Time varying mixed effects model with fused lasso regularization

Abstract

The associations between covariates and the outcomes often vary over time, regardless of whether the covariate is time-varying or time-invariant. For example, we hypothesize that the impact of chronic diseases, such as diabetes and heart disease, on people’s physical functions differ with aging. However, the age-varying effect would be missed if one models the covariate simply as a time-invariant covariate (yes/no) with a time-constant coefficient. We propose a fused lasso-based time-varying linear mixed effect (FTLME) model and an efficient two-stage parameter estimation algorithm to estimate the longitudinal trajectories of fixed-effect coefficients. Simulation studies are presented to demonstrate the efficacy of the method and its computational efficiency in estimating smooth time-varying effects in high dimensional settings. A real data example on the Health and Retirement Study (HRS) analysis is used to demonstrate the practical usage of our method to infer age-varying impact of chronic disease on older people’s physical functions.

KEYWORDS:

• Fused lasso
• linear mixed effect model
• longitudinal analysis
• regularization
• time-varying fixed effect

Acknowledgments

We thank the editor and referees for their constructive comments and suggestions, which greatly improved the quality of the paper. This work was supported by National Institute on Aging in National Institutes of Health (NIH/NIA) (1R01AG054467-01A1).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Institute on Aging in National Institutes of Health (NIH/NIA) [grant number 1R01AG054467-01A1].