Regression analysis of general mixed recurrent event data.

Introduction: Recurrent event data are common in many longitudinal studies. Often, a terminating event such as death can be correlated with the recurrent event process. A shared frailty model applied to account for the association between recurrent and terminal events. In some situations, a fraction of subjects experience neither recurrent events nor death; these subjects are cured.
 Methods: In this paper, we discussed the Bayesian approach of a joint frailty model for recurrent and terminal events in the presence of cure fraction. We compared estimates of parameters in the Frequentist and Bayesian approaches via simulation studies in various sample sizes; we applied the joint frailty model in the presence of cure fraction with Frequentist and Bayesian approaches for breast cancer.
 Results: In small sample size Bayesian approach compared to Frequentist approach had a smaller standard error and mean square error, and the coverage probabilities close to nominal level of 95%. Also, in Bayesian approach, the sampling means of the estimated standard errors were close to the empirical standard error.
 Conclusion: The simulation results suggested that when sample size was small, the use of Bayesian joint frailty model in the presence of cure fraction led to more efficiency in parameter estimation and statistical inference.

Recurrent events are frequently encountered in biomedical studies. Evaluating the covariates effects on the marginal recurrent event rate is of practical interest. There are mainly two types of rate models for the recurrent event data: the multiplicative rates model and the additive rates model. We consider a more flexible additive-multiplicative rates model for analysis of recurrent event data, wherein some covariate effects are additive while others are multiplicative. We formulate estimating equations for estimating the regression parameters. The estimators for these regression parameters are shown to be consistent and asymptotically normally distributed under appropriate regularity conditions. Moreover, the estimator of the baseline mean function is proposed and its large sample properties are investigated. We also conduct simulation studies to evaluate the finite sample behavior of the proposed estimators. A medical study of patients with cystic fibrosis suffered from recurrent pulmonary exacerbations is provided for illustration of the proposed method.

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.

Few methods are currently available for group sequential analysis of recurrent events data subject to a terminal event in the clinical trial setting. This research helps fill this gap by developing a completely nonparametric group sequential monitoring procedure for use with the two-sample Tayob and Murray statistic. Advantages of the Tayob and Murray statistic include high power to detect treatment differences when there is correlation between recurrent event times or between recurrent and terminal events in an individual. This statistic does not suffer bias from dependent censoring, regardless of the correlation between event times in an individual. This manuscript briefly reviews the Tayob and Murray statistic, develops and describes how to use methods for its group sequential analysis, and through simulation, compares its operating characteristics with those of Cook and Lawless, which is currently in use as the only available nonparametric method for group sequential analysis of recurrent event data. The merits of our proposed approach are most clearly demonstrated when gap times between recurrent events are correlated; when gap times between events are independent, the Cook and Lawless method is difficult to beat. Simulations demonstrate that as correlation between recurrent event times grows, the reduction in power using the Cook and Lawless approach is substantial when compared to our method. Finally, we use our method to analyze recurrent acute exacerbation outcomes from the azithromycin in chronic obstructive pulmonary disease trial.

Recurrent event data analyses are usually conducted under the assumption that the censoring time is independent of the recurrent event process. In many applications the censoring time can be informative about the underlying recurrent event process, especially in situations where a correlated failure event could potentially terminate the observation of recurrent events. In this article, we consider a semiparametric model of recurrent event data that allows correlations between censoring times and recurrent event process via frailty. This flexible framework incorporates both time-dependent and time-independent covariates in the formulation, while leaving the distributions of frailty and censoring times unspecified. We propose a novel semiparametric inference procedure that depends on neither the frailty nor the censoring time distribution. Large sample properties of the regression parameter estimates and the estimated baseline cumulative intensity functions are studied. Numerical studies demonstrate that the proposed methodology performs well for realistic sample sizes. An analysis of hospitalization data for patients in an AIDS cohort study is presented to illustrate the proposed method.

Panel count data often occur in a long-term recurrent event study, where the exact occurrence time of the recurrent events is unknown, but only the occurrence count between any two adjacent observation time points is recorded. Most traditional methods only handle panel count data for a single type of event. In this paper, we propose a Bayesian semiparameteric approach to analyze panel count data for multiple types of events. For each type of recurrent event, the proportional mean model is adopted to model the mean count of the event, where its baseline mean function is approximated by monotone I-splines. The correlation between multiple types of events is modeled by common frailty terms and scale parameters. Unlike many frequentist estimating equation methods, our approach is based on the observed likelihood and makes no assumption on the relationship between the recurrent process and the observation process. Under the Poisson counting process assumption, we develop an efficient Gibbs sampler based on novel data augmentation for the Markov chain Monte Carlo sampling. Simulation studies show good estimation performance of the baseline mean functions and the regression coefficients; meanwhile, the importance of including the scale parameter to flexibly accommodate the correlation between events is also demonstrated. Finally, a skin cancer data example is fully analyzed to illustrate the proposed methods.

