||In this paper, we consider testing the non-inferiority of two medical|
diagnostic methods in a case-control study where each subject receiving the two
different diagnostics produces correlated paired measurements. Note that it
occurs often in practice that the marginal distributions of the measurements are
right-skewed. Therefore, we first apply the power transformation to the
paired data so that they would behave like the bivariate normal data. One
parametric non-inferiority test is then implemented based on the transformed
data. On the other hand, we suggest and employ appropriate copula function
which links two generalized gamma distributions to describe the joint
distribution of the paired measurements. Under the joint distribution, an
approximate test based on the difference between the partial areas under the two
estimated Receiver Operating Characteristic (ROC) curves is then constructed.
In this paper, we would like to test if the difference between the true areas is
within an allowable region. The results of a simulation investigation of the
level and power performances of the approximate test for different degrees of
correlation in several possible copula functions with a variety of marginal
distributions are reported. Finally, a real data set is illustrated by using the
||1. Li, C.R., Liao, C.T. and Liu, J.P.(2006) A non-inferiority test for diagnostic accuracy based on the paired partial areas under ROC curves. Computational Statistics & Data Analysis. 50: 1855 – 1876.|
2. Box, G.E.P. and Cox, D.R. (1964) An analysis of transformations. Journal of the Royal Statistical Society, Series B. 26:211-252.
3. Cox, C., Chu, H., Schneider, M.F. and Munoz, A .(2007)Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in Medicine. 26:4352-4374.
4. DeLong, E., DeLong, D. and Clarke-Pearson, D.(1988) Comparing the areas under two or more correlated receiver operation characteristic curves: a non-parametric approach. Biometrics.44:837-845.
5. Faraggi, D. and Reiser, B.(2002) Estimation of the area under the ROC curve. Statistics in Medicine. 21:3093-3106.
6. Greiner, M., Pfeiffer, D. and Smith, R.(2005) The partial area under the summary ROC curve. Statistics in Medicine. 24: 2025–2040.
7. Liu, J.P., Ma, M.C., Wu, C.Y. and Tai, J.Y.(2006) Tests of equivalence and non-inferiority for diagnostic accuracy based on the paired areas under ROC curves. Statistics in Medicine. 25:1219-1238.
8. Molodianovitch, K., Faraggi, D. and Reiser, B. (2006) Comparing the areas under two correlated ROC curves: parametric and non-parametric approaches. Biometrical Journal. 48: 745–757
9. Nelsen, R.B.( 2006) An Introduction to Copulas. Second Edition. Springer: New York.
10. Stacy, E.(1962) A generalization of the gamma distribution. Annals of Mathematical Statistics. 33:1187-1192.
11. McClish, D.K.(1989) Analyzing a portion of the ROC curve. Medical Decision Making.9:190–195.
12. Wieand, S., Gail, M.H., James, B.R. and James, K.L.(1989) A family of non-parametric statistics for comparing diagnostic markers with paired or unpaired data. Biometrika. 76:585-592.
13. Zhou, X.H., Obuchowski, N.A., and McClish, D.K.(2002) Statistical Methods in Diagnostic Medicine. Wiley: New York.
14. Pepe, M.S.(2003) The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press:New York.
15. 陳秀琴 (2011). 針對右偏分布資料進行兩個醫學診斷方法之相等性檢定。國立中央大學統計研究所碩士論文。
16. 李念純 (2011). 一維及二維右設限存活資料的適合度檢定。國立中央大學統計研究所碩士論文。