anestablished therapy or placebo. Design-based trial analysis views each trialarm as qualitatively different, but it may be highly credible to assume thatefficacy and adverse effects (AEs) weakly increase with dosage. Optimization ofpatient care requires joint attention to both, as well as to treatment cost.This paper develops methodology to credibly use limited trial evidence tochoose dosage when efficacy and AEs weakly increase with dose. I suppose thatdosage is an integer choice t in (0, 1, . . . , T), T being a specified maximumdose. I study dosage choice when trial evidence on outcomes is available foronly K dose levels, where K < T + 1. Then the population distribution of doseresponse is partially rather than point identified. The identification regionis a convex polygon determined by linear equalities and inequalities. Icharacterize clinical and public-health decision making using theminimax-regret criterion. A simple analytical solution exists when T = 2 andcomputation is tractable when T is larger.

Using Limited Trial Evidence to Credibly Choose Treatment Dosage when Efficacy and Adverse Effects Weakly Increase with Dose