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

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 nonstationary time series. We apply the proposed method to a multiyear 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.