Author: Zheng Li
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Languages : en
Pages :
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A terminal event can stop a series of recurrent events, which commonly occurs in biomedical and clinical studies. In this situation, the non-informative censoring assumption could fail because of potential dependency between these two event processes, leading to invalid inference if we analyze recurrent events alone. The joint frailty model is one of the widely used approaches to jointly model these two processes by sharing the same frailty term. One important assumption is that recurrent and terminal event processes are conditionally independent given the subject-level frailty; however, this could be violated when two processes also depends on time-varying covariates across recurrences. For example, time to death and time to stroke might both depend on the age of the patients. And when we do not include age in the survival models, the subject-level frailty cannot capture the change of the age across recurrences and lead to the violation of the conditional independence assumption. Furthermore, marginal correlation between two event processes based on traditional frailty modeling has no closed form solution for estimation. In order to fill these gaps, we propose a novel joint frailty-copula approach to model recurrent events and a terminal event with modest assumptions under Bayesian framework. Metropolis-Hastings within the Gibbs Sampler algorithm is used for parameter estimation. Extensive simulation studies are conducted to evaluate the efficiency, robustness and predictive performance of our proposal. The simulation results show that compared with the joint frailty model, the bias and mean squared error(MSE) of the propose approach is smaller when the conditional independence assumption is violated. We applied our method into a real example extracted from the MarketScan database to identify potential risk factors and study the association between recurrent strokes and all-cause mortality.Another important assumption under the joint frailty model is that the correlation between the terminal event and the recurrent events is constant over time. This is an unrealistic assumption. For example, when we study myocardial infarctions, time to death might be more correlated with the last myocardial infarction compared with the earlier myocardial infarction. We propose a time-varying joint frailty-copula model to further relax this assumption. Under this model, the dynamic correlation between the terminal event and the recurrent event is modeled by a latent Gaussian AR(1) process. The simulation results show that compared with the joint frailty model and the joint frailty-copula model, the bias, SD, MSE and AB of the time-varying frailty copula model are the smallest. Then, we applied our method to analyze the CHS data to identify potential risk factors to myocardial infarction and stroke.In summary, we propose two methods to jointly model recurrent events and a terminal event. Both methods outperform the traditional joint frailty model when the conditional independence assumption is violated. The time-varying joint frailty-copula model is more flexible, which allows the correlation between the recurrent event process and the terminal event process to change over time. One future topic is to jointly modeling biomarker, recurrent events and death time by the frailty-copula models. Other topics include extending the current model to a cure rate model and modeling multiple types of recurrent events.
Author: Luojun Wang
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Languages : en
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Recurrent events are commonly encountered in biomedical research studies and clinical trials. Many previous studies are done to investigate recurrent event analysis. As introduced in Chapter 1, some of the early work on recurrent event focuses on survival outcomes and others on longitudinal outcomes. If recurrent events arecorrelated with a failure event, such as death, we no longer should assume independent censoring. Many reports in the literature incorporate a latent variable model to account for the correlation between the time to event T and the number of recurrent events N(t).We first jointly model the time to primary outcome and the number of recurrent events with the frailty model, using a Zero-inflated-Poisson-Weibull distribution. We develop the analytical forms and details in the full parametric setting; however, such a model may be over-parameterized and dicult to apply, which limitsus from applying full likelihood-based analyses.Because of the limitation of the frailty model, we propose a joint distribution for (T;N) based on conditional distributions. We illustrate the use of this joint distribution to model the recurrent events of acute kidney injury (AKI) and time to primary outcome (death) in patients with and without chronic kidney disease (CKD) and AKI. In this fully parametric model, we develop the intensity ratio for the recurrent events and the hazard ratios for the failure event among different groups of patients with or without an AKI event at the index hospitalization and with or without CKD at the index hospitalization. Based on our model, we then investigate if recurrent AKI is predictive of death.Further, we are interested in a non-terminal event, such as End Stage Renal Disease (ESRD), which may be censored by a terminal event (Death), but not vice versa. The previous methods, such as a cause-specic hazards model and a subdistribution hazards model are based on the independence assumption, whichis not appropriate in such case. Therefore, we introduce and develop a semi competing risk approach with a Gaussian copula, using the tri-variate Weibull distribution. Then we illustrate the results from different approaches with a simulated data example. Finally, we compare different tri-variate Weibull distributionswith Gaussian copula, Clayton copula or under independence, via a series of simulation studies. Two sets of data are generated by tri-variate Weibull distributions with either Gaussian or Clayton copula, to test the bias of performances with each method.
