Nonparametric group sequential methods for recurrent and terminal events from multiple follow-up windows.

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.

This research develops multivariable restricted time models appropriate for analysis of recurrent events data, where data is repurposed into censored longitudinal time-to-first-event outcomes in τ-length follow-up windows. We develop two approaches for addressing the censored nature of the outcomes: a pseudo-observation (PO) approach and a multiple-imputation (MI) approach. Each of these approaches allows for complete data methods, such as generalized estimating equations, to be used for the analysis of the newly constructed correlated outcomes. Through simulation, this manuscript assesses the performance of the proposed PO and MI methods. Both PO and MI approaches show attractive results with either correlated or independent gap times in an individual. We also demonstrate how to apply the proposed methods in the data from azithromycin in Chronic Obstructive Pulmonary Disease Trial.

There have been many advances in statistical methodology for the analysis of recurrent event data in recent years. Multiplicative semiparametric rate-based models are widely used in clinical trials, as are more general partially conditional rate-based models involving event-based stratification. The partially conditional model provides protection against extra-Poisson variation as well as event-dependent censoring, but conditioning on outcomes post-randomization can induce confounding and compromise causal inference. The purpose of this article is to examine the consequences of model misspecification in semiparametric marginal and partially conditional rate-based analysis through omission of prognostic variables. We do so using estimating function theory and empirical studies.

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.

In this paper, we consider the analysis of recurrent event data that examines the differences between two treatments. The outcomes that are considered in the analysis are the pre-randomisation event count and post-randomisation times to first and second events with associated cure fractions. We develop methods that allow pre-randomisation counts and two post-randomisation survival times to be jointly modelled under a Poisson process framework, assuming that outcomes are predicted by (unobserved) event rates. We apply these methods to data that examine the difference between immediate and deferred treatment policies in patients presenting with single seizures or early epilepsy. We find evidence to suggest that post-randomisation seizure rates change at randomisation and following a first seizure after randomisation. We also find that there are cure rates associated with the post-randomisation times to first and second seizures. The increase in power over standard survival techniques, offered by the joint models that we propose, resulted in more precise estimates of the treatment effect and the ability to detect interactions with covariate effects.

Joint models for recurrent and terminal events have not been yet developed for clustered data. The goals of our study are to develop a statistical framework for modelling clustered recurrent and terminal events and to perform dynamic predictions of the terminal event in family studies. We propose a joint nested frailty model for colonoscopy screening visits and colorectal cancer onset in Lynch Syndrome families. The screening and disease processes could each depend on individuals' screening history and other measured covariates and be correlated within families; our approach allows for familial correlations to affect both the visit process and the terminal event and the dependence between the two processes is specified through frailty distributions. We provide dynamic predictions of colorectal cancer risk for an individual conditional on his/her own screening history, his/her family history of screening and disease and other important clinical covariates. We apply our model to 18 Lynch Syndrome families from Newfoundland for individualized dynamic predictions of colorectal cancer risks. We demonstrate that the screening visits are non-ignorable for estimating the disease risks, and the joint nested frailty model improves dynamic prediction accuracies compared to existing joint frailty models after accounting for familial and individual screening and cancer histories.

Recurrence time data can be regarded as a specific type of correlated survival data in which recurrent event times of a subject are stochastically ordered. Given the ordinal nature of recurrence times, this article focuses on conditional regression analysis. A semiparametric hazards model, including the structural and episode-specific parameters, is proposed for recurrence time data. In this model the order of episodes serves as the stratification variable. Estimation of the structural parameter can be constructed on the basis of all of the observed recurrence times. The structural parameter is estimated by the profile-likelihood approach. Although the structural parameter estimator is asymptotically normal, the episode-specific parameters may or may not be estimated consistently due to the sparseness of data for specific events. Examples are presented to illustrate the performance of the estimators of the structural and episode-specific parameters. An extension of the univariate recurrent events to the bivariate events, which occur repeatedly and sequentially, is discussed with an example.

In a recurrent event 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 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 theoretical mean squared error between the model and the true expected cumulative number of recurrent events and an inseparability term that does not depend on the model. This decomposition is further illustrated on simulations studies. It is also shown that this score should be used in comparison with a reference model, such as a nonparametric estimator that does not include the covariates. Finally, the score is applied for the prediction of hospitalisations on a dataset of patients suffering from atrial fibrillation and a comparison of the prediction performances of different models, such as the Cox model, the Aalen Model or the Ghosh and Lin model, is investigated.

