Confidence intervals or surfaces? Uncertainty on the cost-effectiveness plane

Although cost-effectiveness analysis is not new, it is only recently that economic analysis has been conducted alongside clinical trials. Whereas in the past economic analysts most often used sensitivity analysis to examine the implications of uncertainty for their results, the existence of patient-level data on costs and effects opens up the possibility of statistical analysis of uncertainty. Unfortunately, ratio statistics can cause problems for standard statistical methods of confidence interval estimation. The recent health economics literature contains a number of suggestions for estimating confidence limits for ratios. In this paper, we begin by reviewing the different methods of confidence interval estimation with a view to providing guidance concerning the most appropriate method. We go on to argue that the focus on confidence interval estimation for cost-effectiveness ratios in the recent literature has been concerned more with problems of estimation than with problems of decision-making. We argue that decision-makers are most likely to be interested in one-sided tests of hypothesis and that confidence surfaces are better suited to such tests than confidence intervals. This approach is consistent with decision-making on the cost-effectiveness plane and with the cost-effectiveness acceptability curve approach to presenting uncertainty due to sampling variation in stochastic cost-effectiveness analyses.