Panel-count data arise when each study subject is observed only at discrete time points in a recurrent event study, and only the numbers of the event of interest between observation time points are recorded (Sun and Zhao, 2013). However, sometimes the exact number of events between some observation times is unknown and what we know is only whether the event of interest has occurred. In this article, we will refer this type of data to as mixed panel-count data and propose a likelihood-based semiparametric regression method for their analysis by using the nonhomogeneous Poisson process assumption. However, we establish the asymptotic properties of the resulting estimator by employing the empirical process theory and without using the Poisson assumption. Also, we conduct an extensive simulation study, which suggests that the proposed method works well in practice. Finally, the method is applied to a Childhood Cancer Survivor Study that motivated this study.

Recurrent events arise in many longitudinal medical studies where time to a terminal event or failure is the primary endpoint. With incomplete follow-up data, the analysis of recurrent events is a challenge owing to their association with the failure. One specific quantity of interest rarely addressed in the statistical literature is the recurrence frequency at the failure time; an example is hospitalization frequency, which is often used as a rough measure of lifetime medical cost. In this article we show that a marginal model (e.g., the log-linear model) of the recurrence frequency, although desirable, is typically not identifiable. For this reason, we advocate modeling the recurrent events and the failure time jointly, and propose an approach to forming semiparametric joint models from prespecified marginal ones. We suggest two conceptually simple and nested regression models aiming at the recurrence frequency as a mark of the failure and at the process of recurrent events. We formulate monotone estimating functions and propose novel interval-estimation procedures to accommodate non-smooth estimating functions. The resulting estimators are consistent and asymptotically normal. Simulation studies and the application to an AIDS clinical trial exhibit that these proposals are easy to implement and reliable for practical use. Finally, we generalize our proposals to marked recurrent events, and also devise a global inference procedure for recurrent events of multiple types.

CABG Improves Outcomes in Patients With Ischemic Cardiomyopathy: 10-Year Follow-Up of the STICH Trial

A nonparametric test for the equality of counting processes with panel count data

Panel count data typically refer to data arising from studies with recurrent events, in which subjects are observed only at discrete time points rather than under continuous observations. We investigate a general situation where a recurrent event process is eventually truncated by an informative terminal event and we are particularly interested in behaviors of the recurrent event process near the terminal event. We propose a reversed mean model for estimating the mean function of the recurrent event process. We develop a two-stage sieve likelihood-based method to estimate the mean function, which overcomes the computational difficulties arising from a nuisance functional parameter involved in the likelihood. The consistency and the convergence rate of the two-stage estimator are established. Allowing for the convergence rate slower than the standard rate, we develop the general weak convergence theory of M-estimators with a nuisance functional parameter, and then apply it to the proposed estimator for deriving the asymptotic normality. Furthermore, a class of two-sample tests is developed. The proposed methods are evaluated with extensive simulation studies and illustrated with panel count data from the Chinese Longitudinal Healthy Longevity Study.

Many diseases recur after recovery, for example, recurrences in cancer and infections. However, research is often focused on analysing only time-to-first recurrence, thereby ignoring any subsequent recurrences that may occur after the first. Statistical models for the analysis of recurrent events are available, of which the extended Cox proportional hazards frailty model is the current state-of-the-art. However, this model is too statistically complex for computationally efficient application in high-dimensional data sets, including genome-wide association studies (GWAS). Here, we develop an application for fast and accurate recurrent event analysis in GWAS, called SPARE (SaddlePoint Approximation for Recurrent Event analysis). In SPARE, every DNA variant is tested for association with recurrence risk using a modified score statistic. A saddlepoint approximation is implemented to achieve statistical accuracy. SPARE controls the Type I error, and its statistical power is similar to existing recurrent event models, yet SPARE is significantly faster. An application of SPARE in a recurrent event GWAS on bladder cancer for 6.2 million DNA variants in 1,443 individuals required less than 15 min, whereas existing recurrent event methods would require several weeks.

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.

This article provides a review of recently developed dynamic stochastic models for recurrent events, in particular, recurrent events arising from monitoring of repairable systems. Inference methods such as the estimation of model parameters and goodness‐of‐fit testing are also discussed. The procedures described are demonstrated using a reliability data from load–haul–dump machines.

Modeling recurrent event data with multiple event types has drawn interest in recent biomedical studies due to its flexibility for understanding different risk factors for multiple recurrent event processes. However, in such data type, missing event type appears frequently because of various reasons such as recording ignorance or resource limitation. In this study, we aim to propose an inverse probability weighted estimation that is commonly used in the missing data literature to correct possibly biased estimation by a complete-case analysis. This approach is not limited to a specific form of the recurrent event model. We derive the large sample theory in a general form. We demonstrate that our approach can be applied to either multiplicative or additive rates model with practical sample size via comprehensive simulations. Nonmucoid and mucoid Pseudomonas aeruginosa infections of 14888 patients in 2016 Cystic Fibrosis Foundation Patient Registry data are analyzed to show that, without including 12% events with missing event type in the analysis, several factors may be misidentified as risk factors for the nonmucoid type of infections.