Inference for odds ratio regression models with sparse dependent data

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Genetics

Background:

• Analyzing dependent data in case-control studies, common in family-based or longitudinal designs, presents statistical challenges.
• Traditional methods like noncentral hypergeometric likelihood can be sensitive to unknown dependence structures.

Purpose of the Study:

• To develop robust statistical inference methods for regression models of odds ratios with table-level covariates when within-table observations are dependent.
• To address limitations of existing methods, specifically the poor performance of Wald confidence intervals in additive regression models.

Main Methods:

• Utilized estimating functions based on the Mantel-Haenszel method for consistent estimation of regression parameters (beta).
• Proposed and evaluated a novel Mantel-Haenszel quasi-likelihood function derived from integrating the Mantel-Haenszel estimating function.
• Conducted a simulation study to compare the performance of the proposed method against Wald inference and other approaches.

Main Results:

• The Mantel-Haenszel estimating function approach provides consistent estimators for beta.
• Wald's confidence intervals show good performance for multiplicative regression but poor coverage for additive models.
• The proposed Mantel-Haenszel quasi-likelihood method demonstrated superior inference in additive models and comparable performance to Wald's method in multiplicative models, especially in medium-sized samples.

Conclusions:

• The Mantel-Haenszel quasi-likelihood approach offers a reliable method for statistical inference in regression models with dependent data, particularly under additive models.
• This method provides a valuable tool for analyzing complex epidemiological data, such as familial risk studies, where dependence structures are prevalent.