Maximally selected Chi-squared statistics and non-monotonic associations: An exact approach based on two cutpoints

Computational Statistics and Data Analysis

Volumn 51, Issue 12, 2007, Pages 6295-6306

  Boulesteix, Anne Laure ^a   Strobl, Carolin ^b  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

Adjustment; Contingency table; Multiple testing; Ordinal; Umbrella ordering

Indexed keywords

COMBINATORIAL MATHEMATICS; DATA REDUCTION; OPTIMAL CONTROL SYSTEMS; PROBABILITY DISTRIBUTIONS;

ADJUSTMENT; CONTINGENCY TABLE; MULTIPLE TESTING; UMBRELLA ORDERING;

STATISTICAL METHODS;

EID: 34547152822     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.01.017     Document Type: Article

References (24)

1. Banz K., Wagenpfeil S., Neiss A., Goertz A., Staginnus U., Vollmar J., and Wutzler P. The cost-effectiveness of routine childhood varicella vaccination in Germany. Vaccine 21 (2003) 1256-1267
2. Boulesteix A.L. Maximally selected chi-square statistics and binary splits of nominal variables. Biometrical J. 48 (2006) 838-848
3. Boulesteix A.L. Maximally selected chi-square statistics for ordinal variables. Biometrical J. 48 (2006) 451-462
4. Breiman L., Friedman J.H., Olshen R.A., and Stone J.C. Classification and Regression Trees (1984), Wadsworth, Monterey, CA
5. Halpern A.L. Multiple-changepoint testing for an alternating segments model of a binary sequence. Biometrics 56 (2000) 903-908
6. Halpern J. Maximally selected chi square statistics for small samples. Biometrics 38 (1982) 1017-1023
7. Hans C., and Dunson D.B. Bayesian inferences on umbrella orderings. Biometrics 61 (2005) 1018-1026
8. Holländer N., Sauerbrei W., and Schumacher M. Confidence intervals for the effect of a prognostic factor after selection of an 'optimal' cutpoint. Statist. Medicine 23 (2004) 1701-1713
9. Hothorn T., and Lausen B. On the exact distribution of maximally selected rank statistics. Comput. Statist. Data Anal. 43 (2003) 121-137
10. Koziol J.A. On maximally selected chi-square statistics. Biometrics 47 (1991) 1557-1561
11. Kuiper N. Tests concerning random points on a circle. Proc. Konink Nederl Akad. Wetensch. A 63 (1960) 38-47
12. Lausen B., and Schumacher M. Maximally selected rank statistics. Biometrics 48 (1992) 73-85
13. Lausen B., and Schumacher M. Evaluating the effect of optimized cutoff values in the assessment of prognostic factors. Comput. Statist. Data Anal. 21 (1996) 307-326
14. Lausen B., Lerche R., and Schumacher M. Maximally selected rank statistics for dose-response problems. Biometrical J. 44 (2002) 131-147
15. Lausen B., Hothorn T., Bretz F., and Schumacher M. Assessment of optimal selected prognostic factors. Biometrical J. 46 (2004) 364-374
16. Loh W., and Shih Y. Split selection methods for classification trees. Statist. Sinica 7 (1997) 815-840
17. Miller R., and Siegmund D. Maximally selected chi square statistics. Biometrics 38 (1982) 1011-1016
18. Robertson T., Wright F., and Dykstra R. Order restricted statistical inference (1988), Wiley, New York
19. Royston P., Altman D.G., and Sauerbrei W. Dichotomizing continuous predictors in multiple regression: a bad idea. Statist. Medicine 25 (2006) 127-141
20. Salanti G., and Ulm K. Tests for trend in binary response. Biometrical J. 45 (2003) 277-291
21. Shih Y.S. A note on split selection bias in classification trees. Comput. Statist. Data Anal. 45 (2004) 457-466
22. Siegmund D. Boundary crossing probabilities and statistical applications. Ann. Statist. 14 (1986) 361-404
23. Strobl, C., Boulesteix, A.L., Augustin, T., 2007. Unbiased split selection for classification trees based on the Gini Index. Comput. Statist. Data Anal., in press, doi:10.1016/j.csda.2006.12.030.
24. Wagenpfeil S., Neiss A., Banz K., and Wutzler P. Empirical data on the varicella situation in Germany for vaccination decisions. Clinical Microbiology and Infection 10 (2004) 425-430