### 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) |
---|---|

Pages (from-to) | 317-320 |

Number of pages | 4 |

Journal | Biometrics |

Volume | 55 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1999 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

^{2}statistics for k x 2 tables.

*Biometrics*,

*55*(1), 317-320. https://doi.org/10.1111/j.0006-341X.1999.00317.x

**Maximally selected χ ^{2} statistics for k x 2 tables.** / Betensky, Rebecca; Rabinowitz, Daniel.

Research output: Contribution to journal › Article

^{2}statistics for k x 2 tables',

*Biometrics*, vol. 55, no. 1, pp. 317-320. https://doi.org/10.1111/j.0006-341X.1999.00317.x

^{2}statistics for k x 2 tables. Biometrics. 1999 Jan 1;55(1):317-320. https://doi.org/10.1111/j.0006-341X.1999.00317.x

}

TY - JOUR

T1 - Maximally selected χ2 statistics for k x 2 tables

AU - Betensky, Rebecca

AU - Rabinowitz, Daniel

PY - 1999/1/1

Y1 - 1999/1/1

N2 - It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With such a dichotomized outcome, the usual χ2 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 χ2 reference distributions are incorrect. In this paper, the asymptotic distributions of maximally selected χ2 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.

AB - It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With such a dichotomized outcome, the usual χ2 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 χ2 reference distributions are incorrect. In this paper, the asymptotic distributions of maximally selected χ2 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.

KW - Association

KW - Brownian bridge

KW - Categorical data

KW - Independence

KW - Multivariate diffusion

KW - Trend

UR - http://www.scopus.com/inward/record.url?scp=0032586412&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032586412&partnerID=8YFLogxK

U2 - 10.1111/j.0006-341X.1999.00317.x

DO - 10.1111/j.0006-341X.1999.00317.x

M3 - Article

VL - 55

SP - 317

EP - 320

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 1

ER -