Weighted likelihood, pseudo-likelihood and maximum likelihood methods for logistic regression analysis of two-stage...

Area of Science:

• Biostatistics
• Statistical Modeling
• Epidemiology

Background:

• Binary response models are crucial for analyzing case-control study data.
• Stratified sampling designs, including two-stage sampling, require specialized statistical approaches.
• Existing methods like weighted and pseudo-likelihood have limitations in certain complex designs.

Purpose of the Study:

• To describe efficient computational algorithms for estimating regression coefficients in two-stage sampling.
• To compare the performance of weighted, pseudo-, and full maximum likelihood methods.
• To extend the application of two-stage methods to case-control studies with validation subsampling for measurement error control.

Main Methods:

• Development of computational algorithms for weighted, pseudo-, and full maximum likelihood estimation.
• Large sample theory and methodology for logistic regression in two-stage case-control data.
• Simulation studies with continuous covariates and analysis of real case-control data.

Main Results:

• Full maximum likelihood demonstrated superior performance compared to weighted and pseudo-likelihood methods in simulations involving continuous covariates.
• The study illustrates key relationships among the three estimation methods using real-world case-control data.
• Efficient algorithms were developed for practical implementation of these methods.

Conclusions:

• Full maximum likelihood is recommended for fitting logistic regression models to two-stage case-control data, especially with continuous covariates.
• The developed algorithms facilitate efficient estimation in complex survey designs.
• Two-stage methods are applicable for addressing measurement error in case-control studies through validation subsampling.