A Wald test comparing medical costs based on log-normal distributions with zero valued costs

Abstract

Medical cost data often exhibit strong skewness and sometimes contain large proportions of zero values. Such characteristics prevent the analysis of variance (ANOVA) F-test and other frequently used standard tests from providing the correct inferences when the comparison of means is of interest. One solution to the problem is to introduce a parametric structure based on log-normal distributions with zero values and then construct a likelihood ratio test. While such a likelihood ratio test possesses excellent type I error control and power, its implementation requires a rather complicated iterative optimization program. In this paper, we propose a Wald test with simple computation. We then conduct a Monte Carlo simulation to compare the type I error rates and powers of the proposed Wald test with those of the likelihood ratio test. Our simulation study indicates that although the likelihood ratio test slightly outperforms the Wald test, the performance of the Wald test is also satisfactory, especially when the sample sizes are reasonably large. Finally, we illustrate the use of the proposed Wald test by analysing a clinical study assessing the effects of a computerized prospective drug utilization intervention on in-patient charges.