Types Of Recurrent Events Research Articles

Determination of correlations in multivariate count data with informative observation times.

We consider there are various types of recurrent events and the total number of occurrences are collected at the random observation times. It has concerned that the observation process may not be independent to the multivariate event processes, hence the total counts and observation times may be correlated and the dependence may exist among different types of the event processes as well. Many methods have developed nonparametric models to accommodate such unknown structures; however, it is difficult to assess and directly quantify their correlation relationships. A multivariate frailty model is proposed to this study, in which the event and observation processes are linked by frailty variables whose joint distribution can be implicitly specified through the multivariate normal distribution with some unknown covariance matrix. The Bayesian inference method is conducted to obtain the estimates of the regression coefficients and correlation parameters. We use a form of trigonometric functions to represent the covariance matrix, so that it meets the positive-definiteness condition efficiently during the estimation schemes. The simulation studies demonstrate the utility of the proposed models. We apply the model to a skin cancer prevention study, and aim to determine the covariate and association effects. We found treatment is significant in determining the duration of examination times; prior-counts, age and gender are significant variables on the occurrence rates of tumor counts. Using the covariance matrix to access the underlying dependent structure, the mutual correlations among them are all positive, and the basal cell counts are more related to the examination times.

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.

Bayesian Semiparametric Regression Analysis of Multivariate Panel Count Data

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.

Semiparametric analysis of multivariate panel count data with nonlinear interactions.

Multivariate panel count data frequently arise in follow up studies involving several related types of recurrent events. For univariate panel count data, several varying coefficient models have been developed. However, varying coefficient models for multivariate panel count data remain to be studied. In this paper, we propose a varying coefficient mean model for multivariate panel count data to describe the possible nonlinear interact effects between the covariates and the local logarithm partial likelihood procedure is considered to estimate the unknown covariate effects. Furthermore, a Breslow-type estimator is constructed for the baseline mean functions. The consistency and asymptotic normality of the proposed estimators are established under some mild conditions. The utility of the proposed approach is evaluated by some numerical simulations and an application to a dataset of skin cancer study.

Endovascular Therapy Versus Medical Treatment for Symptomatic Intracranial Artery Stenosis

