OBJECTIVES

For reimbursement, economic evaluations such as healthcare costs are often as important as clinical outcomes. However, estimating the standard error (SE) of the difference in mean costs between two treatments using the zero-inflated Gamma distribution is currently limited to bootstrapping and the method of Mills (2013). We propose an exact, closed-form solution for estimating SE based on a parametric model, and compare the results to those of bootstrapping and Mills’ method.

METHODS

Data were generated using the gamma distribution with varied shape parameters (0.5, 1, 2, 5, 7.5, 10, 20) and a fixed scale parameter(1000) The proportion of zeroes for costs in each data set were also varied (0.5, 0.7, 0.9). Each simulation data set contained 10,000 observations. We calculated the SE’s of the mean difference in cost between two treatments, using three methods.

RESULTS : For small shape parameters ( 0.5, 1, 2), the SEs of all methods showed similar results across different proportions of zeroes (0.5, 0.7, 0.9), with the SEs from the Mills method being slightly larger than that of the bootstrap method (10000 repetitions) or our exact method. However, when the shape parameter was greater than 2, the SEs estimated by the Mills method were significantly larger than that of the other methods. Our proposed approach produced similar SEs compared to those of the bootstrap method across all different proportions of zeroes.

CONCLUSIONS

Our proposed method has a nice property: it is not only an exact method based on a parametric model, but also produces the similar SEs to the bootstrap method. The Bootstrap method is a consistent estimator, though it is not exact and computational costs are a consideration. One should use the Mills method with care, because the estimated SE may be significantly larger across a range of parameters.