LASSO type penalized spline regression for binary data.

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Generalized linear mixed models (GLMMs) are adapted for data smoothing via semiparametric mixed models (SPMMs).
• Ridge regression penalty in SPMMs is equivalent to assuming normal distribution for random knot coefficients.
• LASSO penalty is introduced in SPMMs by assuming Laplace double exponential distribution for knot coefficients.

Purpose of the Study:

• To introduce and evaluate the LASSO penalty within the SPMM framework for data smoothing.
• To compare the performance of LASSO versus ridge penalties in SPMMs for binary data analysis.
• To apply the LASSO-SPMM method to model the smoking pack-years and COPD risk relationship.

Main Methods:

• Bayesian approach utilizing Markov Chain Monte Carlo (MCMC) for model fitting.
• Simulation studies to compare LASSO and ridge penalty performance in SPMMs.
• Application to real-world data on smoking and chronic obstructive pulmonary disease (COPD).

Main Results:

• LASSO penalty demonstrates comparable performance to ridge penalty for simple associations.
• LASSO penalty outperforms ridge penalty for complex or linear association shapes.
• The proposed method successfully generates smooth curves from correlated data.

Conclusions:

• LASSO penalty in SPMMs is superior for capturing complex dose-response associations.
• SPMMs with LASSO penalty offer an effective approach for smoothing and analyzing correlated data with complex relationships.
• The method provides a valuable tool for epidemiological studies, such as quantifying smoking impact on COPD risk.