A new approach for sample size calculation in cost-effectiveness studies based on value of information

Abstract

Background: Value of information is now recognized as a reference method in the decision process underpinning cost-effectiveness evaluation. The expected value of perfect information (EVPI) is the expected value from completely reducing the uncertainty surrounding the cost-effectiveness of an innovative intervention. Among sample size calculation methods used in cost-effectiveness studies, only one is coherent with this decision framework. It uses a Bayesian approach and requires data of a pre-existing cost-effectiveness study to derive a valid prior EVPI. When evaluating the cost-effectiveness of innovations, no observed prior EVPI is usually available to calculate the sample size. We here propose a sample size calculation method for cost-effectiveness studies, that follows the value of information theory, and, being frequentist, can be based on assumptions if no observed prior EVPI is available.

Methods: The general principle of our method is to define the sampling distribution of the incremental net monetary benefit (ΔB), or the distribution of ΔB that would be observed in a planned cost-effectiveness study of size n. Based on this sampling distribution, the EVPI that would remain at the end of the trial (EVPI_n) is estimated. The optimal sample size of the planned cost-effectiveness study is the n for which the cost of including an additional participant becomes equal or higher than the value of the information gathered through this inclusion.

Results: Our method is illustrated through four examples. The first one is used to present the method in depth and describe how the sample size may vary according to the parameters' value. The three other examples are used to illustrate in different situations how the sample size may vary according to the ceiling cost-effectiveness ratio, and how it compares with a test statistic-based method. We developed an R package (EBASS) to run these calculations.

Conclusions: Our sample size calculation method follows the value of information theory that is now recommended for analyzing and interpreting cost-effectiveness data, and sets the size of a study that balances its cost and the value of its information.

Keywords: Clinical trials; Comparative studies; Cost-benefit analysis; Epidemiologic methods; Sample size; Value of information.

Fig. 1

Expected gain from including an additional participant in each group according to the sample size (n) (logarithmic scale)

Fig. 2

Influence of variation of parameters’ values on total sample size (n)

Fig. 3

Impact of variation of λ on sample size according to three ongoing cost-effectiveness studies described in Tables 2 and 3