Parameter solicitation for planning cost effectiveness studies with dichotomous outcomes

When economic endpoints are included alongside clinical effectiveness measures in randomized clinical trials (RCT), they are summarized together by the incremental cost effectiveness ratio (ICER). Adding economic endpoints to an RCT complicates the planning of experiments because investigators must now solicit their beliefs about costs, but even more challenging, they must also specify their association with effectiveness. Solicitation of correlations between costs and effects can be unintuitive, and so potentially highly inaccurate. This is unfortunate because power is highly sensitive to the association between costs and effects. Mis-specification in this association may lead to substantially underpowered or overpowered studies. We show that when clinical effectiveness measures are dichotomous, specification of the correlation between costs and effects can be avoided by instead describing their association with a mixture model. This representation leads to simple and highly intuitive parameter specifications. It may also be used to generate realistic raw data that can be used to evaluate experiment power with simulation. We give particular attention to evaluating and interpreting power when Fieller's theorem method (FTM) is used to calculate confidence for, and test hypotheses about, the ICER. Data from a previously published clinical trial are used to demonstrate the use of this new method to calculate sample size for a cost effectiveness study.