Background Intracranial atherosclerotic stenosis (ICAS) is an arterial narrowing in the brain that can cause stroke. Endovascular therapy and medical management may be used to prevent recurrent ischaemic stroke caused by ICAS. However, there is no consensus on the best treatment for people with ICAS. Objectives To compare the safety and efficacy of endovascular therapy (ET) plus conventional medical treatment (CMT) with CMT alone for the management of symptomatic ICAS. Search methods We searched the Cochrane Stroke Group Trials Register (30 August 2019), Cochrane Central Register of Controlled Trials (CENTRAL: to 30 August 2019), MEDLINE Ovid (1946 to 30 August 2019), Embase Ovid (1974 to 30 August 2019), Scopus (1960 to 30 August 2019), Science Citation Index Web of Science (1900 to 30 July 2019), Academic Source Complete EBSCO (ASC: 1982 to 30 July 2019), and China Biological Medicine Database (CBM: 1978 to 30 July 2019). We also searched the following trial registers: ClinicalTrials.gov, WHO International Clinical Trials Registry Platform, and Stroke Trials Registry. We also contacted trialists and researchers where additional information was required. Selection criteria Randomised controlled trials (RCTs) comparing ET plus CMT with CMT alone for the treatment of symptomatic ICAS. ET modalities included angioplasty alone, balloon-mounted stent, and angioplasty followed by placement of a self-expanding stent. CMT included antiplatelet therapy in addition to control of risk factors such as hypertension, hyperlipidaemia, and diabetes. Data collection and analysis Two review authors independently screened trials to select potentially eligible RCTs and extracted data. Any disagreements were resolved by discussing and reaching consensus decisions with the full team. We assessed risk of bias and applied the GRADE approach to assess the quality of the evidence. The primary outcome was death of any cause or non-fatal stroke of any type within three months of randomisation. Secondary outcomes included any-cause death or non-fatal stroke of any type more than three months of randomisation, ipsilateral stroke, type of recurrent event, death, restenosis, dependency, and health-related quality of life. Main results We included three RCTs with 632 participants who had symptomatic ICAS with an age range of 18 to 85 years. The included trials had high risks of performance bias and other potential sources of bias due to the impossibility of blinding of the endovascular intervention and early termination of the trials. Moreover, one trial had a high risk of attrition bias because of the high rate of loss of one-year follow-up and the high proportion of participants transferred from endovascular therapy to medical management. The quality of evidence ranged from low to moderate, downgraded for imprecision. Compared to CMT, ET probably results in a higher rate of 30-day death or stroke (risk ratio (RR) 3.07, 95% confidence interval (CI) 1.80 to 5.24; 3 RCTs, 632 participants, moderate-quality evidence), 30-day ipsilateral stroke (RR 3.54, 95% CI 1.98 to 6.33; 3 RCTs, 632 participants, moderate-quality evidence), 30-day ischaemic stroke (RR 2.52, 95% CI 1.37 to 4.62; 3 RCTs, 632 participants, moderate-quality evidence), and 30-day haemorrhagic stroke (RR 15.53, 95% CI 2.10 to 115.16; 3 RCTs, 632 participants, low-quality evidence). ET was also likely associated with a worse outcome in one-year death or stroke (RR 1.69, 95% CI 1.21 to 2.36; 3 RCTs, 632 participants, moderate-quality evidence), one-year ipsilateral stroke (RR 2.28, 95% CI 1.52 to 3.42; 3 RCTs, 632 participants, moderate-quality evidence), one-year ischaemic stroke (RR 2.07, 95% CI 1.37 to 3.13; 3 RCTs, 632 participants, moderate-quality evidence), and one-year haemorrhagic stroke (RR 10.13, 95% CI 1.31 to 78.51; 2 RCTs, 521 participants, low-quality evidence). There were no significant differences between ET and CMT in 30-day transient ischaemic attacks (TIA) (RR 0.52, 95% CI 0.11 to 2.35, P = 0.39; 2 RCTs, 181 participants, moderate-quality evidence), 30-day death (RR 5.53, 95% CI 0.98 to 31.17, P = 0.05; 3 RCTs, 632 participants, low-quality evidence), one-year TIA (RR 0.82, 95% CI 0.32 to 2.12; 2 RCTs, 181 participants, moderate-quality evidence), one-year death (RR 1.20, 95% CI 0.50 to 2.86, P = 0.68; 3 RCTs, 632 participants, moderate-quality evidence), and one-year dependency (RR 1.90, 95% CI 0.91 to 3.97, P = 0.09; 3 RCTs, 613 participants, moderate-quality evidence). No data on restenosis and health-related quality of life for meta-analysis were available from the included trials. Two RCTs are ongoing. Authors' conclusions This systematic review provides moderate-quality evidence showing that ET, compared with CMT, in people with recent symptomatic severe intracranial atherosclerotic stenosis probably does not prevent recurrent stroke and appears to carry an increased hazard. The impact of delayed ET intervention (more than three weeks after a qualifying event) is unclear and may warrant further study.

Maximum Likelihood Estimation for Semiparametric Regression Models With Panel Count Data.

Panel count data, in which the observation for each study subject consists of the number of recurrent events between successive examinations, are commonly encountered in industrial reliability testing, medical research, and various other scientific investigations. We formulate the effects of potentially time-dependent covariates on one or more types of recurrent events through non-homogeneous Poisson processes with random effects. We adopt nonparametric maximum likelihood estimation under arbitrary examination schemes and develop a simple and stable EM algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that achieves the semiparametric efficiency bound and can be estimated through profile likelihood. We evaluate the performance of the proposed methods through extensive simulation studies and present a skin cancer clinical trial.

