## Abstract

It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With such a dichotomized outcome, the usual χ^{2} statistics for association or trend can be used to test for equality of proportions across strata of the study population. However, if the threshold is chosen to maximize the test statistic, the nominal χ^{2} reference distributions are incorrect. In this paper, the asymptotic distributions of maximally selected χ^{2} statistics for association and for trend for the k x 2 table are derived. The methodology is illustrated with data from an AIDS clinical trial. The results of simulation experiments that assess the accuracy of the asymptotic distributions in moderate sample sizes are also reported.

Original language | English (US) |
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Pages (from-to) | 317-320 |

Number of pages | 4 |

Journal | Biometrics |

Volume | 55 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1999 |

## Keywords

- Association
- Brownian bridge
- Categorical data
- Independence
- Multivariate diffusion
- Trend

## ASJC Scopus subject areas

- Statistics and Probability
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics

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