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Mobile technology enables unprecedented continuous monitoring of anindividual's behavior, social interactions, symptoms, and other healthconditions, presenting an enormous opportunity for therapeutic advancements andscientific discoveries regarding the etiology of psychiatric illness.Continuous collection of mobile data results in the generation of a new type ofdata: entangled multivariate time series of outcome, exposure, and covariates.Missing data is a pervasive problem in biomedical and social science research,and the Ecological Momentary Assessment (EMA) using mobile devices inpsychiatric research is no exception. However, the complex structure ofmultivariate time series introduces new challenges in handling missing data forproper causal inference. Data imputation is commonly recommended to enhancedata utility and estimation efficiency. The majority of available imputationmethods are either designed for longitudinal data with limited follow-up timesor for stationary time series, which are incompatible with potentiallynon-stationary time series. In the field of psychiatry, non-stationary data arefrequently encountered as symptoms and treatment regimens may experiencedramatic changes over time. To address missing data in possibly non-stationarymultivariate time series, we propose a novel multiple imputation strategy basedon the state space model (SSMmp) and a more computationally efficient variant(SSMimpute). We demonstrate their advantages over other widely used missingdata strategies by evaluating their theoretical properties and empiricalperformance in simulations of both stationary and non-stationary time series,subject to various missing mechanisms. We apply the SSMimpute to investigatethe association between social network size and negative mood using amulti-year observational smartphone study of bipolar patients, controlling forconfounding variables.

State space model multiple imputation for missing data in non-stationary multivariate time series with application in digital Psychiatry