Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/30998 
Year of Publication: 
2006
Series/Report no.: 
Discussion Paper No. 476
Publisher: 
Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen, München
Abstract: 
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.
Subjects: 
Chi-square test
classification
cutpoint
non-monotonic
changepoint
threshold
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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