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) |
---|---|
Pages (from-to) | 136-147 |
Number of pages | 12 |
Journal | Biometrics |
Volume | 54 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1998 |
Externally published | Yes |
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
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics