Asynchronous and Error-prone Longitudinal Data Analysis via Functional Calibration

TL;DR

This paper introduces a functional calibration method for analyzing asynchronous, error-prone longitudinal data, improving estimation accuracy and convergence rates over existing approaches, with proven theoretical properties and real-world application.

Contribution

A novel functional calibration approach based on functional principal component analysis for longitudinal data with measurement error and asynchrony.

Findings

Estimator is asymptotically unbiased and root-n consistent for time-invariant models.

Achieves optimal convergence rate with inflated asymptotic variance for time-varying models.

Method outperforms existing kernel-based methods in simulations and real data application.

Abstract

In many longitudinal settings, time-varying covariates may not be measured at the same time as responses and are often prone to measurement error. Naive last-observation-carried-forward methods incur estimation biases, and existing kernel-based methods suffer from slow convergence rates and large variations. To address these challenges, we propose a new functional calibration approach to efficiently learn longitudinal covariate processes based on sparse functional data with measurement error. Our approach, stemming from functional principal component analysis, calibrates the unobserved synchronized covariate values from the observed asynchronous and error-prone covariate values, and is broadly applicable to asynchronous longitudinal regression with time-invariant or time-varying coefficients. For regression with time-invariant coefficients, our estimator is asymptotically unbiased, root-n consistent, and asymptotically normal; for time-varying coefficient models, our estimator has the optimal varying coefficient model convergence rate with inflated asymptotic variance from the calibration. In both cases, our estimators present asymptotic properties superior to the existing methods. The feasibility and usability of the proposed methods are verified by simulations and an application to the Study of Women's Health Across the Nation, a large-scale multi-site longitudinal study on women's health during mid-life.