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.