Inference for odds ratio regression models with sparse dependent data

John J. Hanfelt, Kung Yee Liang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 languageEnglish (US)
Pages (from-to)136-147
Number of pages12
Issue number1
StatePublished - Mar 1998
Externally publishedYes


  • 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
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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