### Abstract

In this paper, we consider the problem of interval estimation for the mean of diagnostic test charges. Diagnostic test charge data may contain zero values, and the nonzero values can often be modeled by a log-normal distribution. Under such a model, we propose three different interval estimation procedures: A percentile-t bootstrap interval based on sufficient statistics and two likelihood-based confidence intervals. For theoretical properties, we show that the two likelihood-based one-sided confidence intervals are only first-order accurate and that the bootstrap-based one-sided confidence interval is second-order accurate. For two-sided confidence intervals, all three proposed methods are second-order accurate. A simulation study in finite-sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator (MVUE)-based interval except for the case of one-sided lower end-point intervals when the skewness is very small. Among the proposed one-sided intervals, the bootstrap interval has the best coverage accuracy. For the two-sided intervals, when the sample size is small, the bootstrap method still yields the best coverage accuracy unless the skewness is very small, in which case the bias-corrected ML method has the best accuracy. When the sample size is large, all three proposed intervals have similar coverage accuracy. Finally, we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression.

Original language | English |
---|---|

Pages (from-to) | 1118-1125 |

Number of pages | 8 |

Journal | Biometrics |

Volume | 56 |

Issue number | 4 |

State | Published - 2000 |

### Fingerprint

### Keywords

- Bootstrap method
- Confidence intervals
- Cost data
- Depression
- Log normal
- Skewed distribution
- Zero charges

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Public Health, Environmental and Occupational Health
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
- Statistics and Probability

### Cite this

*Biometrics*,

*56*(4), 1118-1125.

**Confidence intervals for the mean of diagnostic test charge data containing zeros.** / Zhou, Xiao Hua; Tu, Wanzhu.

Research output: Contribution to journal › Article

*Biometrics*, vol. 56, no. 4, pp. 1118-1125.

}

TY - JOUR

T1 - Confidence intervals for the mean of diagnostic test charge data containing zeros

AU - Zhou, Xiao Hua

AU - Tu, Wanzhu

PY - 2000

Y1 - 2000

N2 - In this paper, we consider the problem of interval estimation for the mean of diagnostic test charges. Diagnostic test charge data may contain zero values, and the nonzero values can often be modeled by a log-normal distribution. Under such a model, we propose three different interval estimation procedures: A percentile-t bootstrap interval based on sufficient statistics and two likelihood-based confidence intervals. For theoretical properties, we show that the two likelihood-based one-sided confidence intervals are only first-order accurate and that the bootstrap-based one-sided confidence interval is second-order accurate. For two-sided confidence intervals, all three proposed methods are second-order accurate. A simulation study in finite-sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator (MVUE)-based interval except for the case of one-sided lower end-point intervals when the skewness is very small. Among the proposed one-sided intervals, the bootstrap interval has the best coverage accuracy. For the two-sided intervals, when the sample size is small, the bootstrap method still yields the best coverage accuracy unless the skewness is very small, in which case the bias-corrected ML method has the best accuracy. When the sample size is large, all three proposed intervals have similar coverage accuracy. Finally, we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression.

AB - In this paper, we consider the problem of interval estimation for the mean of diagnostic test charges. Diagnostic test charge data may contain zero values, and the nonzero values can often be modeled by a log-normal distribution. Under such a model, we propose three different interval estimation procedures: A percentile-t bootstrap interval based on sufficient statistics and two likelihood-based confidence intervals. For theoretical properties, we show that the two likelihood-based one-sided confidence intervals are only first-order accurate and that the bootstrap-based one-sided confidence interval is second-order accurate. For two-sided confidence intervals, all three proposed methods are second-order accurate. A simulation study in finite-sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator (MVUE)-based interval except for the case of one-sided lower end-point intervals when the skewness is very small. Among the proposed one-sided intervals, the bootstrap interval has the best coverage accuracy. For the two-sided intervals, when the sample size is small, the bootstrap method still yields the best coverage accuracy unless the skewness is very small, in which case the bias-corrected ML method has the best accuracy. When the sample size is large, all three proposed intervals have similar coverage accuracy. Finally, we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression.

KW - Bootstrap method

KW - Confidence intervals

KW - Cost data

KW - Depression

KW - Log normal

KW - Skewed distribution

KW - Zero charges

UR - http://www.scopus.com/inward/record.url?scp=0033636936&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033636936&partnerID=8YFLogxK

M3 - Article

C2 - 11129469

AN - SCOPUS:0033636936

VL - 56

SP - 1118

EP - 1125

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 4

ER -