Power and sample size assessments for tests of hypotheses on cost-effectiveness ratios

We address the issue of statistical power and sample size for cost-effectiv eness studies. Tests of hypotheses on the cost-effectiveness ratio (CER) ar e constructed from the net cost and incremental effectiveness measures. Whe n the difference in effectiveness is known, we derive formulae for statisti cal power and sample size assessments for one- and two-sided tests of hypot heses of the CER. We also construct a test of the joint hypothesis of cost- effectiveness and effectiveness and derive an expression connecting power a nd sample size. Our methods account for the correlation between cost and ef fectiveness and lead to smaller sample size requirements than comparative m ethods that ignore the correlation. The implications of our formulae for co st-effectiveness studies are illustrated through numerical examples. When c ompared with trials designed to demonstrate effectiveness alone, our result s indicate that a trial appropriately powered to demonstrate cost-effective ness might require sample sizes many times greater. Copyright (C) 2000 John Wiley & Sons, Ltd.