Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Quantile-based Nonparametric Test for Comparing Two Diagnostic Tests

  • Kim, Young-Min (Department of Biostatistics, The Catholic University of Korea) ;
  • Song, Hae-Hiang (Department of Biostatistics, The Catholic University of Korea)
  • Published : 2007.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Diagnostic test results, which are approximately normal with a few number of outliers, but non-normal probability distribution, are frequently observed in practice. In the evaluation of two diagnostic tests, Greenhouse and Mantel (1950) proposed a parametric test under the assumption of normality but this test is inappropriate for the above non-normal case. In this paper, we propose a computationally simple nonparametric test that is based on quantile estimators of mean and standard deviation, instead of the moment-based mean and standard deviation as in some parametric tests. Parametric and nonparametric tests are compared with simulations under the assumption of, respectively, normality and non-normality, and under various combinations of the probability distributions for the normal and diseased groups.

Keywords

References

  1. Beam, C. A. and Wieand, H. S. (1991). A statistical method for the comparison of a discrete diagnostic test with several continuous diagnostic tests. Biometrics, 47, 907-919 https://doi.org/10.2307/2532648
  2. Bennett, B. M. (1972). On comparisons of sensitivity, specificity and predictive value of a number of diagnostic procedures. Biometrics, 28, 793-800 https://doi.org/10.2307/2528763
  3. Benson, F. (1949). A note on the estimation of mean and standard deviation from quantiles. Journal of the Royal Statistical Society, Ser. B, 11, 91-100
  4. Brown, B. M.(1981). Symmetric quantile averages and related estimators. Biometrika, 68, 235-242 https://doi.org/10.1093/biomet/68.1.235
  5. Cramer, H. (1946). Mathematical Methods of Statistics. Princeton: Princeton University Press
  6. Greenhouse, S. W. and Mantel, N. (1950). The evaluation of diagnostic tests. Biometrics, 6, 399-412 https://doi.org/10.2307/3001784
  7. Kendall, M. G. (1969). The Advanced Theory of Statistics. 3ed, Charles Griffin & Co, London
  8. Obuchowski, N. A., Beiden S. V., Berbaum K. S., Hillis S. L., Ishwaran H., Song H. H. and Wagner R. F. (2004). Multireader, multicase receiver operating characteristic analysis: an empirical comparison of five methodsl. Academic Radiology, 11, 980-995
  9. Pearson, K. (1920). On the probable errors of frequency constants. Biometrika, 13, 113-132
  10. Powell, K. A., Obuchowski, N. A., Chilcote, W. A., Barry, M. M., Ganobcik, S. N. and Cardenosa, G. (1999). Film-screen versus digitized mammography: assessment of clinical equivalence. American Journal of Roentgenology, 173, 889-894 https://doi.org/10.2214/ajr.173.4.10511142
  11. Wieand, S., Gail, M. H., James, B. R. and James, K. L. (1989). A family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data. Biometrika, 76, 585-592 https://doi.org/10.1093/biomet/76.3.585
  12. Zaykin, D. V., Zhivotovsky, L. A., Westfall, P. H. and Weir, B. S. (2002). Truncated product method for combining p-values. Genetic Epidemiology, 22, 170-185 https://doi.org/10.1002/gepi.0042