Combining mixed effects hidden Markov models with latent alternating recurrent event processes to model diurnal active-rest cycles.

Data collected from wearable devices can shed light on an individual's pattern of behavioral and circadian routine. Phone use can be modeled as alternating processes, between the state of active use and the state of being idle. Markov chains and alternating recurrent event models are commonly used to model state transitions in cases such as these, and the incorporation of random effects can be used to introduce diurnal effects. While state labels can be derived prior to modeling dynamics, this approach omits informative regression covariates that can influence state memberships. We instead propose an alternating recurrent event proportional hazards (PH) regression to model the transitions between latent states. We propose an expectation-maximization algorithm for imputing latent state labels and estimating parameters. We show that our E-step simplifies to the hidden Markov model (HMM) forward-backward algorithm, allowing us to recover an HMM with logistic regression transition probabilities. In addition, we show that PH modeling of discrete-time transitions implicitly penalizes the logistic regression likelihood and results in shrinkage estimators for the relative risk. This new estimator favors an extended stay in a state and is useful for modeling diurnal rhythms. We derive asymptotic distributions for our parameter estimates and compare our approach against competing methods through simulation as well as in a digital phenotyping study that followed smartphone use in a cohort of adolescents with mood disorders.

Modeling post-holiday surge in COVID-19 cases in Pennsylvania counties.

COVID-19 arrived in the United States in early 2020, with cases quickly being reported in many states including Pennsylvania. Many statistical models have been proposed to understand the trends of the COVID-19 pandemic and factors associated with increasing cases. While Poisson regression is a natural choice to model case counts, this approach fails to account for correlation due to spatial locations. Being a contagious disease and often spreading through community infections, the number of COVID-19 cases are inevitably spatially correlated as locations neighboring counties with a high COVID-19 case count are more likely to have a high case count. In this analysis, we combine generalized estimating equations (GEEs) for Poisson regression, a popular method for analyzing correlated data, with a semivariogram to model daily COVID-19 case counts in 67 Pennsylvania counties between March 20, 2020 to January 23, 2021 in order to study infection dynamics during the beginning of the pandemic. We use a semivariogram that describes the spatial correlation as a function of the distance between two counties as the working correlation. We further incorporate a zero-inflated model in our spatial GEE to accommodate excess zeros in reported cases due to logistical challenges associated with disease monitoring. By modeling time-varying holiday covariates, we estimated the effect of holiday timing on case count. Our analysis showed that the incidence rate ratio was significantly greater than one, 6-8 days after a holiday suggesting a surge in COVID-19 cases approximately one week after a holiday.

Measuring Daily Activity Rhythms in Young Adults at Risk of Affective Instability Using Passively Collected Smartphone Data: Observational Study.

BACKGROUND: Irregularities in circadian rhythms have been associated with adverse health outcomes. The regularity of rhythms can be quantified using passively collected smartphone data to provide clinically relevant biomarkers of routine. OBJECTIVE: This study aims to develop a metric to quantify the regularity of activity rhythms and explore the relationship between routine and mood, as well as demographic covariates, in an outpatient psychiatric cohort. METHODS: Passively sensed smartphone data from a cohort of 38 young adults from the Penn or Children's Hospital of Philadelphia Lifespan Brain Institute and Outpatient Psychiatry Clinic at the University of Pennsylvania were fitted with 2-state continuous-time hidden Markov models representing active and resting states. The regularity of routine was modeled as the hour-of-the-day random effects on the probability of state transition (ie, the association between the hour-of-the-day and state membership). A regularity score, Activity Rhythm Metric, was calculated from the continuous-time hidden Markov models and regressed on clinical and demographic covariates. RESULTS: Regular activity rhythms were associated with longer sleep durations (P=.009), older age (P=.001), and mood (P=.049). CONCLUSIONS: Passively sensed Activity Rhythm Metrics are an alternative to existing metrics but do not require burdensome survey-based assessments. Low-burden, passively sensed metrics based on smartphone data are promising and scalable alternatives to traditional measurements.