Endovascular therapy versus medical treatment for symptomatic intracranial artery stenosis.

Intracranial atherosclerotic stenosis (ICAS) is an arterial narrowing in the brain that can cause stroke. Endovascular therapy and medical management may be used to prevent recurrent ischaemic stroke caused by ICAS. However, there is no consensus on the best treatment for people with ICAS. To compare the safety and efficacy of endovascular therapy (ET) plus conventional medical treatment (CMT) with CMT alone for the management of symptomatic ICAS. We searched the Cochrane Stroke Group Trials Register (30 August 2019), Cochrane Central Register of Controlled Trials (CENTRAL: to 30 August 2019), MEDLINE Ovid (1946 to 30 August 2019), Embase Ovid (1974 to 30 August 2019), Scopus (1960 to 30 August 2019), Science Citation Index Web of Science (1900 to 30 July 2019), Academic Source Complete EBSCO (ASC: 1982 to 30 July 2019), and China Biological Medicine Database (CBM: 1978 to 30 July 2019). We also searched the following trial registers: ClinicalTrials.gov, WHO International Clinical Trials Registry Platform, and Stroke Trials Registry. We also contacted trialists and researchers where additional information was required. Randomised controlled trials (RCTs) comparing ET plus CMT with CMT alone for the treatment of symptomatic ICAS. ET modalities included angioplasty alone, balloon-mounted stent, and angioplasty followed by placement of a self-expanding stent. CMT included antiplatelet therapy in addition to control of risk factors such as hypertension, hyperlipidaemia, and diabetes. Two review authors independently screened trials to select potentially eligible RCTs and extracted data. Any disagreements were resolved by discussing and reaching consensus decisions with the full team. We assessed risk of bias and applied the GRADE approach to assess the quality of the evidence. The primary outcome was death of any cause or non-fatal stroke of any type within three months of randomisation. Secondary outcomes included any-cause death or non-fatal stroke of any type more than three months of randomisation, ipsilateral stroke, type of recurrent event, death, restenosis, dependency, and health-related quality of life. We included three RCTs with 632 participants who had symptomatic ICAS with an age range of 18 to 85 years. The included trials had high risks of performance bias and other potential sources of bias due to the impossibility of blinding of the endovascular intervention and early termination of the trials. Moreover, one trial had a high risk of attrition bias because of the high rate of loss of one-year follow-up and the high proportion of participants transferred from endovascular therapy to medical management. The quality of evidence ranged from low to moderate, downgraded for imprecision. Compared to CMT, ET probably results in a higher rate of 30-day death or stroke (risk ratio (RR) 3.07, 95% confidence interval (CI) 1.80 to 5.24; 3 RCTs, 632 participants, moderate-quality evidence), 30-day ipsilateral stroke (RR 3.54, 95% CI 1.98 to 6.33; 3 RCTs, 632 participants, moderate-quality evidence), 30-day ischaemic stroke (RR 2.52, 95% CI 1.37 to 4.62; 3 RCTs, 632 participants, moderate-quality evidence), and 30-day haemorrhagic stroke (RR 15.53, 95% CI 2.10 to 115.16; 3 RCTs, 632 participants, low-quality evidence). ET was also likely associated with a worse outcome in one-year death or stroke (RR 1.69, 95% CI 1.21 to 2.36; 3 RCTs, 632 participants, moderate-quality evidence), one-year ipsilateral stroke (RR 2.28, 95% CI 1.52 to 3.42; 3 RCTs, 632 participants, moderate-quality evidence), one-year ischaemic stroke (RR 2.07, 95% CI 1.37 to 3.13; 3 RCTs, 632 participants, moderate-quality evidence), and one-year haemorrhagic stroke (RR 10.13, 95% CI 1.31 to 78.51; 2 RCTs, 521 participants, low-quality evidence). There were no significant differences between ET and CMT in 30-day transient ischaemic attacks (TIA) (RR 0.52, 95% CI 0.11 to 2.35, P = 0.39; 2 RCTs, 181 participants, moderate-quality evidence), 30-day death (RR 5.53, 95% CI 0.98 to 31.17, P = 0.05; 3 RCTs, 632 participants, low-quality evidence), one-year TIA (RR 0.82, 95% CI 0.32 to 2.12; 2 RCTs, 181 participants, moderate-quality evidence), one-year death (RR 1.20, 95% CI 0.50 to 2.86, P = 0.68; 3 RCTs, 632 participants, moderate-quality evidence), and one-year dependency (RR 1.90, 95% CI 0.91 to 3.97, P = 0.09; 3 RCTs, 613 participants, moderate-quality evidence). No data on restenosis and health-related quality of life for meta-analysis were available from the included trials. Two RCTs are ongoing. This systematic review provides moderate-quality evidence showing that ET, compared with CMT, in people with recent symptomatic severe intracranial atherosclerotic stenosis probably does not prevent recurrent stroke and appears to carry an increased hazard. The impact of delayed ET intervention (more than three weeks after a qualifying event) is unclear and may warrant further study.

