# Imputation-Based Variable Selection Method for Block-Wise Missing Data When Integrating Multiple Longitudinal Studies

## TL;DR

This paper introduces a new method for selecting important variables when combining longitudinal data with block-wise missing values, improving accuracy in studies like Alzheimer's.

## Contribution

A novel imputation-based variable selection method for longitudinal data with block-wise missingness.

## Key findings

- The proposed method outperforms existing approaches in numerical experiments.
- It successfully identifies early-stage Alzheimer's biomarkers in real-world data.
- The method is theoretically grounded with established asymptotic properties.

## Abstract

When integrating data from multiple sources, a common challenge is block-wise missing. Most existing methods address this issue only in cross-sectional studies. In this paper, we propose a method for variable selection when combining datasets from multiple sources in longitudinal studies. To account for block-wise missing in covariates, we impute the missing values multiple times based on combinations of samples from different missing pattern and predictors from different data sources. We then use these imputed data to construct estimating equations, and aggregate the information across subjects and sources with the generalized method of moments. We employ the smoothly clipped absolute deviation penalty in variable selection and use the extended Bayesian Information Criterion criteria for tuning parameter selection. We establish the asymptotic properties of the proposed estimator, and demonstrate the superior performance of the proposed method through numerical experiments. Furthermore, we apply the proposed method in the Alzheimer’s Disease Neuroimaging Initiative study to identify sensitive early-stage biomarkers of Alzheimer’s Disease, which is crucial for early disease detection and personalized treatment.