Causal estimands and identification of time-varying effects in non-stationary time series from N-of-1 mobile device data

TL;DR

This paper introduces new causal estimands and a g-formula estimator for analyzing time-varying effects in non-stationary multivariate time series from N-of-1 mobile health data, enabling personalized dynamic treatment effect assessment.

Contribution

It develops a novel framework for identifying and estimating dynamic causal effects in non-stationary time series, addressing feedback and heterogeneity in mobile health data.

Findings

Revealed heterogeneity in treatment effects over time and individuals.

Demonstrated the method on a bipolar disorder smartphone study.

Proposed a simulation-based approach for personalized treatment recommendations.

Abstract

Mobile technology (mobile phones and wearable devices) generates continuous data streams encompassing outcomes, exposures and covariates, presented as intensive longitudinal or multivariate time series data. The high frequency of measurements enables granular and dynamic evaluation of treatment effect, revealing their persistence and accumulation over time. Existing methods predominantly focus on the contemporaneous effect, temporal-average, or population-average effects, assuming stationarity or invariance of treatment effects over time, which are inadequate both conceptually and statistically to capture dynamic treatment effects in personalized mobile health data. We here propose new causal estimands for multivariate time series in N-of-1 studies. These estimands summarize how time-varying exposures impact outcomes in both short- and long-term. We propose identifiability assumptions and a g-formula estimator that accounts for exposure-outcome and outcome-covariate feedback. The g-formula employs a state space model framework innovatively to accommodate time-varying behavior of treatment effects in non-stationary time series. We apply the proposed method to a multi-year smartphone observational study of bipolar patients and estimate the dynamic effect of phone-based communication on mood of patients with bipolar disorder in an N-of-1 setting. Our approach reveals substantial heterogeneity in treatment effects over time and across individuals. A simulation-based strategy is also proposed for the development of a short-term, dynamic, and personalized treatment recommendation based on patient's past information, in combination with a novel positivity diagnostics plot, validating proper causal inference in time series data.