Maximally selected chi-square statistics and umbrella orderings

Arbeitspapier

Binary outcomes that depend on an ordinal predictor in a nonmonotonic way are common in medical data analysis. Such patterns can be addressed in terms of cutpoints: for example, one looks for two cutpoints that define an interval in the range of the ordinal predictor for which the probability of a positive outcome is particularly high (or low). A chi-square test may then be performed to compare the proportions of positive outcomes in and outside this interval. However, if the two cutpoints are chosen to maximize the chi-square statistic, referring the obtained chi-square statistic to the standard chi-square distribution is an inappropriate approach. It is then necessary to correct the p-value for multiple comparisons by considering the distribution of the maximally selected chi-square statistic instead of the nominal chi-square distribution. Here, we derive the exact distribution of the chi-square statistic obtained by the optimal two cutpoints. We suggest a combinatorial computation method and illustrate our approach by a simulation study and an application to varicella data.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Paper ; No. 476

Classification and Topics

• Subject: Chi-square test ; classification ; cutpoint ; non-monotonic ; changepoint ; threshold

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Boulesteix, Anne-Laure ; Strobl, Carolin
• Event: Veröffentlichung
• (who): Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen
• (where): München
• (when): 2006

Further information

• DOI: doi:10.5282/ubm/epub.1844
• Handle: http://hdl.handle.net/10419/30998
• URN: urn:nbn:de:bvb:19-epub-1844-2
• Last update: 10.03.2025, 11:41 AM CET