Subgroup Analysis for Longitudinal Data via Semiparametric Additive Mixed Effects Model

This paper proposed a general framework based on semiparametric additive mixed effects model to identify subgroups on each covariate and estimate the corresponding regression functions simultaneously for longitudinal data, thus it could reveal which covariate contributes to the existence of subgroups among population. A backfitting combined with k-means algorithm was developed to detect subgroup structure on each covariate and estimate each semiparametric additive component across subgroups. A Bayesian information criterion is employed to estimate the actual number of groups. The efficacy and accuracy of the proposed procedure in identifying the subgroups and estimating the regression functions are illustrated through numerical studies. In addition, the authors demonstrate the usefulness of the proposed method with applications to PBC data and Industrial Portfolio's Return data and provide meaningful partitions of the populations.