Joint Modeling of Multivariate Survival Data With an Application to Retirement

The Cox proportional hazards model has been pervasively used in many social science areas to examine the effects of covariates on timing to an event. The standard Cox model is intended to study univariate survival data where there is a singular event of interest, which can only be experienced once. However, we may additionally wish to explore a number of other complexities that are prevalent in survival data. For example, an individual may experience events of the same type more than once or may experience multiple types of events. This study introduces innovations in recurrent (repeatable) event analysis, jointly modeling several endogenous survival processes. As an example and an application, we simultaneously model two types of recurrent events in the presence of a dependent terminal event. This model not only correctly handles different types of recurrent events but also explicitly estimates the direction and magnitude of relationships between recurrences and survival. This article concludes with an example of the model to examine how the timing of retirement is associated with the risks of multiple spells of employment and childbearing. The theoretical discussions and empirical analyses suggest that the multivariate joint models have much to offer to a wide variety of substantive research areas.

Joint model for bivariate zero-inflated recurrent event data with terminal events

Bivariate recurrent event data are observed when subjects are at risk of experiencing two different type of recurrent events. In this paper, our interest is to suggest statistical model when there is a substantial portion of subjects not experiencing recurrent events but having a terminal event. In a context of recurrent event data, zero events can be related with either the risk free group or a terminal event. For simultaneously reflecting both a zero inflation and a terminal event in a context of bivariate recurrent event data, a joint model is implemented with bivariate frailty effects. Simulation studies are performed to evaluate the suggested models. Infection data from AML (acute myeloid leukemia) patients are analyzed as an application.

Dependence modeling for multi-type recurrent events via copulas.

When several types of recurrent events may arise, interest often lies in marginal modeling and studying the nature of the dependence structure. In this paper, we propose a multivariate mixed-Poisson model with the dependence between events accommodated by type-specific random effects which are associated through use of a Gaussian copula. Such models retain marginal features with a simple interpretation, reflect the heterogeneity in risk for each type of event, and provide insight into the dependence between the different types of events. Semiparametric inference is proposed based on composite likelihood to avoid high dimensional integration. An application to a study of nutritional supplements in malnourished children is given in which the goal is to evaluate the reduction in the rate of several different kinds of infection.

