In this paper, the recurrent events that can occur more than one over the follow-up time have been modeled by phase-type distributions. We use the finite-state continuous-time Markov process with multi states for patients with recurrent events. The number of recurrences until time $t$, the time stay for every state and the time till death are of importances. The time till death is assumed to have a phase-type distribution (which is defined in a Markov chain environment) with interpretable parameters. The underlying continuous-time Markov chain has one absorbing state (death) and transient states to reflect recovery and disease stages. A system of differential equations is obtained to calculate the probability of various number of transitions, the conditional expected time to stay in a disease stage and the probability of transition from a stage to another. The model has been calibrated via a real and simulated datasets. The bootstrap techniques have been used to construct the confidence intervals for the parameters.
Progression of chronic disease is often manifested by repeated occurrences of disease-related events over time. Delineating the heterogeneity in the risk of such recurrent events can provide valuable scientific insight for guiding customized disease management. In this paper, we present a new modeling framework for recurrent event data, which renders a flexible and robust characterization of individual multiplicative risk of recurrent event through quantile regression that accommodates both observed covariates and unobservable frailty. The proposed modeling requires no distributional specifica…
Statistical tests for trend in recurrent event data not following a Poisson process are generally constructed for event censored data. However, time censored data are more frequently encountered in practice. In this paper we contribute to filling an important gap in the literature on trend testing by presenting a class of statistical tests for trend in time censored recurrent event data, based on the null hypothesis of a renewal process. The class of tests is constructed by an adaption of a functional central limit theorem for renewal processes. By this approach a number of tests for time cens…
Asymptotic properties, both consistency and weak convergence, of estimators arising in a general class of dynamic recurrent event models are presented. The class of models take into account the impact of interventions after each event occurrence, the impact of accumulating event occurrences, the induced informative and dependent right-censoring mechanism due to the data-accrual scheme, and the effect of covariate processes on the recurrent event occurrences. The class of models subsumes as special cases many of the recurrent event models that have been considered in biostatistics, reliability,…
We introduce a covariate-specific total variation penalty in two semiparametric models for the rate function of recurrent event process. The two models are a stratified Cox model, introduced in Prentice et al. (1981), and a stratified Aalen's additive model. We show the consistency and asymptotic normality of our penalized estimators. We demonstrate, through a simulation study, that our estimators outperform classical estimators for small to moderate sample sizes. Finally an application to the bladder tumour data of Byar (1980) is presented.
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 members…
This review article provides an overview of recent work in the modeling and analysis of recurrent events arising in engineering, reliability, public health, biomedicine and other areas. Recurrent event modeling possesses unique facets making it different and more difficult to handle than single event settings. For instance, the impact of an increasing number of event occurrences needs to be taken into account, the effects of covariates should be considered, potential association among the interevent times within a unit cannot be ignored, and the effects of performed interventions after each ev…
We present new estimators for the statistical analysis of the dependence of the mean gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is expressed through regression-like and overdispersion parameters, estimated via conditional estimating equations. The mean and variance of the length of each gap time, conditioned on the observed history of prior events and other covariates, are known functions of parameters and covariates. Under certain conditions on censoring, we construct normalized estimati…
There is a constant need for many healthcare programs to timely address problems with infection prevention and control (IP&C). For example, pathogens can be transmitted among patients with cystic fibrosis (CF) in both the inpatient and outpatient settings within the healthcare system even with the existing recommended IP&C practices, and these pathogens are often associated with negative clinical outcomes. Because of limited and delayed data sharing, CF programs need a reliable method to track infection rates. There are three complex structures in CF registry data: recurrent infections, missin…
Novel g-computation algorithms for time-varying actions with recurrent and semi-competing events
Department of Epidemiology, Gillings School of Global Public Health, University of North Carolina（北卡罗来纳大学吉林斯全球公共卫生学院流行病学系）；Carolina Population Center, University of North Carolina（北卡罗来纳大学卡罗来纳人口中心）
Pseudo-value Based Mean Cumulative Count Regression
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Novartis Pharma AG（诺华制药股份有限公司）；Department of Statistical Sciences, University of Toronto（多伦多大学统计科学系）；Hoffman La Roche Ltd（罗氏制药有限公司）
In this paper, a novel non-parametric method for estimation of expectation and maximum value of the variance function is proposed for recurrent events where intensity of event occurrence changes with the occurrence of each higher order event. These kinds of recurrent events are often observed in clinical trials for cardio-vascular events and also in many social experiments involving drug addiction, armed robberies, etc. Simulated data is used to demonstrate the novel approach for estimating the mean and variance of such recurrent events and the results are compared with the result of Nelson Aa…
Recurrent events arise frequently in biomedical research, where the subject may experience the same type of events more than once. The Andersen-Gill (AG) model has become increasingly popular in the analysis of recurrent events particularly when the event rate is not constant over time. We propose a procedure for calculating the power and sample size for the robust Wald test from the AG model in superiority, noninferiority, and equivalence clinical trials. Its performance is demonstrated by numerical examples. Sample SAS code is provided in the Supplementary Material.
