  Data collected from wearable devices and smartphones can shed light on an
individual's pattern of behavioral and circadian routine. Phone use can be
modeled as alternating event process, 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 (EM) algorithm for imputing latent state labels and
estimating regression parameters. We show that our E-step simplifies to the
hidden Markov model (HMM) forward-backward algorithm, allowing us to recover a
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. We derive asymptotic distributions for our model 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.
