Recurrent Event Data Research Articles

Conditional modeling of recurrent event data with terminal event.

Recurrent event data with a terminal event arise in follow-up studies. The current literature has primarily focused on the effect of covariates on the recurrent event process using marginal estimating equation approaches or joint modeling approaches via frailties. In this article, we propose a conditional model for recurrent event data with a terminal event, which provides an intuitive interpretation of the effect of the terminal event: at an early time, the rate of recurrent events is nearly independent of the terminal event, but the dependence gets stronger as time goes close to the terminal event time. A two-stage likelihood-based approach is proposed to estimate parameters of interest. Asymptotic properties of the estimators are established. The finite-sample behavior of the proposed method is examined through simulation studies. A real data of colorectal cancer is analyzed by the proposed method for illustration.

Analysis of recurrent event data with spatial random effects using a Bayesian approach.

Recurrent event data, which represent the occurrence of repeated incidences, are common in observational studies. Furthermore, collecting possible spatial correlations in health and environmental data is likely to provide more information for risk prediction. This article proposes a comprehensive proportional intensity model considering spatial random effects for recurrent event data using a Bayesian approach. The spatial information for areal data (where the spatial location is known up to a geographic unit such as a county) and georeferenced data (where the location is exactly observed) is examined. A traditional constant baseline intensity function, as well as a flexible piecewise constant baseline intensity function, are both under consideration. To estimate the parameters, a Markov chain Monte Carlo method with the Metropolis-Hastings algorithm and the adaptive Metropolis algorithm are applied. To assess the performance of model fitting, the deviance information criterion and log pseudo marginal likelihood are proposed. Overall, simulation studies demonstrate that the proposed model is significantly better than models that do not consider spatial effects if spatial correlations exist. Finally, our approach is implemented using a dataset related to the recurrence of cardiovascular diseases, which incorporates spatial information.

Semiparametric Transformation Models for Mixed Recurrent Event and Panel Count Data with Multiple Causes of Failure

Semiparametric Transformation Models for Mixed Recurrent Event and Panel Count Data with Multiple Causes of Failure

Systematic review of methods used in prediction models with recurrent event data

BackgroundPatients who suffer from chronic conditions or diseases are susceptible to experiencing repeated events of the same type (e.g. seizures), termed ‘recurrent events’. Prediction models can be used to predict the risk of recurrence so that intervention or management can be tailored accordingly, but statistical methodology can vary. The objective of this systematic review was to identify and describe statistical approaches that have been applied for the development and validation of multivariable prediction models with recurrent event data. A secondary objective was to informally assess the characteristics and quality of analysis approaches used in the development and validation of prediction models of recurrent event data.MethodsSearches were run in MEDLINE using a search strategy in 2019 which included index terms and phrases related to recurrent events and prediction models. For studies to be included in the review they must have developed or validated a multivariable clinical prediction model for recurrent event outcome data, specifically modelling the recurrent events and the timing between them.The statistical analysis methods used to analyse the recurrent event data in the clinical prediction model were extracted to answer the primary aim of the systematic review. In addition, items such as the event rate as well as any discrimination and calibration statistics that were used to assess the model performance were extracted for the secondary aim of the review.ResultsA total of 855 publications were identified using the developed search strategy and 301 of these are included in our systematic review. The Andersen-Gill method was identified as the most commonly applied method in the analysis of recurrent events, which was used in 152 (50.5%) studies. This was closely followed by frailty models which were used in 116 (38.5%) included studies. Of the 301 included studies, only 75 (24.9%) internally validated their model(s) and three (1.0%) validated their model(s) in an external dataset.ConclusionsThis review identified a variety of methods which are used in practice when developing or validating prediction models for recurrent events. The variability of the approaches identified is cause for concern as it indicates possible immaturity in the field and highlights the need for more methodological research to bring greater consistency in approach of recurrent event analysis. Further work is required to ensure publications report all required information and use robust statistical methods for model development and validation.PROSPERO registrationCRD42019116031.

Robust inference for causal mediation analysis of recurrent event data.

