System unavailability analysis based on window‐observed recurrent event data

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.

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.

Warranty return data from repairable systems, such as home appliances, lawn mowers, computers and automobiles, result in recurrent event data. The nonhomogeneous Poisson process (NHPP) model is used widely to describe such data. Seasonality in the repair frequencies and other variabilities, however, complicate the modeling of recurrent event data. Not much work has been done to address the seasonality, and this paper provides a general approach for the application of NHPP models with dynamic covariates to predict seasonal warranty returns. The methods presented here, however, can be applied to other applications that result in seasonal recurrent event data. A hierarchical clustering method is used to stratify the population into groups that are more homogeneous than the overall population. The stratification facilitates modeling the recurrent event data with both time-varying and time-constant covariates. We demonstrate and validate the models using warranty claims data for two different types of products. The results show that our approach provides important improvements in the predictive power of monthly events compared with models that do not take the seasonality and covariates into account.

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.

In studies involving diseases associated with high rates of mortality, trials are frequently conducted to evaluate the effects of therapeutic interventions on recurrent event processes terminated by death. In this setting, cumulative mean functions form a natural basis for inference for questions of a health economic nature, and Ghosh and Lin (2000) recently proposed a relevant class of test statistics. Trials of patients with cancer metastatic to bone, however, involve multiple types of skeletal complications, each of which may be repeatedly experienced by patients over their lifetime. Traditionally the distinction between the various types of events is ignored and univariate analyses are conducted based on a composite recurrent event. However, when the events have different impacts on patients' quality of life, or when they incur different costs, it can be important to gain insight into the relative frequency of the specific types of events and treatment effects thereon. This may be achieved by conducting separate marginal analyses with each analysis focusing on one type of recurrent event. Global inferences regarding treatment benefit can then be achieved by carrying out multiplicity adjusted marginal tests, more formal multiple testing procedures, or by constructing global test statistics. We describe methods for testing for differences in mean functions between treatment groups which accommodate the fact that each particular event process is ultimately terminated by death. The methods are illustrated by application to a motivating study designed to examine the effect of bisphosphonate therapy on the incidence of skeletal complications among patients with breast cancer metastatic to bone. We find that there is a consistent trend towards a reduction in the cumulative mean for all four types of skeletal complications with bisphosphonate therapy; there is a significant reduction in the need for radiation therapy for the treatment of bone. The global test suggests that bisphosphonate therapy significantly reduces the overall number of skeletal complications.

SummaryAutobiographical memories are thought to serve three basic functions: self‐definition, social connection, and directing future behavior. Previous research suggests that the function a memory comes to serve may differ by the type of event recalled (e.g., single unique events vs. repeated or recurring events). In two studies, we compared memories for different event types on function served. Results from Study 1 suggest that narratives of single events serve more of a self and directive function compared with recurring events, whereas recurring events serve more of a social function. Extended events, however, were high on all three functions. Study 2 specifically examined single and recurring events. Results replicated and extended Study 1 using both narrative coding and questionnaire measures. Implications of the examination of multiple event types and functional approaches to autobiographical memory for understanding links between experiences and psychological outcomes are discussed. Copyright © 2013 John Wiley & Sons, Ltd.

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.

BackgroundDespite over a decade of efforts to reduce the adverse event rate in healthcare, the rate has remained relatively unchanged. Root cause analysis (RCA) is a process used by hospitals...

