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 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. 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. This article is protected by copyright. All rights reserved.

/pdf/combining-mixed-effects-hidden-markov-models-with-latent-2imoo0ez.pdf

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

/pdf/special-issue-dedicated-to-jack-kalbfleisch-51xl7kxg01.pdf

Special issue dedicated to Jack Kalbfleisch.

A cross sectional population is defined as a population of living individuals at the sampling or observational time. Cross-sectionally sampled data with binary disease outcome are commonly analyzed in observational studies for identifying how covariates correlate with disease occurrence. It is generally understood that cross-sectional binary outcome is not as informative as longitudinally collected time-to-event data, but there is insufficient understanding as to whether bias can possibly exist in cross-sectional data and how the bias is related to the population risk of interest. As the progression of a disease typically involves both time and disease status, we consider how the binary disease outcome from the cross-sectional population is connected to birth-illness-death process in the target population. We argue that the distribution of cross-sectional binary outcome is different from the risk distribution from the target population and that bias would typically arise when using cross-sectional data to draw inference for population risk. In general, the cross-sectional risk probability is determined jointly by the population risk probability and the ratio of duration of diseased state to the duration of disease-free state. Through explicit formulas we conclude that bias can almost never be avoided from cross-sectional data. We present age-specific risk probability (ARP) and argue that models based on ARP offers a compromised but still biased approach to understand the population risk. An analysis based on Alzheimer's disease data is presented to illustrate the ARP model and possible critiques for the analysis results.

Complexity and bias in cross-sectional data with binary disease outcome in observational studies.

In the literature studying recurrent event data, a large amount of work has been focused on univariate recurrent event processes where the occurrence of each event is treated as a single point in time. There are many applications, however, in which univariate recurrent events are insufficient to characterize the feature of the process because patients experience nontrivial durations associated with each event. This results in an alternating event process where the disease status of a patient alternates between exacerbations and remissions. In this paper, we consider the dynamics of a chronic disease and its associated exacerbation-remission process over two time scales: calendar time and time-since-onset. In particular, over calendar time, we explore population dynamics and the relationship between incidence, prevalence and duration for such alternating event processes. We provide nonparametric estimation techniques for characteristic quantities of the process. In some settings, exacerbation processes are observed from an onset time until death; to account for the relationship between the survival and alternating event processes, nonparametric approaches are developed for estimating exacerbation process over lifetime. By understanding the population dynamics and within-process structure, the paper provide a new and general way to study alternating event processes.

Alternating event processes during lifetimes: population dynamics and statistical inference

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Alternating event processes during lifetimes: population dynamics and statistical inference