Recurrent events, including cardiovascular events, are commonly observed in biomedical studies. Understanding the effects of various treatments on recurrent events and investigating the underlying mediation mechanisms by which treatments may reduce the frequency of recurrent events are crucial tasks for researchers. Although causal inference methods for recurrent event data have been proposed, they cannot be used to assess mediation. This study proposed a novel methodology of causal mediation analysis that accommodates recurrent outcomes of interest in a given individual. A formal definition of causal estimands (direct and indirect effects) within a counterfactual framework is given, and empirical expressions for these effects are identified. To estimate these effects, a semiparametric estimator with triple robustness against model misspecification was developed. The proposed methodology was demonstrated in a real-world application. The method was applied to measure the effects of two diabetes drugs on the recurrence of cardiovascular disease and to examine the mediating role of kidney function in this process.

Estimation and reduction of bias in self-controlled case series with non-rare event dependent outcomes and heterogeneous populations.

The self-controlled case series (SCCS) is a commonly adopted study design in the assessment of vaccine and drug safety. Recurrent event data collected from SCCS studies are typically analyzed using the conditional Poisson model which assumes event times are independent within-cases. This assumption is violated in the presence of event dependence, where the occurrence of an event influences the probability and timing of subsequent events. When event dependence is suspected in an SCCS study, the standard recommendation is to include only the first event from each case in the analysis. However, first event analysis can still yield biased estimates of the exposure relative incidence if the outcome event is not rare. We first demonstrate that the bias in first event analysis can be even higher than previously assumed when subpopulations with different baseline incidence rates are present and describe an improved method for estimating this bias. Subsequently, we propose a novel partitioned analysis method and demonstrate how it can reduce this bias. We provide a recommendation to guide the number of partitions to use with the partitioned analysis, illustrate this recommendation with an example SCCS study of the association between beta-blockers and acute myocardial infarction, and compare the partitioned analysis against other SCCS analysis methods by simulation.

New tests for trend in time censored recurrent event data

AbstractWe consider testing for trend in recurrent event data. More precisely, for such data we consider testing of the null hypothesis of data coming from a renewal process. The new tests are essentially obtained by considering appropriate integrated versions of classical trend tests. Moreover, adaptive versions of earlier considered tests versus non‐monotonic alternatives, like bathtub trend, are suggested. A simulation study shows that the new tests have favorable properties and sometimes outperform classical tests. Examples with real data are also considered.

Regression analysis of multivariate recurrent event data allowing time-varying dependence with application to stroke registry data.

In multivariate recurrent event data, each patient may repeatedly experience more than one type of event. Analysis of such data gets further complicated by the time-varying dependence structure among different types of recurrent events. The available literature regarding the joint modeling of multivariate recurrent events assumes a constant dependency over time, which is strict and often violated in practice. To close the knowledge gap, we propose a class of flexible shared random effects models for multivariate recurrent event data that allow for time-varying dependence to adequately capture complex correlation structures among different types of recurrent events. We developed an expectation-maximization algorithm for stable and efficient model fitting. Extensive simulation studies demonstrated that the estimators of the proposed approach have satisfactory finite sample performance. We applied the proposed model and the estimating method to data from a cohort of stroke patients identified in the University of Texas Houston Stroke Registry and evaluated the effects of risk factors and the dependence structure of different types of post-stroke readmission events.

-Inflated beta regression model for censored recurrent events.

This research introduces a multivariate -inflated beta regression ( -IBR) modeling approach for the analysis of censored recurrent event data that is particularly useful when there is a mixture of (a) individuals who are generally less susceptible to recurrent events and (b) heterogeneity in duration of event-free periods amongst those who experience events. The modeling approach is applied to a restructured version of the recurrent event data that consists of censored longitudinal times-to-first-event in length follow-up windows that potentially overlap. Multiple imputation (MI) and expectation-solution (ES) approaches appropriate for censored data are developed as part of the model fitting process. A suite of useful analysis outputs are provided from the -IBR model that include parameter estimates to help interpret the (a) and (b) mixture of event times in the data, estimates of mean -restricted event-free duration in a -length follow-up window based on a patient's covariate profile, and heat maps of raw -restricted event-free durations observed in the data with censored observations augmented via averages across MI datasets. Simulations indicate good statistical performance of the proposed -IBR approach to modeling censored recurrent event data. An example is given based on the Azithromycin for Prevention of COPD Exacerbations Trial.