BackgroundGlobally, the estimated recurrent childbirth of one forth of women happens every two years or fewer. Next to Nigeria, Ethiopia is the second populist country in Africa and the first populist country in sub-Saharan Africa which consists of over 114 million population. There are prevalent short successive birth intervals problems in underdeveloped nations such as Ethiopia that contributes to adverse effects on mother and child health. However, studies that explore recurrent birth events and associated factors are very limited. Thus, this study aimed to explore and model the recurrent birth event by considering its subsequent within a mother and identifying its important determinants. As a result, the research findings of this study will be one of the preliminary research papers on the recurrent birth events that take into account the subsequent event and enable to be input for the policymakers, health institutions, and future researchers.MethodsA total of 4676 mothers with their 16833 corresponding children were involved in this study. The data was obtained from the 2019 Ethiopian Mini Demographic and Health Survey (EMDHS). In this study, extended cox regression models such as Andersen-Gill (AG), Prentice, Williams, and Peterson total time (PWP-TT) model, PWP-gap time (PWP-GT) model, and Frailty model were employed. These all models are used to consider recurrent events within mothers and determine the potential determinants. AG, PWP-TT, and PWP-GT estimate the effect of covariates by considering the correlation between event times for a person can be explained by past events given the covariates, kth event since the entry time, kth event since the time from the previous event, respectively.ResultsAmong mothers who have first and ninth recurrent birth events, 75.5% and 80.1% of them respectively were rural residents while 57.6% and 70.6% of them respectively were a place of delivery in the health sector. The highest prevalence of first recurrent births (44.3%) was obtained from Muslim mothers. Mothers' education level (HR: 1.210; 95%CI: 1.010, 1.460), mothers' age at first birth (HR: 0.713; 95% CI: 0.614, 0.828), household wealth index (HR: 0.776; 95% CI: 0.625, 0.965), child mortality (HR: 0.673; 95%CI: 0.514, 0.881), household size (HR: 1.914; 95%CI:1.539,2.381) and sex of child (HR:0.836; 95%CI = 0.755,0.926) were important determinants of recurrent birth event. This indicates mothers’ education level and household size were positively associated with recurrent birth events. Whereas mothers’ age at first birth, household wealth index, child mortality, and sex of the child was negatively associated with recurrent birth events.ConclusionThe WHO recommends a minimum of 33 months between two consecutive births, which is longer than the Ethiopian recurrent birth intervals observed in this study. The highest recurrent birth occurred during the age of fewer than twenty years old of mothers at first birth as compared to mothers whose age was older at first birth. Mothers, children, and household characteristics had significant effects on recurrent birth events. We authors would like to recommend communities, governmental and non-governmental stakeholders consider the associated factors of frequent recurrence of birth noticed in this study. Besides, we would also like to recommend women start birth while they got mature in age to reduce frequent recurrent birth and its corresponding adverse effects.

To investigate pairwise interactions arising from recurrent event processes in a longitudinal network, the framework of the stochastic block model is followed, where every node belongs to a latent group and interactions between node pairs from two specified groups follow a conditional nonhomogeneous Poisson process. Our focus lies on discrete observation times, which are commonly encountered in reality for cost-saving purposes. The variational EM algorithm and variational maximum likelihood estimation are applied for statistical inference. A specific method based on the defined distribution function F and self-consistency algorithm for recurrent events is used when estimating the intensity functions of edges. Numerical simulations illustrate the performance of our proposed estimation procedure in uncovering the underlying structure in the longitudinal networks with recurrent event processes. The dataset of interactions between French schoolchildren for influenza monitoring is analyzed.

Recurrent events such as repeated hospital admissions for the same health outcome occur frequently in environmental health studies. Dewanji and Moolgavkar proposed a flexible parametric model and a conditional likelihood analysis for recurrent events based on a Poisson process formulation. In this paper, we examine the statistical properties of the Dewanji-Moolgavkar (DM) estimator of the risk of an adverse health outcome associated with environmental exposures based on recurrent event data using computer simulation. We also compare the DM approach with both case-crossover analysis for multiple observations and time series analysis when there are no subject-specific covariates. When using a correctly specified model, the DM method produced better estimates with respect to relative mean square error when each subject had constant or curved baseline intensity functions than it did when baseline intensities were increasing or decreasing in a linear fashion. For under-specified models, the DM method outperformed case-crossover analysis for decreasing straight line intensity functions, was outperformed by case-crossover analysis for increasing straight line intensity functions, and was roughly equivalent to case-crossover analysis for constant and curved intensity functions. Case-crossover analysis produced superior risk estimates more frequently than the other two methods in the cases considered here, especially for linear representations of the baseline intensities.

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.