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

Abstract

We address the issue of statistical power and sample size for cost-effectiveness studies. Tests of hypotheses on the cost-effectiveness ratio (CER) are constructed from the net cost and incremental effectiveness measures. When the difference in effectiveness is known, we derive formulae for statistical power and sample size assessments for one- and two-sided tests of hypotheses of the CER. We also construct a test of the joint hypothesis of cost-effectiveness and effectiveness and derive an expression connecting power and sample size. Our methods account for the correlation between cost and effectiveness and lead to smaller sample size requirements than comparative methods that ignore the correlation. The implications of our formulae for cost-effectiveness studies are illustrated through numerical examples. When compared with trials designed to demonstrate effectiveness alone, our results indicate that a trial appropriately powered to demonstrate cost-effectiveness might require sample sizes many times greater.

No economic benefit of early knee reconstruction over optional delayed reconstruction for ACL tears: registry enriched randomised controlled trial data

“…Finally, the sample size of the KANON-trial was determined by differences in clinical outcomes of the two treatment strategies at two years. Sample sizes required for cost-effectiveness analysis are generally larger than those for clinical evaluation,22 23 and the wide CIs in our study imply that our findings should be interpreted with some caution.…”

Sample Size Determination for Cost-Effectiveness Trials

“…However, the analyst faced with a pre-determined sample size can use the above methods to assess its appropriateness from a cost-effectiveness perspective. For example, if the pre-determined sample size is 300 patients per arm for the CADET-Hp trial, then figure 3b provides the ellipsoid on the costeffectiveness plane containing those combinations of D e and D c for which the power is inadequate using the methods of Willan and O'Brien, [19] while, for combinations of D e and D c between the vertical lines, the power will be inadequate using the methods of Gardiner et al [20] Rearranging equation 9 to read b A ¼ ðz 1 À þ z 1 À Þ þ ffiffi ffi n p allows the analyst to determine for a given sample size the SCID for which there is adequate power. For the Bayesian approach, assuming accrual equals incidence and a follow-up time of zero, a sample size of 300 per arm would provide an expected net gain of $Can1 350 676, representing a 5.54% reduction from the optimum provided by a sample size of 511.…”

Cost–utility analysis conducted alongside randomized controlled trials: Are economic end points considered in sample size calculations and does it matter?

“…We believe that this is unlikely, but future research could explore this by examining protocols available in the trial registries. The elements required for a simple economic sample size calculation, frequentist or Bayesian, comprise the expected variances of and correlations between the costs and effects of both interventions, the societal willingness to pay for a QALY [6,7]. One barrier to the incorporation of economic data in trial design is the lack of information on the variance and correlations of cost and QALYs.…”