### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 1703-1720 |

Number of pages | 18 |

Journal | Statistics in Medicine |

Volume | 20 |

Issue number | 11 |

DOIs | |

State | Published - Jun 15 2001 |

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### ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability

### Cite this

*Statistics in Medicine*,

*20*(11), 1703-1720. https://doi.org/10.1002/sim.780

**Methods for testing equality of means of health care costs in a paired design study.** / Zhou, Xiao Hua; Li, Chunming; Gao, Sujuan; Tierney, William M.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 20, no. 11, pp. 1703-1720. https://doi.org/10.1002/sim.780

}

TY - JOUR

T1 - Methods for testing equality of means of health care costs in a paired design study

AU - Zhou, Xiao Hua

AU - Li, Chunming

AU - Gao, Sujuan

AU - Tierney, William M.

PY - 2001/6/15

Y1 - 2001/6/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035876156&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035876156&partnerID=8YFLogxK

U2 - 10.1002/sim.780

DO - 10.1002/sim.780

M3 - Article

C2 - 11391697

AN - SCOPUS:0035876156

VL - 20

SP - 1703

EP - 1720

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 11

ER -