Semiparametric regression analysis of doubly censored recurrent event data

Semiparametric regression analysis of doubly censored recurrent event data

Marginal versus conditional rate estimation for count and recurrent event data with an estimand framework

Count and recurrent event endpoints are common key efficacy endpoints in clinical research. For example, in clinical research of pulmonary diseases such as chronic obstructive pulmonary disease (COPD) or asthma, the reduction of the occurrence of a recurrent event, pulmonary exacerbation (PEx) caused by acute respiratory symptoms, is often used to measure the treatment effect. The occurrence of PEx is often analyzed with nonlinear models, such as Poisson regression or Negative Binomial regression. It is observed that model-estimated within-group PEx rates are often lower than the descriptive statistics of within-group PEx rates. Motivated by this observation, we explore their relationship mathematically and demonstrate that it is due to the difference between conditional PEx rates and population-level PEx rates (marginal rates). Our findings corroborate the recent FDA guidance (2023) [1], which discusses considerations for covariate adjustment in nonlinear models, and that conditional or subgroup treatment effects with covariate adjustment may differ from marginal treatment effects. In this article, we demonstrate how covariate adjustment impacts the estimation of event rates and rate ratios with both closed form and simulation studies. Additionally, following the ICH E9 addendum on the estimand framework [2], we discuss the estimand framework for count and recurrent event data.

SURVIVAL ANALYSIS FOR RECURRENT EVENT DATA USING COUNTING PROCESS APPROACH: APPLICATION TO DIABETICS

Survival analysis is a branch of statistics for analyzing the duration of time until one or more events occur. Time to recurrence of diabetics including survival data. Diabetes can’t be cured but it can be controlled. Diabetics who don’t maintain their health and lifestyle will experience recurrence. Factors thought to influence the recurrence of diabetics are internal factors such as genetics and external factors such as lifestyle. The recurrence time of an object includes recurrent events because each object can experience the same recurrent event during the follow-up. One of the analysis to determine factors that are thought to influence the recurrence time of diabetics is survival analysis. Survival data can be modeled into a regression model if the survival time of an object is influenced by other factors. One of the regression models for survival data is Cox regression. One of the Cox regression models for recurrent event data is the AG model which uses a counting process approach. This study used data on the recurrence of diabetics at MH Thamrin Cileungsi Hospital. Based on data analysis, factors that influence the recurrence of diabetics are age, gender, and type of complication.

Joint Frailty Mixing Model for Recurrent Event Data with an Associated Terminal Event: Application to Hospital Readmission Data

Joint Frailty Mixing Model for Recurrent Event Data with an Associated Terminal Event: Application to Hospital Readmission Data

Semiparametric regression analysis of window-observation recurrent event data with multiple causes of failure

Semiparametric regression analysis of window-observation recurrent event data with multiple causes of failure

Evaluating dynamic and predictive discrimination for recurrent event models: use of a time-dependent C-index.

Interest in analyzing recurrent event data has increased over the past few decades. One essential aspect of a risk prediction model for recurrent event data is to accurately distinguish individuals with different risks of developing a recurrent event. Although the concordance index (C-index) effectively evaluates the overall discriminative ability of a regression model for recurrent event data, a local measure is also desirable to capture dynamic performance of the regression model over time. Therefore, in this study, we propose a time-dependent C-index measure for inferring the model's discriminative ability locally. We formulated the C-index as a function of time using a flexible parametric model and constructed a concordance-based likelihood for estimation and inference. We adapted a perturbation-resampling procedure for variance estimation. Extensive simulations were conducted to investigate the proposed time-dependent C-index's finite-sample performance and estimation procedure. We applied the time-dependent C-index to three regression models of a study of re-hospitalization in patients with colorectal cancer to evaluate the models' discriminative capability.

Variable Selection for Recurrent Events Using Heuristic Approaches: Identifying Informative Variables for Rehospitalization in Schizophrenia Patients

Introduction: Recurrent event data, as a generalization of survival data, are frequently observed in various areas of medical research, including sequential hospitalizations in patients with schizophrenia. As experiencing multiple relapses during schizophrenia can have many implications, such as self-harm or harm to others, loss of education or employment, or other adverse outcomes, identifying and determining the most critical factors related to relapses in this disorder is essential. This study aimed to utilize heuristic approaches for selecting predictor variables in the field of recurrent events with an application to schizophrenia disorder
 Methods: A two-step algorithm was employed to apply a combination of two variable selection methods, recursive feature elimination (RFE) and genetic algorithm feature selection (GAFS), and four modeling techniques: Gradient boosting (GB), artificial neural network (ANN), random forest (RF), and support vector machine (SVM) to simulated recurrent event datasets.
 Results: In most simulation scenarios, the results indicated that the combination of RFE and RF applied to the deviance residual (DR) outperforms the other methods. The RFE-RF-DR selected the following predictor variables: Number of children, age, marital status, and history of substance abuse.
 Conclusion: Our findings revealed that the proposed machine learning-based model is a promising technique for selecting predictor variables associated with a recurrent outcome when analyzing multivariate time-toevent data with recurrent events.

