Selecting Shrinkage Parameters for Effect Estimation: The Multi-Ethnic Study of Atherosclerosis

Area of Science:

• Statistics
• Epidemiology
• Biostatistics

Background:

• Linear regression models are widely used but can be imprecise in moderate-sized samples.
• Shrinkage techniques like ridge regression and LASSO offer improved estimation by reducing variance.
• Standard methods for selecting shrinkage parameters are lacking for inference-focused goals.

Purpose of the Study:

• To develop and validate a new method for selecting penalty parameters in shrinkage estimators for linear regression.
• To improve the accuracy of statistical inference in moderate sample sizes common in epidemiologic studies.
• To provide a robust approach for estimating both point estimates and standard errors.

Main Methods:

• The proposed method selects shrinkage penalty parameters by minimizing bias and variance using the posterior predictive distribution.
• This approach integrates causal inference principles with shrinkage estimation techniques.
• Simulations were conducted to compare the new method against cross-validation for parameter selection.

Main Results:

• The proposed method demonstrated superior mean squared error compared to cross-validation in simulation studies.
• The technique effectively balances bias and variance for improved estimation.
• Application to the Multi-Ethnic Study of Atherosclerosis data provided insights into smoking and carotid intima-media thickness.

Conclusions:

• The novel penalty parameter selection method enhances the performance of shrinkage estimators in linear regression for moderate sample sizes.
• This approach offers a more reliable way to perform statistical inference in epidemiologic research.
• The method provides accurate point estimates and standard errors, outperforming existing techniques like cross-validation.