Miracles, Temporality, and Unfulfillment in A Diagram for Fire

Miracles, Temporality, and Unfulfillment in A Diagram for Fire Bruno Reinhardt Jon Bialecki, Vineyard Movement, charismatic, Pentecostalism, Gilles Deleuze, Holy Spirit, necromancy, exorcism, Bruno Reinhardt Miracles are one of the most widely acknowledged indexes of "religion" in secular scholarship and common sense. Yet, their theoretical role remains paradoxically residual, as if miracles were good to recognize but not to account for religious lifeworlds. The fundamental pressures imposed by the miraculous upon secular knowledges justify such opaqueness. By following empathetically miraculous veridiction, scholars can be led astray from basic epistemological principles such as neutrality and critical reflexivity, becoming theologians. A possible solution has been to circumvent miracles by sticking to their human co-participants, proposing theories of recognition that bracket their existence while focusing on their institutional, sociocultural, historical, ethical, or cognitive conditions of receptivity or construction. From this angle, the ultimate object of study of disciplines like the anthropology of religion or religious studies would not be miracles, but the media whereby miraculous truth is relayed, from social structures, symbolic systems, and semiotic ideologies to culturally embodied schema and the nervous system. Scholars might also import miracles into social theory through analogy and substitution. A classic example is Max Weber's secularized notion of charisma, borrowed from Pauline Christianity through theologian Rudolf Sohm and converted into a type of legitimate authority. What Weber calls pure charisma is explicitly residual, existing "only in the process of originating."1 Pure charisma nevertheless introduces a strategic dose of freedom and unexpectedness into Weber's otherwise bleak theory of modern rationalization, becoming a deterrent for determinism. Carl Schmitt's political theology performs similar work through the analogy between miracles and sovereignty: it selects a particular property of miracles—their extra-normative givenness— [End Page 456] and imports it to political philosophy as a critique of liberal democracy. 2 A more recent example of such procedure is Hent de Vries's argument about the "structural resemblances" between miracles and special effects, which—like the arguments of Weber and Schmitt—establishes parallels between religious and secular phenomena (leadership, sovereignty, mediation) and oscillates between analogy and substitution.3 Miracles for these authors operate primarily as tools for reading secular modernity otherwise, often against its self-image. Is it possible to propose a theoretical approach to religion that does not dilute the originary force of the miraculous through either constructivism or analogical thinking? Moreover, can we do that while still recognizing the otherness of social theory vis-à-vis theology or religious experience? Jon Bialecki's A Diagram for Fire faces bravely these major ethical and theoretical challenges through a rich ethnographic engagement with the evangelical Charismatic Vineyard Church. Bialecki's initial research problem was how to account for the dazzling plurality as well as the inchoate family resemblances he encountered in the field under the umbrella "Vineyard Church." How to recognize such inner difference without reifying the Vineyard in terms of stable doctrines, identities, or centralized organization, which ultimately do not empirically exist? This initial problematic expands in the book two ways: it scales up to wider objects that share similar qualities, such as "actually existing Christianity" and "religion" itself, and it scales down ethnographically from the Vineyard movement (they avoid denomination) to particular churches at different locations, small meetings, practices, and experiences. The resulting argument has a fractal design, which oscillates recursively between what we conventionally understand as "micro" and "macro" levels of analysis while showing these terms' inappropriateness. Such design reflects Bialecki's attempt to avoid both nominalism and essentialism. If there is a religious atom or lowest common denominator in the book, it is not substantial, but an iterable pattern of differentiation traceable across various scales, a "type of recurrent event" (xviii), which is best accessed through what Vineyard members call miracles. This spreadable but aggregating, elusive but affective force is diagrammatic: "a diagram for fire." According to Bialecki, diagrams are "abstract maps of how forces play out that point as much toward [End Page 457] the different potentials in outcomes as they do toward a similarity in relations or constitution" (69). Such focus on a set of fundamental relations reminded me of classic structural analysis, with the exception that the stuff of diagrams is...

