The precision of regression-type estimator for incremental cost-effectiveness ratio

The estimation of incremental cost-effectiveness ratio (ICER) has received increasing attention recently. It is expressed in terms of the ratio of the change in costs of a therapeutic intervention to the change in the effects of the intervention. Despite the intuitive interpretation of ICER as an additional cost per additional benefit unit, it is a challenge to estimate the distribution of a ratio of two stochastically dependent distributions. A vast literature regarding the statistical methods of ICER has developed in the past two decades, but none of these methods provide an unbiased estimator. Here, to obtain the unbiased estimator of the cost-effectiveness ratio (CER), the zero intercept of the bivariate normal regression is assumed. In equal sample sizes, the Iman-Conover algorithm is applied to construct the desired variance-covariance matrix of two random bivariate samples, and the estimation then follows the same approach as CER to obtain the unbiased estimator of ICER. The bootstrapping method with the Iman-Conover algorithm is employed for unequal sample sizes. Simulation experiments are conducted to evaluate the proposed method. The regression-type estimator performs overwhelmingly better than the sample mean estimator in terms of mean squared error in all cases.