### Abstract

Suppose the number of 2 x 2 tables is large relative to the average table size, and the observations within a given table are dependent, as occurs in longitudinal or family-based case-control studies. We consider fitting regression models to the odds ratios using table-level covariates. The focus is on methods to obtain valid inferences for the regression parameters β when the dependence structure is unknown. In this setting, Liang (1985, Biometrika 72, 678-682) has shown that inference based on the noncentral hypergeometric likelihood is sensitive to misspecification of the dependence structure. In contrast, estimating functions based on the Mantel- Haenszel method yield consistent estimators of β. We show here that, under the estimating function approach, Wald's confidence interval for β performs well in multiplicative regression models but unfortunately has poor coverage probabilities when an additive regression model is adopted. As an alternative to Wald inference, we present a Mantel-Haenszel quasi-likelihood function based on integrating the Mantel-Haenszel estimating function. A simulation study demonstrates that, in medium-sized samples, the Mantel-Haenszel quasi- likelihood approach yields better inferences than other methods under an additive regression model and inferences comparable to Wald's method under a multiplicative model. We illustrate the use of this quasi-likelihood method in a study of the familial risk of schizophrenia.

Original language | English (US) |
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Pages (from-to) | 136-147 |

Number of pages | 12 |

Journal | Biometrics |

Volume | 54 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1998 |

### Keywords

- Additive odds ratio
- Case-control study
- Conditional logistic regression
- Familial risk
- Mantel-Haenszel method
- Quasi-likelihood
- Score test
- Wald test

### ASJC Scopus subject areas

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

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## Cite this

*Biometrics*,

*54*(1), 136-147. https://doi.org/10.2307/2534002