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**Boulesteix, Anne-Laure and Strobl, Carolin (2006): Maximally selected chi-square statistics and umbrella orderings. Collaborative Research Center 386, Discussion Paper 476 [PDF, 272kB]**

## Abstract

Binary outcomes that depend on an ordinal predictor in a non-monotonic 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.

Item Type: | Paper |
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Faculties: | Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386 Special Research Fields > Special Research Field 386 |

Subjects: | 500 Science > 510 Mathematics |

URN: | urn:nbn:de:bvb:19-epub-1844-2 |

Language: | English |

Item ID: | 1844 |

Date Deposited: | 11. Apr 2007 |

Last Modified: | 04. Nov 2020, 12:46 |