Author: Menglu Liang
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Languages : en
Pages : 0
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Recurrent events are commonly observed in follow-up studies where the observation could be terminated by drop-out or a terminal event (e.g., death). In this dissertation, we focused on joint modelling approaches for handling recurrent and terminal events. Specifically, in our proposed joint modeling, the residual dependence of recurrent and failure event processes is modelled through a copula function after adjusted for subject-level frailties. The models have been extended for general applications to dynamically capture time-varying unobserved characteristics by allowing the copula parameters to be time-dependent, thus beneficial for precision medicine and risk prediction. We developed comprehensive strategies to quantify the prediction accuracy of our proposed modeling regarding the terminal behaviours. We also evaluated the performance of our proposal in both internal and external validation. As a particular application of our methods in the studies of dynamic prediction of disease, the rate of recurrent events could start to shift, accelerate or decelerate at a specific time prior to the occurrence of a primary failure event. Given accumulative history of recurrent data up to pre-specific landmark time, our model can be dynamically estimate the survival probability for subjects in the risk set at any subsequent post-landmark time points. We also further generalized our models to analyze multiple-type recurrent events data subject to a terminal event. Joint modelling multi-modal events altogether is challenging because of complex data structure and incomplete data due to (informative) censoring, where multivariate recurrent events are usually correlated and they are also associated with the failure time. In our work, we quantified the correlation between different types of recurrent events and the one between these recurrent and failure-time processes by considering multiple latent (frailty) terms and also a multivariate copula function. The properties of the parameter estimates and their empirical performances via simulation studies and real data applications were exclusively explored. In addition, the dynamic prediction based upon combined and cumulative history of recurrent events from joint modeling was performed.
Author: Cong Xu
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Languages : en
Pages :
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In longitudinal studies, matched designs are often employed to control the potential confounding effects in the field of biomedical research and public health. It is common to collect both repeated measures of risk factors (e.g., biomarkers) and time-to-event data for each subject, such as recurrent events and death. There are existing standard approaches to model the data separately. Mixed effects models are commonly used to model the association between repeated measures and covariates, which can incorporate the correlation among repeated measures. The Cox PH models or accelerated failure time (AFT) model are often used to estimate the covariate effects on the risk of the event. However, separate modeling may lead to biased results and are less efficient when the two processes are related through some unobserved variables. In many instances, the terminal event of death may prevent the observations and even the occurrence of any further recurrent events, but not vice versa. Thus, the common assumption of independent censoring for recurrent events is violated due to the competing risk of death because these two event processes are often correlated. For instance, if recurrent events (e.g., heart attacks) have a substantially negative effect on health condition, then the hazard for death could be increased. In addition, longitudinal biomarkers are often measured repeatedly over time for investigating their association with the event recurrence or death, thus identifying the candidate biomarker with enhance predictive accuracy is crucial for clinical practice. %Moreover, when the objective is to estimate the hazard of the events (e.g., death, cardiovascular disease) and the impact of prognostic biomarkers on the hazard of the event, a joint analysis taking their dependency into account is needed for valid inference. Motivated by the the Assessment, Serial Evaluation, and Subsequent Sequelae in Acute Kidney Injury (ASSESS-AKI) study, several challenges are recognized for joint modeling: 1) A certain large portion of subjects may not have any recurrent events during the study period due to non-susceptibility to events or censoring; 2) there exists left-censoring issue for some longitudinal biomarkers due to inherent limit of detection; 3) The correlation within matched cohorts need to be incorporated; 4) the informative censoring due to competing risk of death need to be adjusted. In this dissertation, first, we propose a joint frailty model with zero-inflated recurrent events and death in a matched study, where a matched logistic model is adopted to adjust for structural zero recurrent events. We incorporated two frailties to measure the dependency between subjects within a match pair and that among recurrent events within each individual. By sharing the random effects, two event processes of recurrent events and death are dependent with each other. Furthermore, because of left-censoring of the assay used to quantify the marker, longitudinal data could be complicated by left-censoring of some measures. Next, we propose a joint model of longitudinal biomarkers, recurrent events and death which can accommodate left-censoring biomarkers. The maximum likelihood based approach is applied for parameter estimation, where the Monte Carlo Expectation-Maximization (MCEM) algorithm is adopted and implemented in R. In addition, alternative estimation methods such as Gaussian quadrature (PROC NLMIXED) and a Bayesian approach (PROC MCMC) are also considered for comparison to show our method's superiority. Extensive simulations are conducted and a real data application on acute ischemic studies is provided.
