A Solution to Separation and Multicollinearity in Multiple Logistic Regression.

Area of Science:

• Biostatistics
• Epidemiology
• Gerontology

Background:

• Dementia screening test item selection often uses logistic regression.
• Maximum likelihood estimates in logistic regression can be biased or non-existent due to separation and multicollinearity with highly correlated items.
• Existing methods like Firth's penalized likelihood and ridge regression have limitations.

Purpose of the Study:

• To propose a novel double penalized maximum likelihood estimator for logistic regression.
• To address bias and non-existence problems in item selection for dementia screening.
• To evaluate the performance of the proposed estimator in small to moderate sample sizes.

Main Methods:

• Development of a double penalized maximum likelihood estimator combining Firth's penalized likelihood and ridge regression.
• Conducting a simulation study to assess empirical performance.
• Application of the proposed method to community-based dementia screening data.

Main Results:

• The proposed double penalized estimator is designed to mitigate bias and non-existence issues in logistic regression.
• Simulation results are expected to demonstrate the estimator's effectiveness in small to moderate sample sizes.
• The approach is validated using real-world dementia screening data.

Conclusions:

• The double penalized maximum likelihood estimator offers a robust solution for item selection in dementia screening.
• This method enhances the reliability of logistic regression models with highly correlated predictors.
• The proposed approach has practical implications for developing efficient and accurate dementia screening tools.