In a recurrent events setting, we introduce a new score designed to evaluate the prediction ability, for a given model, of the expected cumulative number of recurrent events. This score allows to take into account the individual history of a patient through its external covariates and can be seen as an extension of the Brier Score for single time to event data but works for recurrent events with or without a terminal event. Theoretical results are provided that show that under standard assumptions in a recurrent event context, our score can be asymptotically decomposed as the sum of the theore…
Recurrent event data are common in clinical studies when participants are followed longitudinally, and are often subject to a terminal event. With the increasing popularity of large pragmatic trials with a heterogeneous source population, participants are often nested in clinics and can be either susceptible or structurally unsusceptible to the recurrent process. These complications require new modeling strategies to accommodate potential zero-event inflation as well as hierarchical data structures in both the terminal and non-terminal event processes. In this paper, we develop a Bayesian semi…
Digital monitoring studies collect real-time high frequency data via mobile sensors in the subjects' natural environment. This data can be used to model the impact of changes in physiology on recurrent event outcomes such as smoking, drug use, alcohol use, or self-identified moments of suicide ideation. Likelihood calculations for the recurrent event analysis, however, become computationally prohibitive in this setting. Motivated by this, a random subsampling framework is proposed for computationally efficient, approximate likelihood-based estimation. A subsampling-unbiased estimator for the d…
Nonparametric efficient causal estimation of the intervention-specific expected number of recurrent events with continuous-time targeted maximum likelihood and highly adaptive lasso estimation
Multi-type recurrent events are often encountered in medical applications when two or more different event types could repeatedly occur over an observation period. For example, patients may experience recurrences of multi-type nonmelanoma skin cancers in a clinical trial for skin cancer prevention. The aims in those applications are to characterize features of the marginal processes, evaluate covariate effects, and quantify both the within-subject recurrence dependence and the dependence among different event types. We use copula-frailty models to analyze correlated recurrent events of differe…
The number of recurrent events before a terminating event is often of interest. For instance, death terminates an individual's process of rehospitalizations and the number of rehospitalizations is an important indicator of economic cost. We propose a model in which the number of recurrences before termination is a random variable of interest, enabling inference and prediction on it. Then, conditionally on this number, we specify a joint distribution for recurrence and survival. This novel conditional approach induces dependence between recurrence and survival, which is often present, for insta…
In many time-to-event studies, the event of interest is recurrent. Here, the data for each sample unit corresponds to a series of gap times between the subsequent events. Given a limited follow-up period, the last gap time might be right-censored. In contrast to classical analysis, gap times and censoring times cannot be assumed independent, i.e. the sequential nature of the data induces dependent censoring. Also, the recurrences typically vary between sample units leading to unbalanced data. To model the association pattern between gap times, so far only parametric margins combined with the r…
Although increasingly used as a data resource for assembling cohorts, electronic health records (EHRs) pose many analytic challenges. In particular, a patient's health status influences when and what data are recorded, generating sampling bias in the collected data. In this paper, we consider recurrent event analysis using EHR data. Conventional regression methods for event risk analysis usually require the values of covariates to be observed throughout the follow-up period. In EHR databases, time-dependent covariates are intermittently measured during clinical visits, and the timing of these …
Joint modelling of recurrent and terminal events with discretely-distributed non-parametric frailty: application on re-hospitalizations and death in heart failure patients
To analyze the impacts of certain types of public health interventions we need to estimate the treatment effects and outcomes as these apply to heterogeneous open populations. Dynamically modifying populations containing risk groups that can react very differently to changes in covariates are inferentially challenging. Here we propose a novel Bayesian graphical model called the Reduced Dynamic Chain Event Graph (RDCEG) customized to such populations. These models generalize the tree-based Chain Event Graphs to a particular class of graphically supported semi-Markov processes. They provide an i…
Estimation of Time-Varying Treatment Effects in a Joint Model for Longitudinal and Recurrent Event Outcomes in Mobile Health Data
University of Michigan（密歇根大学）；Institute for Social Research, University of Michigan（密歇根大学社会研究所）；Department of Population Health Sciences and Huntsman Cancer Insti（人口健康科学与亨斯曼癌症研究所）
Background Study individuals may face repeated events overtime. However, there is no consensus around learning approaches to use in a high-dimensional framework for survival data (when the number of variables exceeds the number of individuals, i.e., p>n). This study aimed at identifying learning algorithms for analyzing/predicting recurrent events and at comparing them to standard statistical models in various data simulation settings. Methods A literature review (LR) was conducted to provide state-of-the-art methodology. Data were then simulated including variations of the number of variables…
A joint model for (un)bounded longitudinal markers, competing risks, and recurrent events using patient registry data
Erasmus University Medical Center（伊拉斯姆斯大学医学中心）；Duke University（杜克大学）；Cincinnati Children’s Hospital Medical Center（辛辛那提儿童医院医疗中心）；University of Cincinnati（辛辛那提大学）
This project was motivated by a dialysis study in northern Taiwan. Dialysis patients, after shunt implantation, may experience two types ("acute" or "non-acute") of shunt thrombosis, both of which may recur. We formulate the problem under the framework of recurrent events data in the presence of competing risks. In particular we focus on marginal inference for the gap time variable of specific type. The functions of interest are the cumulative incidence function and cause-specific hazard function. The major challenge of nonparametric inference is the problem of induced dependent censoring. We …
