Statistical interactions and Bayes estimation of log odds in case-control studies

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Accurate estimation of disease odds is crucial in epidemiological studies.
• Evaluating risk factors often involves complex interactions that can affect statistical models.
• Distinguishing between removable and nonremovable interactions is key for appropriate model selection.

Purpose of the Study:

• To develop a robust statistical method for estimating the logarithm of disease odds (log odds).
• To address the challenge of unknown interactions (removable vs. nonremovable) when evaluating multiple risk factors.
• To provide a Bayes estimator that optimizes bias-variance trade-offs in statistical modeling.

Main Methods:

• Development of a Bayes estimator utilizing a squared error loss function.
• Application of invertible transformations to handle removable interactions.
• Simulation studies and empirical analysis of endometrial cancer case-control data.

Main Results:

• The proposed Bayes estimator demonstrates favorable bias-variance trade-offs compared to traditional methods.
• The approach effectively handles both removable and nonremovable interactions in log odds estimation.
• Empirical illustrations confirm the practical utility of the method in real-world epidemiological data.

Conclusions:

• The developed Bayes estimator offers a flexible and precise approach to log odds estimation in the presence of unknown interactions.
• This method enhances statistical modeling for risk factor evaluation in epidemiological research.
• An R program implementing the methods is freely available for broader application.