Bayesian Multivariate Joint Modeling for Multiple Events Time Data and Survival

Individuals may experience multiple recurrent events and a dependent terminal event during their life period of a disease. Follow-up may be interrupted for some reasons. Also, death can stop the follow-up. Therefore, it is considered as a terminal event. In this article, we propose a Bayesian multivariate joint frailty model that jointly analyzes two types of recurrent events with a dependent terminal event. The Markov chain Monte Carlo methods are used to estimate the posterior distributions of model parameters. The performance of this approach is examined based on simulation study using exponential distribution. We apply the proposed method to a real dataset on breast cancer, which motivated this research. The main purpose was to model the dependency between multiple recurrent events (locoregional and metastatic) and the terminal event (death) after a breast cancer. Funding: This work was supported by tarbiat modares university, faculty of medical science. The collection of cancer data used in this study was supported by Shahid Beheshti Breast Cancer Research Center in Iran. Declaration of Interest: The authors declare that they have no competing interests.

Methods for multivariate recurrent event data with measurement error and informative censoring.

In multivariate recurrent event data regression, observation of recurrent events is usually terminated by other events that are associated with the recurrent event processes, resulting in informative censoring. Additionally, some covariates could be measured with errors. In some applications, an instrumental variable is observed in a subsample, namely a calibration sample, which can be applied for bias correction. In this article, we develop two non-parametric correction approaches to simultaneously correct for the informative censoring and measurement errors in the analysis of multivariate recurrent event data. A shared frailty model is adopted to characterize the informative censoring and dependence among different types of recurrent events. To adjust for measurement errors, a non-parametric correction method using the calibration sample only is proposed. In the second approach, the information from the whole cohort is incorporated by the generalized method of moments. The proposed methods do not require the Poisson-type assumption for the multivariate recurrent event process and the distributional assumption for the frailty. Moreover, we do not need to impose any distributional assumption on the underlying covariates and measurement error. Both methods perform well, but the second approach improves efficiency. The proposed methods are applied to the Nutritional Prevention of Cancer trial to assess the effect of selenium treatment on the recurrences of basal cell carcinoma and squamous cell carcinoma.

Factors associated with breast cancer recurrences or mortality and dynamic prediction of death using history of cancer recurrences: the French E3N cohort

BackgroundIn addition to tumor characteristics and lifestyle factors, cancer relapses are often related to the risk of death but have not been jointly studied. We investigate the prognostic factors of recurrent events and death after a diagnosis of breast cancer and predict individual deaths including a history of recurrences.MethodsThe E3N (Etude Epidémiologique auprès de Femmes de la Mutuelle Générale de l’Education Nationale) study is a prospective cohort study that was initiated in 1990 to investigate factors associated with the most common types of cancer. Overall survival and three types of recurrent events were considered: locoregional recurrence, metastasis, and second primary breast cancer. Recurrent events and death were analyzed using a joint frailty model.ResultsThe analysis included 4926 women from the E3N cohort diagnosed with a first primary invasive breast cancer between June 1990 and June 2008; during the follow-up, 1334 cases had a recurrence (median time of follow-up is 7.2 years) and 469 women died. Cases with high grade, large tumor size, axillary nodal involvement, and negative estrogen and progesterone receptors had a higher risk of recurrence or death. Furthermore, smoking increased the risk of relapse. For cases with a medium risk profile in terms of tumor characteristics and lifestyle factors, the probability of dying between 5 and 10 years after diagnosis was 6, 20 and 36% for 0, 1 or 2 recurrences within the first 5 years after diagnosis, respectively.ConclusionsOur study showed the importance of considering baseline lifestyle characteristics and history of relapses to dynamically predict the risk of death in breast cancer cases. Medical experience coupled with an estimate of a patient’s survival probability that considers all available information for this patient would enable physicians to make better informed decisions regarding their actions and thus improve clinical output.