Regression analysis of general mixed recurrent event data.

In modern biomedical datasets, it is common for recurrent outcomes data to be collected in an incomplete manner. More specifically, information on recurrent events is routinely recorded as a mixture of recurrent event data, panel count data, and panel binary data; we refer to this structure as general mixed recurrent event data. Although the aforementioned data types are individually well-studied, there does not appear to exist an established approach for regression analysis of the three component combination. Often, ad-hoc measures such as imputation or discarding of data are used to homogenize records prior to the analysis, but such measures lead to obvious concerns regarding robustness, loss of efficiency, and other issues. This work proposes a maximum likelihood regression estimation procedure for the combination of general mixed recurrent event data and establishes the asymptotic properties of the proposed estimators. In addition, we generalize the approach to allow for the existence of terminal events, a common complicating feature in recurrent event analysis. Numerical studies and application to the Childhood Cancer Survivor Study suggest that the proposed procedures work well in practical situations.

On interquantile smoothness of censored quantile regression with induced smoothing.

Quantile regression has emerged as a useful and effective tool in modeling survival data, especially for cases where noises demonstrate heterogeneity. Despite recent advancements, non-smooth components involved in censored quantile regression estimators may often yield numerically unstable results, which, in turn, lead to potentially self-contradicting conclusions. We propose an estimating equation-based approach to obtain consistent estimators of the regression coefficients of interest via the induced smoothing technique to circumvent the difficulty. Our proposed estimator can be shown to be asymptotically equivalent to its original unsmoothed version, whose consistency and asymptotic normality can be readily established. Extensions to handle functional covariate data and recurrent event data are also discussed. To alleviate the heavy computational burden of bootstrap-based variance estimation, we also propose an efficient resampling procedure that reduces the computational time considerably. Our numerical studies demonstrate that our proposed estimator provides substantially smoother model parameter estimates across different quantile levels and can achieve better statistical efficiency compared to a plain estimator under various finite-sample settings. The proposed method is also illustrated via four survival datasets, including the HMO (health maintenance organizations) HIV (human immunodeficiency virus) data, the primary biliary cirrhosis (PBC) data, and soforth.

Semiparametric Trend Analysis for Stratified Recurrent Gap Times Under Weak Comparability Constraint

Recurrent event data are frequently encountered in many longitudinal studies where each individual may experience more than one event. Wang and Chen (Biometrics 56(3):789–794, 2000) proposed a comparability constraint to estimate the time trend for the gap times, where the gap time pairs that satisfy the constraint have the same conditional distribution. However, the comparable paired gap times are also independent. Therefore, the comparable gap time pairs will be subject to a stronger constraint than needed for the estimation. Thus their procedure is subject to information loss. Under the accelerated failure time model, we propose a new comparability constraint that can overcome the drawback mentioned above. The gap time pairs being selected by the proposed comparability constraint will still have the same distribution, but they do not need to be independent of each other. We showed that the proposed comparability constraint will utilize more gap time data pairs than the strong comparability. And we showed via various simulation studies that the variance will be smaller than Wang and Chen’s (2000) estimator. We apply the proposed method to the HIV Prevention Trial Network 052 study.

Clustered Coefficient Regression Models for Poisson Process with an Application to Seasonal Warranty Claim Data

Motivated by a product warranty claims dataset, we propose clustered coefficient regression models in a nonhomogeneous Poisson process for recurrent event data. The proposed method, referred as CLUPP, can estimate the group structure and parameters simultaneously. In our proposed method, a penalized regression approach is used to identify the group structure. Numerical studies show that the proposed approach can identify the group structure well, and outperforms traditional methods such as hierarchical clustering and K-means. We also establish theoretical properties, which show that the proposed estimators can converge to true parameters in high probability. In the end, we apply our proposed methods to the product warranty claims dataset, which achieve better prediction than the state-of-the-art methods.