Regression analysis of the log odds ratio: a method for retrospective studies

Area of Science:

• Epidemiology
• Biostatistics
• Retrospective Studies

Background:

• Assessing the odds ratio's dependence on covariates is crucial in retrospective epidemiological studies.
• Zelen's regression model provides a method for quantifying these dependencies across multiple 2x2 tables.
• Exact analysis using conditional likelihood is asymptotically equivalent to unconditional log-linear models.

Purpose of the Study:

• To apply and evaluate Zelen's regression model for quantifying the odds ratio's dependence on concomitant variables.
• To reanalyze existing epidemiological data on obstetric radiation and childhood cancer using this statistical approach.

Main Methods:

• Utilizing Zelen's regression model for analyzing 2x2 tables.
• Employing conditional likelihood for an "exact" analysis by fixing marginal totals.
• Comparing the conditional approach with unconditional log-linear models asymptotically.

Main Results:

• The study successfully reanalyzed Kneale's data on obstetric radiation and childhood cancer.
• Demonstrated the practical application of Zelen's model in quantifying covariate effects on the odds ratio.
• Confirmed the asymptotic equivalence between exact conditional and unconditional log-linear analyses.

Conclusions:

• Zelen's regression model is a valuable tool for analyzing confounding variables in retrospective epidemiological studies.
• The method provides a robust way to quantify the odds ratio's relationship with covariates.
• The reanalysis supports the utility of this statistical technique in public health research.