Tutorial in Joint Modeling and Prediction: A Statistical Software for Correlated Longitudinal Outcomes, Recurrent Events and a Terminal Event

Extensions in the field of joint modeling of correlated data and dynamic predictions improve the development of prognosis research. The R package frailtypack provides estimations of various joint models for longitudinal data and survival events. In particular, it fits models for recurrent events and a terminal event (frailtyPenal), models for two survival outcomes for clustered data (frailtyPenal), models for two types of recurrent events and a terminal event (multivPenal), models for a longitudinal biomarker and a terminal event (longiPenal) and models for a longitudinal biomarker, recurrent events and a terminal event (trivPenal). The estimators are obtained using a standard and penalized maximum likelihood approach, each model function allows to evaluate goodness-of-fit analyses and plots of baseline hazard functions. Finally, the package provides individual dynamic predictions of the terminal event and evaluation of predictive accuracy. This paper presents theoretical models with estimation techniques, applies the methods for predictions and illustrates frailtypack functions details with examples.

The proportional hazards model for multiple type recurrent gap times

Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies, and often more than one type of recurrent events is of interest. In this paper, we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covariates on the censored event processes of interest. An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions. We examine asymptotic properties of the proposed estimators. Finite sample properties of these estimators are demonstrated by simulations.

Bayesian analysis of multi-type recurrent events and dependent termination with nonparametric covariate functions.

Multi-type recurrent event data occur frequently in longitudinal studies. Dependent termination may occur when the terminal time is correlated to recurrent event times. In this article, we simultaneously model the multi-type recurrent events and a dependent terminal event, both with nonparametric covariate functions modeled by B-splines. We develop a Bayesian multivariate frailty model to account for the correlation among the dependent termination and various types of recurrent events. Extensive simulation results suggest that misspecifying nonparametric covariate functions may introduce bias in parameter estimation. This method development has been motivated by and applied to the lipid-lowering trial component of the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial.

Time-varying coefficients in a multivariate frailty model: Application to breast cancer recurrences of several types and death

During their follow-up, patients with cancer can experience several types of recurrent events and can also die. Over the last decades, several joint models have been proposed to deal with recurrent events with dependent terminal event. Most of them require the proportional hazard assumption. In the case of long follow-up, this assumption could be violated. We propose a joint frailty model for two types of recurrent events and a dependent terminal event to account for potential dependencies between events with potentially time-varying coefficients. For that, regression splines are used to model the time-varying coefficients. Baseline hazard functions (BHF) are estimated with piecewise constant functions or with cubic M-Splines functions. The maximum likelihood estimation method provides parameter estimates. Likelihood ratio tests are performed to test the time dependency and the statistical association of the covariates. This model was driven by breast cancer data where the maximum follow-up was close to 20 years.

An additive-multiplicative rates model for multivariate recurrent events with event categories missing at random

Multivariate recurrent event data arises when study subjects may experience more than one type of recurrent events. In some situations, however, although event times are always observed, event categories may be partially missing. In this paper, an additive-multiplicative rates model is proposed for the analysis of multivariate recurrent event data when event categories are missing at random. A weighted estimating equations approach is developed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a model-checking technique is presented to assess the adequacy of the model. Simulation studies are conducted to evaluate the finite sample behavior of the proposed estimators, and an application to a platelet transfusion reaction study is provided.

Multivariate frailty models for two types of recurrent events with a dependent terminal event: Application to breast cancer data

Individuals may experience more than one type of recurrent event and a terminal event during the life course of a disease. Follow-up may be interrupted for several reasons, including the end of a study, or patients lost to follow-up, which are non informative censoring events. Death could also stop the follow-up, hence, it is considered as a dependent terminal event. We propose a multivariate frailty model that jointly analyzes two types of recurrent events with a dependent terminal event. Two estimation methods are proposed: a semiparametrical approach using penalized likelihood estimation where baseline hazard functions are approximated by M-s plines, and another one with piecewise constant baseline hazard functions. Finally, we derived martingale residuals to check the goodness-of-fit. We illustrate our proposals with a real dataset on breast cancer. The main objective was to model the dependency between the two types of recurrent events (locoregional and metastatic) and the terminal event (death) after a breast cancer.