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Methods for testing equality of means of health care costs in a paired design study
Author(s) -
Zhou XiaoHua,
Li Chunming,
Gao Sujuan,
Tierney William M.
Publication year - 2001
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.780
Subject(s) - statistics , nominal level , wilcoxon signed rank test , type i and type ii errors , parametric statistics , mathematics , score test , test statistic , likelihood ratio test , statistic , percentile , nonparametric statistics , bivariate analysis , sample size determination , skewness , statistical hypothesis testing , ratio test , confidence interval , mann–whitney u test
In this paper we propose five new tests for the equality of paired means of health care costs. The first two tests are the parametric tests, a Z ‐score test and a likelihood ratio test, both derived under the bivariate normality assumption for the log‐transformed costs. The third test ( Z ‐score with jack‐knife) is a semi‐parametric Z ‐score method, which only requires marginal log‐normal assumptions. The last two tests are the non‐parametric bootstrap tests: one is based on a t ‐test statistic, and the other is based on Johnson's modified t ‐test statistic. We conduct a simulation study to compare the performance of these tests, along with some commonly used tests when the sample size is small to moderate. The simulation results demonstrate that the commonly used paired t ‐test on the log‐scale and the Wilcoxon signed rank for differences of the two original scales can yield type I error rates larger than the preset nominal levels. The commonly used paired t ‐test on the original data performs well with slightly skewed data, but can yield inaccurate results when two populations have different skewness. The likelihood ratio test, the parametric and semi‐parametric Z ‐score tests all have very good type I error control with the likelihood ratio test being the best. However, the semi‐parametric Z ‐score test requires less distributional assumptions than the two parametric tests. The percentile‐ t bootstrap test and bootstrapped Johnson's modified t ‐test have better type I error control than the paired t ‐test on the original‐scale and Johnson's modified t ‐test, respectively. Combining with the propensity‐score method, we can also apply the proposed methods to test the mean equality of two cost outcomes in the presence of confounders. Our two applications are from health services research. In the first one, we want to know the effect of Medicaid reimbursement policy change on outpatient health care costs. The second one is to evaluate the effect of a hospitalist programme on health care costs in an observational study, and the imbalanced covariates between intervention and control patients are taken into account using a propensity score approach. Copyright © 2001 John Wiley & Sons, Ltd.