### Abstract

It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With paired data and with a threshold chosen without reference to the outcomes, McNemar's test of marginal homogeneity may be applied to the resulting dichotomous pairs when testing for equality of the marginal distributions of the underlying continuous outcomes. If the threshold is chosen to maximize the test statistic, however, referring the resulting test statistic to the nominal χ^{2} distribution is incorrect; Instead, the p-value must be adjusted for the multiple comparisons. Here the distribution of a maximally selected McNemar's statistic is derived, and it is shown that an approximation due to Durbin (1985, Journal of Applied Probability 22, 99-122) may be used to estimate approximate p-values. The methodology is illustrated by an application to measurements of insulin-like growth factor-I (IGF-I)in matched prostate cancer cases and controls from the Physicians' Health Study. The results of Simulation experiments that assess the accuracy of the approximation in moderate sample sizes are reported.

Original language | English (US) |
---|---|

Pages (from-to) | 897-902 |

Number of pages | 6 |

Journal | Biometrics |

Volume | 56 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2000 |

### Fingerprint

### Keywords

- Boundary crossing
- Durbin's approximation
- Matched pairs
- Maximally selected χ statistic

### 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

*Biometrics*,

*56*(3), 897-902. https://doi.org/10.1111/j.0006-341X.2000.00897.x

**Approximating the distribution of maximally selected McNemar's statistics.** / Rabinowitz, Daniel; Betensky, Rebecca.

Research output: Contribution to journal › Article

*Biometrics*, vol. 56, no. 3, pp. 897-902. https://doi.org/10.1111/j.0006-341X.2000.00897.x

}

TY - JOUR

T1 - Approximating the distribution of maximally selected McNemar's statistics

AU - Rabinowitz, Daniel

AU - Betensky, Rebecca

PY - 2000/1/1

Y1 - 2000/1/1

N2 - It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With paired data and with a threshold chosen without reference to the outcomes, McNemar's test of marginal homogeneity may be applied to the resulting dichotomous pairs when testing for equality of the marginal distributions of the underlying continuous outcomes. If the threshold is chosen to maximize the test statistic, however, referring the resulting test statistic to the nominal χ2 distribution is incorrect; Instead, the p-value must be adjusted for the multiple comparisons. Here the distribution of a maximally selected McNemar's statistic is derived, and it is shown that an approximation due to Durbin (1985, Journal of Applied Probability 22, 99-122) may be used to estimate approximate p-values. The methodology is illustrated by an application to measurements of insulin-like growth factor-I (IGF-I)in matched prostate cancer cases and controls from the Physicians' Health Study. The results of Simulation experiments that assess the accuracy of the approximation in moderate sample sizes are reported.

AB - It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With paired data and with a threshold chosen without reference to the outcomes, McNemar's test of marginal homogeneity may be applied to the resulting dichotomous pairs when testing for equality of the marginal distributions of the underlying continuous outcomes. If the threshold is chosen to maximize the test statistic, however, referring the resulting test statistic to the nominal χ2 distribution is incorrect; Instead, the p-value must be adjusted for the multiple comparisons. Here the distribution of a maximally selected McNemar's statistic is derived, and it is shown that an approximation due to Durbin (1985, Journal of Applied Probability 22, 99-122) may be used to estimate approximate p-values. The methodology is illustrated by an application to measurements of insulin-like growth factor-I (IGF-I)in matched prostate cancer cases and controls from the Physicians' Health Study. The results of Simulation experiments that assess the accuracy of the approximation in moderate sample sizes are reported.

KW - Boundary crossing

KW - Durbin's approximation

KW - Matched pairs

KW - Maximally selected χ statistic

UR - http://www.scopus.com/inward/record.url?scp=0033858015&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033858015&partnerID=8YFLogxK

U2 - 10.1111/j.0006-341X.2000.00897.x

DO - 10.1111/j.0006-341X.2000.00897.x

M3 - Article

VL - 56

SP - 897

EP - 902

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 3

ER -