Statistics and Its Interface

Volume 17 (2024)

Number 1

Special issue in honor of Professor Lincheng Zhao

A review of nonparametric regression methods for longitudinal data

Pages: 127 – 142

DOI: https://dx.doi.org/10.4310/23-SII801

Authors

Changxin Yang (Department of Statistics and Data Science, Fudan University, Shanghai, China)

Zhongyi Zhu (Department of Statistics and Data Science, Fudan University, Shanghai, China)

Abstract

Longitudinal data, which involve measuring a group of subjects repeatedly over time, frequently arise in many clinical and biomedical applications. To identify the complex patterns of change in the outcome and their association with covariates over time, a sufficiently flexible model is always required. Nonparametric regression, known for being data-adaptive and less restrictive than parametric approaches, becomes a promising tool for handling longitudinal data. This paper reviews various nonparametric regression methods for longitudinal data, including specific traditional nonparametric methods for the univariate case and several representative methods for the multivariate case, among which tree-based techniques are dominant. We summarize their motivations and provide a brief practical performance comparison of these methods in simulations, as well as discuss potential future research directions.

Keywords

longitudinal data, repeated measurements, nonparametric regression, machine learning, regression tree

Received 30 December 2022

Accepted 25 May 2023

Published 27 November 2023