Testing Whether Treatment is “better” than control with Ordered Categorical Data: Definitions and Complete Class Theorems

Statistics and Risk Modeling

Volumn 18, Issue 1, 2000, Pages 1-26

  Cohen, Arthur ^a   Sackrowitz, Harold B ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

concordance monotonicity; Contingency tables; continuation odds ratio order; hazard rate order; likelihood ratio order; positive quadrant dependence; stochastic order; Wilcoxon Mann Whitney test

Indexed keywords

EID: 85025267151     PISSN: 21931402     EISSN: 21967040     Source Type: Journal    
DOI: 10.1524/strm.2000.18.1.1     Document Type: Article

References (37)

1. Agresti, A. and Coull, B.A. (1998). Order restricted inference using odds ratios for monotone trend alternatives in contingency tables. Computational Statistics and Data Analysis 28, 139-155.
2. Agresti, A., Mehta, C.R. and Patel, N.R. (1990). Exact inference for contingency tables with ordered categories. Journal of the American Statistical Association 85, 453-458.
3. Berger, V. (1998). Admissibility of exact conditional tests of stochastic order. Journal of Statistical Planning and Inference 66, 39-50.
4. Berger, V., Permutt, T., and Ivanova, A. (1998). Convex hull tests for ordered categorical data. Biometrics, 1541-1550.
5. Berger, V., and Sackrowitz, H.B. (1997). Improving tests of stochastic order. Journal of the American Statistical Association 92.
6. Bhattacharya, B., and Dykstra, R.L. (1994). Statistical inference for stochastic ordering. Stochastic Orders and Their Applications, M. Shaked and J. George Shantikumar, Academic Press, New York, Chapter 8, pages 221-249.
7. Cohen, A., and Sackrowitz, H.B. (1991). Tests for independence in contingency tables with ordered categories. Journal of Multivariate Analysis 36, 56-67.
8. Cohen, A., and Sackrowitz, H.B. (1992). An evaluation of some tests of trend in contingency tables. Journal of the American Statistical Association 87, 470-475.
9. Cohen, A., and Sackrowitz, H.B. (1998). Directional tests for one-sided alternatives in multivariate models. Annals of Statistics 26, 2321-2338.
10. Cohen, A., and Sackrowitz, H.B. (1999). Properties of likelihood inference for order restricted models. Journal of Multivariate Analysis, (to appear).
11. Cohen, A., Sackrowitz, H.B., and Sackrowitz, M. (1999). Testing whether treatment is “better” than control with ordered categorical data: An evaluation of new methodology. Submitted.
12. Douglas, R., Fienberg, S.E., Lee, M.-L.T., Sampson, A.R., and Whitaker, L.R. (1991). Positive dependence concepts for ordinal contingency tables. Topics in Statistical Dependence, H.W. Block, A.R. Sampson and T.H. Savits, Eds., IMS Lecture Notes-Monograph Series, 189-202.
13. Eaton, M.L. (1970). A complete class theorem for multidimensional one sided alternatives. Ann. Math. Statist. 41, 1884-1888.
14. Emerson, J.D., and Moses, L.E. (1985). A note on the Wilcoxon-Mann-Whitney test for 2 x k ordered tables. Biometrics 41, 303-309.
15. Goodman, L.A., and Kruskal, W.H. (1954). Measures of associations for cross classifications. Journal of the American Statistical Association 49, 732-764.
16. Graubard, B.I. and Korn, E.I. (1987). Choice of column scores for testing independence in ordered 2 × K contingency tables. Biometrics 43, 471-476.
17. Grove, D.M. (1980). A test of independence against a class of ordered alternatives in a 2 × C contingency table. Journal of the American Statistical Association 75, 454-459.
18. Grove, D.M. (1984). Positive association in a two way contingency table: Likelihood ratio tests. Communications in Statistics, Part A, Theory and Methods 13 931-945.
19. Hilton, J.F., and Mehta, C.R. (1993). Power and sample size calculations for exact conditional tests with ordered categorical data. Biometrics 49, 609-616.
20. Hirotsu, C. (1982). Use of cumulant efficient scores for testing ordered alternatives in discrete models. Biometrika 69, 567-577.
21. Ledwina, T. (1978). Admissible tests for exponential families with finite support. Mathematische Operationsforschung und Statist., Ser. Statistics 9, 105-118.
22. Ledwina, T. (1984). A note of admissibility of some tests of independence against “positive dependence” in R × C contingency tables. Mathematische Operationsforschung und Statist., Ser. Statistics 4, 565-570.
23. Lehmann, E.L. (1966). Some concepts of dependence. Ann. Math. Statist. 37, 11371153.
24. Lehmann, E.L. (1966). Testing Statistical Hypotheses, Wiley, New York.
25. Matthes, T.K., and Truax, D.R. (1967). Tests of composite hypotheses for multivariate exponential family. Ann. Math. Statist. 38, 681-697.
26. McCullagh, P. (1980). Regression models for ordinal data. J. R. Statist. Soc. B 42, 109-142.
27. Mehta, C.R., Patel, N.R., and Tsiatis, A.A. (1984). Exact significance testing to establish treatment equivalence with ordered categorical data. Biometrics 40, 819825.
28. Moses, L.E., Emerson, J.D., and Hosseini, H. (1984). Analyzing data for ordered categories. New England Journal of Medicine 311, 442-448.
29. Nguyen, T.T., and Sampson, A.R. (1987). Testing for positive quadrant dependence in ordinal contingency tables. Naval Research Logistics 34, 859-877.
30. Oluyede, B.O. (1994). Test of independence against a class of ordered alternatives in an R × C contingency table. Biom. J. 36, 935-951.
31. Patefield, W.M. (1982). Exact tests for trends for ordered contingency tables. Appl. Statist. 31, 32-43.
32. Rahlfs, V.W., and Zimmerman, H. (1993). Scores: Ordinal data with few categories - how they should be analyzed. Drug Information Journal 27, 1227-1240.
33. Rao, M.B., Krishnaiah, P.R., and Subramanyam, K. (1987). A structure theorem on bivariate quadrant dependent distributions and tests for independence in two-way
34. contingency tables. Journal of Multivariate Analysis 23, 93-118.
35. Shaked, M. and Shanthikumar, J.G. (1994). Stochastic Orders and Their Applications, Academic Press, San Diego.
36. Stein, C. (1956). The admissibility of Hotelling's T2-test. Ann. Math. Statist. 27, 616-623.
37. Subramanyan, K., and Rao, M.B. (1988). Analysis of odds ratios in 2 × n ordinal contingency tables. Journal of Multivariate Analysis 27, 478-493.