Did you miss me? Making the most of digital phenotyping data by imputing missingness with point process models: observational study.

OBJECTIVES: Smartphone-based digital phenotyping can provide low-burden behavioural measures for mental disorder monitoring. However, progress in making inferences from these data is challenged by the common occurrence of missing data. We propose a method to impute missingness using non-homogeneous Poisson point process models (PPPMs), where activities (overall phone, social media, communication app usage, outgoing/incoming calls) are modelled as 'points'. METHODS: We evaluate personalised PPPMs for imputation and investigate their influence on downstream analysis. In a ground truth evaluation (in and out-of-sample), we evaluate time-varying covariates ('hour of the day', 'day of the week'; encoded using one-hot encoding and sine-cosine transformation) to model behavioural patterns in participants from SMARD (depression; n=26). We train a hidden Markov model (HMM) on data simulated by the PPPMs and compare this to a ground truth HMM. We then perform a replication of a prior HMM analysis in PRISM (Alzheimer's disease, schizophrenia, healthy controls; n=65) and Hersenonderzoek studies (Alzheimer's disease, memory complaints, healthy controls; n=283). RESULTS: In the ground truth evaluation, 'hour' was consistently significant in in-sample likelihood ratio tests and 'day' was less commonly significant. PPPMs including one-hot encoded hour generally provided the highest out-of-sample likelihood. Using this PPPM variant, HMM properties were preserved, and prior findings were replicated. DISCUSSION: Personalised PPPMs provide behavioural simulations that can be used for temporal imputation. These models capture average patterns and could be extended to include further temporal components. CONCLUSION: Non-homogeneous PPPMs are a promising imputation tool that may contribute to improved utility of digital phenotyping by providing realistic temporal imputations.