Individualized Time‐Varying Nonparametric Model With an Application in Mobile Health

ABSTRACT Individualized modeling has become increasingly popular in recent years with its growing application in fields such as personalized medicine and mobile health studies. With rich longitudinal measurements, it is of great interest to model certain subject‐specific time‐varying covariate effects. In this paper, we propose an individualized time‐varying nonparametric model by leveraging the subgroup information from the population. The proposed method approximates the time‐varying covariate effect using nonparametric B‐splines and aggregates the estimated nonparametric coefficients that share common patterns. Moreover, the proposed method can effectively handle various missing data patterns that frequently arise in mobile health data. Specifically, our method achieves subgrouping by flexibly accommodating varying dimensions of B‐spline coefficients due to missingness. This capability sets it apart from other fusion‐type approaches for subgrouping. The subgroup information can also potentially provide meaningful insight into the characteristics of subjects and assist in recommending an effective treatment or intervention. An efficient ADMM algorithm is developed for implementation. Our numerical studies and application to mobile health data on monitoring pregnant women's deep sleep and physical activities demonstrate that the proposed method achieves better performance compared to other existing methods.