Missing data in non-stationary multivariate time series from digital studies in Psychiatry

TL;DR

This paper introduces a Monte Carlo Expectation Maximization algorithm tailored for imputing missing data in complex, non-stationary multivariate time series from digital psychiatric studies, improving inference accuracy.

Contribution

We develop a novel MCEM-SSM method specifically designed for non-stationary, entangled multivariate time series with missing data, addressing limitations of existing imputation techniques.

Findings

MCEM-SSM outperforms traditional imputation methods in simulations.

The method effectively handles complex temporal dependencies.

Application reveals associations between social connectivity and mood in psychiatric patients.

Abstract

Mobile technology (e.g., mobile phones and wearable devices) provides scalable methods for collecting physiological and behavioral biomarkers in patients' naturalistic settings, as well as opportunities for therapeutic advancements and scientific discoveries regarding the etiology of psychiatric illness. Continuous data collection through mobile devices generates highly complex data: entangled multivariate time series of outcomes, exposures, and covariates. Missing data is a pervasive problem in biomedical and social science research, and Ecological Momentary Assessment (EMA) data in psychiatric research is no exception. However, the complex data structure of multivariate time series and their non-stationary nature make missing data a major challenge for proper inference. Additional historical information included in time series analyses exacerbates the issue of missing data and also introduces problems for confounding adjustment. The majority of existing imputation methods are either designed for stationary time series or for longitudinal data with limited follow-up periods. The limited work on non-stationary time series either focuses on missing exogenous information or ignores the complex temporal dependence among outcomes, exposures, and covariates. We propose a Monte Carlo Expectation Maximization algorithm for the state space model (MCEM-SSM) to effectively handle missing data in non-stationary entangled multivariate time series. We demonstrate the method's advantages over other widely used missing data imputation strategies through simulations of both stationary and non-stationary time series, subject to various missing mechanisms. Finally, we apply the MCEM-SSM to a multi-year smartphone observational study of bipolar and schizophrenia patients to investigate the association between digital social connectivity and negative mood.