Confidence intervals for cost‐effectiveness ratios: An application of Fieller's theorem

Application of cost‐effectiveness analysis (CEA) is growing rapidly in health care. Two general approaches to analysis are differentiated by the type of data available: (i) deterministic models based upon secondary analysis of retrospective data from one or more trials and other sources; and (ii) stochastic analyses in which the design of a randomized controlled trial is adapted to collect prospectively patient‐specific data on costs and effectiveness. An important methodological difference between these two approaches is in how uncertainty is handled. Deterministic CEA models typically rely upon sensitivity analysis to determine the robustness of findings to alternative assumptions, whereas stochastic (CEA) analysis, as part of prospective studies, permits the use of conventional statistical methods on the cost and effectiveness data for both inference (hypothesis testing) and estimation. This paper presents a procedure for the statistical analysis of cost‐effectiveness data, with specific application to those studies for which effectiveness is measured as a binary outcome. Specifically, Fieller's Theorem was used to calculate confidence intervals for ratios of the two random variables of between‐treatment differences in observed costs and effectiveness, i.e. the incremental cost‐effectiveness ratio. It is also shown how this approach can be used to determine sample size requirements for cost‐effectiveness studies.