Constructing confidence intervals for cost-effectiveness ratios: an evaluation of parametric and non-parametric techniques using Monte Carlo simulation.

The statistic of interest in most health economic evaluations is the incremental cost-effectiveness ratio. Since the variance of a ratio estimator is intractable, the health economics literature has suggested a number of alternative approaches to estimating confidence intervals for the cost-effectiveness ratio. In this paper, Monte Carlo simulation techniques are employed to address the question of which of the proposed methods is most appropriate. By repeatedly sampling from a known distribution and applying the different methods of confidence interval estimation, it is possible to calculate the coverage properties of each method to see if these correspond to the chosen confidence level. As the results of a single Monte Carlo experiment would be valid only for that particular set of circumstances, a series of experiments was conducted in order to examine the performance of the different methods under a variety of conditions relating to the sample size, the coefficient of variation of the numerator and denominator of the ratio, and the covariance between costs and effects in the underlying data. Response surface analysis was used to analyse the results and substantial differences between the different methods of confidence interval estimation were identified. The methods, both parametric and non-parametric, which assume a normal sampling distribution performed poorly, as did the approach based on simply combining the separate intervals on costs and effects. The choice of method for confidence interval estimation can lead to large differences in the estimated confidence limits for cost-effectiveness ratios. The importance of such differences is an empirical question and will depend to a large extent on the role of hypothesis testing in economic appraisal. However, where it is suspected that the sampling distribution is skewed, normal approximation methods produce particularly poor results and should be avoided.