Probabilistic measures of cost‐effectiveness

Abstract

Several probability-based measures are introduced in order to assess the cost-effectiveness of a treatment. The basic measure consists of the probability that one treatment is less costly and more effective compared with another. Several variants of this measure are suggested as flexible options for cost-effectiveness analysis. The proposed measures are invariant under monotone transformations of the cost and effectiveness measures. Interval estimation of the proposed measures are investigated under a parametric model, assuming bivariate normality, and also non-parametrically. The delta method and a generalized pivotal quantity approach are both investigated under the bivariate normal model. A non-parametric U-statistics-based approach is also investigated for computing confidence intervals. Numerical results show that under bivariate normality, the solution based on generalized pivotal quantities exhibits accurate performance in terms of maintaining the coverage probability of the confidence interval. The non-parametric U-statistics-based solution is accurate for sample sizes that are at least moderately large. The results are illustrated using data from a clinical trial for prostate cancer therapy. Copyright © 2016 John Wiley & Sons, Ltd.

Cost‐effectiveness analysis under multiple effectiveness outcomes: A probabilistic approach

“…Since it may be unrealistic to demand that a new treatment be less costly and more effective than a standard treatment, the CEP metric introduced in Bebu et al 7 can be adapted to include appropriate thresholds 𝛿 C and 𝛿 E for the cost and the effectiveness, respectively:…”

“…The present paper develops cost‐effectiveness metrics that simultaneously utilize multiple effectiveness outcomes. The metrics proposed extend the cost‐effectiveness probability (CEP) metric in Bebu et al 7 to multiple effectiveness measures. The CEP is defined as the probability that a new treatment is less costly and more effective compared to a standard treatment.…”

“…Statistical inference based on the new CEP criteria can be performed in a parametric framework or in a non‐parametric framework, as done in Bebu et al 7 The parametric framework assumes a multivariate normal model for the log‐transformed cost and the effectiveness outcomes. Under this set up, lower confidence limits for the CEP criteria are constructed utilizing a percentile bootstrap approach.…”

“…In the context of a single effectiveness measure, the cost‐effectiveness proportion (CEP) metric is introduced in Bebu et al 7 Consider a randomized clinical trial with two arms, and let $$$ \left({C}_1,{E}_1\right) $$$ and $$$ \left({C}_2,{E}_2\right) $$$ denote the cost and effectiveness for the two treatments, with larger effectiveness indicating better health. Throughout this work the new treatment is denoted by $$$ i=1 $$$ and the standard treatment by $$$ i=2 $$$.…”

“…The CEP is defined as the probability that the new treatment is less costly and more effective than the standard treatment, $$$$ CEP=P\left({C}_1\le {C}_2,{E}_1\ge {E}_2\right). $$$$ Since it may be unrealistic to demand that a new treatment be less costly and more effective than a standard treatment, the CEP metric introduced in Bebu et al 7 can be adapted to include appropriate thresholds $$$ {\delta}_C $$$ and $$$ {\delta}_E $$$ for the cost and the effectiveness, respectively: $$$$ CEP\left({\delta}_C,{\delta}_E\right)=P\left({C}_1\le {C}_2+{\delta}_C,\kern0.3em {E}_1\ge {E}_2+{\delta}_E\right). $$$$ The metric $$$ CEP\left({\delta}_C,{\delta}_E\right) $$$ is the probability that the new treatment is at most $$$ {\delta}_C $$$ more costly than the standard treatment and it is at least $$$ {\delta}_E $$$ more effective than the standard treatment.…”