Comparison of Longitudinal Trajectories Using a High-dimensional Partial Linear Semiparametric Mixed-Effects Model

In longitudinal research, it is essential to compare sets of trajectories, commonly seen as changes over time in different treatment or patient groups. This paper presents a partial linear semiparametric mixed-effects model (PLSMM) for the analysis and comparison of nonlinear longitudinal trajectories with high-dimensional covariates across groups. Our flexible modeling framework can effectively handle complex temporal effects and extensive data while providing statistical inference. This method is particularly useful for evaluating differences in both linear and nonlinear components between groups, with a key strength being its ability to model nonlinear patterns without requiring prior knowledge of the functional forms. Instead, it employs a dictionary search strategy to automatically select appropriate basis functions to capture the nonlinear trends. This approach is also capable of handling longitudinal observations with irregular time points. A novel debiasing procedure is proposed for the post-selection inference on the linear components of PLSMM, and a bootstrap method is used for the comparison of nonlinear components. The model has been tested in different simulation settings and applied to a cohort study examining the evolution of oral Candida albicans concentration in young children from birth to two years of age in different racial groups.