Author: Lei Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 210
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Author: Jiejie Wang
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Category : Mathematical models
Languages : en
Pages : 0
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"Survival analysis is used to study the time until the occurrence of an event of interest. Some events of interest can occur more than once in a subject. These events are termed recurrent events. In this thesis, we consider survival analysis of bivariate recurrent events in which each subject may experience two distinct types of recurrent events. For example, in the peritonitis dialysis study conducted in Taichung Veterans General Hospital in Taiwan, both Gram-positive and Non-Gram-positive peritonitis are observed on 575 patients over time. Each of these two types of peritonitis may occur more than once in a patient. Clearly these two types of recurrent events are clustered by subject. In addition, the recurrent events of each type are further clustered by the type of events. To characterize those clustering effects in our analysis, we incorporate two levels of nested frailties into Cox survival models to analyze bivariate recurrent events jointly. There are many different approaches to the estimation of nested frailty Cox survival models in the literature. In this thesis, we propose a Poisson modelling approach to the estimation of our nested frailty Cox Survival models for bivariate recurrent events. This approach enables us to develop an optimal model estimation based on orthodox best linear unbiased predictor of frailties in an auxiliary frailty Poisson model. An important feature of this approach is that the principal results depend only on the first and second moments of the unobserved frailties. Our approach deals with an unspecified baseline hazard function. In addition, the treatment of ties and stratification is explicitly incorporated in our approach in the same way as in the standard Cox model. The usefulness of our proposed method is illustrated through analysis of peritonitis dialysis data and a simulation study.”—pages ii-iii.
Author: Liqun Diao
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Languages : en
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This thesis considers statistical issues in the analysis of data in the studies of chronic diseases which involve modeling dependencies between life history processes using copula functions. Many disease processes feature recurrent events which represent events arising from an underlying chronic condition; these are often modeled as point processes. In addition, however, there often exists a random variable which is realized upon the occurrence of each event, which is called a mark of the point process. When considered together, such processes are called marked point processes. A novel copula model for the marked point process is described here which uses copula functions to govern the association between marks and event times. Specifically, a copula function is used to link each mark with the next event time following the realization of that mark to reflect the pattern in the data wherein larger marks are often followed by longer time to the next event. The extent of organ damage in an individual can often be characterized by ordered states, and interest frequently lies in modeling the rates at which individuals progress through these states. Risk factors can be studied and the effect of therapeutic interventions can be assessed based on relevant multistate models. When chronic diseases affect multiple organ systems, joint modeling of progression in several organ systems is also important. In contrast to common intensity-based or frailty-based approaches to modelling, this thesis considers a copula-based framework for modeling and analysis. Through decomposition of the density and by use of conditional independence assumptions, an appealing joint model is obtained by assuming that the joint survival function of absorption transition times is governed by a multivariate copula function. Different approaches to estimation and inference are discussed and compared including composite likelihood and two-stage estimation methods. Special attention is paid to the case of interval-censored data arising from intermittent assessment. Attention is also directed to use of copula models for more general scenarios with a focus on semiparametric two-stage estimation procedures. In this approach nonparametric or semiparametric estimates of the marginal survivor functions are obtained in the first stage and estimates of the association parameters are obtained in the second stage. Bivariate failure time models are considered for data under right-censoring and current status observation schemes, and right-censored multistate models. A new expression for the asymptotic variance of the second-stage estimator for the association parameter along with a way of estimating this for finite samples are presented under these models and observation schemes.
Author: Takeshi Emura
Publisher: Springer
ISBN: 9811335168
Category : Medical
Languages : en
Pages : 118
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Book Description
This book introduces readers to advanced statistical methods for analyzing survival data involving correlated endpoints. In particular, it describes statistical methods for applying Cox regression to two correlated endpoints by accounting for dependence between the endpoints with the aid of copulas. The practical advantages of employing copula-based models in medical research are explained on the basis of case studies. In addition, the book focuses on clustered survival data, especially data arising from meta-analysis and multicenter analysis. Consequently, the statistical approaches presented here employ a frailty term for heterogeneity modeling. This brings the joint frailty-copula model, which incorporates a frailty term and a copula, into a statistical model. The book also discusses advanced techniques for dealing with high-dimensional gene expressions and developing personalized dynamic prediction tools under the joint frailty-copula model. To help readers apply the statistical methods to real-world data, the book provides case studies using the authors’ original R software package (freely available in CRAN). The emphasis is on clinical survival data, involving time-to-tumor progression and overall survival, collected on cancer patients. Hence, the book offers an essential reference guide for medical statisticians and provides researchers with advanced, innovative statistical tools. The book also provides a concise introduction to basic multivariate survival models.
Author: Richard J. Cook
Publisher: Springer Science & Business Media
ISBN: 0387698094
Category : Medical
Languages : en
Pages : 415
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Book Description
This book presents models and statistical methods for the analysis of recurrent event data. The authors provide broad, detailed coverage of the major approaches to analysis, while emphasizing the modeling assumptions that they are based on. More general intensity-based models are also considered, as well as simpler models that focus on rate or mean functions. Parametric, nonparametric and semiparametric methodologies are all covered, with procedures for estimation, testing and model checking.
Author: Luc Duchateau
Publisher: Springer Science & Business Media
ISBN: 038772835X
Category : Mathematics
Languages : en
Pages : 329
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Book Description
Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.