111 Background: Local prostate radiotherapy (LPRT) is associated with improved overall survival in patients with low metastatic burden (MB) and is now standard of care. However, the role of LPRT in reducing symptomatic local events (SLE) in metastatic prostate cancer (MPC) remains unclear and requires long-term follow-up. The purpose of this study was two-fold: i) identify the risk factors associated with SLE, and ii) evaluate the association between LPRT and SLE in MPC. Methods: We conducted a retrospective, population-based cohort study of patients diagnosed with initial MPC between 2005 and 2016. Patients were identified through the Alberta Cancer Registry and patient, tumour, and treatment characteristics were collected by chart review. Data were linked to physician billing claims between 2004 and 2017 for diagnostic or therapeutic procedures potentially related to genitourinary (GU) and gastrointestinal (GI) SLE including percutaneous nephrostomy (PCN) and ureteric stent insertion (USI), cystoscopy, TURP, TURBT, colonoscopy and proctosigmoidoscopy. Both Andersen-Gill recurrent event and multivariable Cox regression time to first event analyses were conducted to evaluate the effect of LPRT on the occurrence of these procedures. Patients who underwent radical prostatectomy were excluded. LPRT was defined as 40 Gy or higher total dose to the prostate within one year of diagnosis. Patients with a SLE occurring after diagnosis but prior to LPRT were allocated to the control group. MB was defined as per STAMPEDE. Covariates for both models included MB, age at diagnosis, PSA at diagnosis, clinical T- and N-stage, and Gleason score (GS). Results: Of a total cohort of 1363 patients, 745 (54.7%) had high MB and 450 (33%) had low MB. Fifty-four (4%) received LPRT, of which 14.8% had high MB. Of those receiving LPRT, median PSA was 9.4, 79.6% had GS of 8-10, and 59.3% had T3-T4 disease. One or more SLE were observed in 43.5% and 37% of the control and LPRT groups, respectively. Among those with SLE, the median SLE frequency was 2 (interquartile range [IQR], 2-5) and 1 (IQR, 1-2.3) for the control and LPRT groups, respectively. On recurrent event analysis, LPRT was associated with lower risk of composite GU SLE (HR 0.34, 95% CI 0.17-0.67; p = 0.002), PCN and USI (HR 0.20, 95% CI 0.05-0.84; p = 0.027) and cystoscopy (HR 0.38, 95% CI 0.15-0.96; p = 0.041). Risk factors for GU SLE were T4 disease, GS of 8-10 and unknown GS. Risk factors for PCN and USI were T3, TX and N1 disease, GS of 8-10 and unknown GS. On time to first event analysis, there were no statistically significant differences for all outcomes between the control and LPRT groups. MB was not a risk factor for SLE in both analyses. Conclusions: LPRT was associated with lower risk for recurrent GU SLE, PCN and USI, and cystoscopy. The associated benefit in SLE reduction with LPRT warrants further study to determine if this effect is modified by MB and whether there may be a role for LPRT in patients with high MB.

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.

ABSTRACTMedical care costs are commonly used by health policy-makers and decision-maker for evaluating health care service and decision on treatment plans. This type of data is commonly recorded in surveillance systems when inpatient or outpatient care service is provided. In this paper, we formulate medical cost data as a recurrent marker process, which is composed of recurrent events (inpatient or outpatient cares) and repeatedly measured marker measurements (medical charges). We consider nonparametric estimation of the quantiles of cost distribution among survivors in the absence or presence of competing terminal events. Statistical methods are developed for quantile estimation of the cost distribution for the purposes of evaluating cost performance in relation to recurrent events, marker measurements and time to the terminal event for different competing risk groups. The proposed approaches are illustrated by an analysis of data from the Surveillance, Epidemiology, and End Results (SEER) and Medicare linked database.

Recurrent event and terminal event data commonly arise in clinical and observational studies. To evaluate the efficacy of a treatment effect for both types of events, a composite endpoint has been used as a possible assessment, particularly when faced with high costs and a longer follow-up study. To model recurrent event processes complicated by the existence of a terminal event, joint frailty modeling has been typically employed. In this study, the objective was to develop some target-driven response adaptive randomization strategies using a composite endpoint based on joint frailty modeling. We first implemented a balanced randomized design and then investigated the response adaptive randomization. The former is intuitively first adopted while the latter is expected to be desirable and ethical in terms of allocating more subjects to the more effective treatment. The results show that the proposed procedures using a composite endpoint are capable of reducing the number of trial participants who receive inferior treatment while simultaneously reaching a desired optimal target as compared to a balanced randomized design. The R shiny application for calculating the sample size and allocation probabilities is also available. Finally, two clinical trials were used as pilot datasets to introduce the proposed procedures.

Recurrent events data refers to the observation of individuals, which contains the recurrent event time of interest. In this paper, we focus on the statistical analysis of recurrent event, and present a composite model based on the proportional intensity function and additive hazard function, and then prove the consistency and asymptotic properties of the estimation under certain regularity conditions.