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Author: Kunasekaran Nirmalkanna
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The analysis of past developments of processes through dynamic covariates is useful to understand the present and future of processes generating recurrent events. In this study, we consider two essential features of recurrent event processes through dynamic models. These features are related to monotonic trends and clustering of recurrent events, and frequently seen in medical studies. We discuss the estimation of these features through dynamic models for event counts. We also focus on the settings in which unexplained excess heterogeneity is present in the data. Furthermore, we show that the violation of the strong assumption of independent gap times may introduce substantial bias in the estimation of these features with models for event counts. To address these issues, we apply a copula-based estimation method for the gap time models. Our approach does not rely on the strong independent gap time assumption, and provides a valid estimation of model parameters. We illustrate the methods developed in this study with data on repeated asthma attacks in children. Finally, we propose some goodness-of-fit procedures as future research.
Author: Kunasekaran Nirmalkanna
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The analysis of past developments of processes through dynamic covariates is useful to understand the present and future of processes generating recurrent events. In this study, we consider two essential features of recurrent event processes through dynamic models. These features are related to monotonic trends and clustering of recurrent events, and frequently seen in medical studies. We discuss the estimation of these features through dynamic models for event counts. We also focus on the settings in which unexplained excess heterogeneity is present in the data. Furthermore, we show that the violation of the strong assumption of independent gap times may introduce substantial bias in the estimation of these features with models for event counts. To address these issues, we apply a copula-based estimation method for the gap time models. Our approach does not rely on the strong independent gap time assumption, and provides a valid estimation of model parameters. We illustrate the methods developed in this study with data on repeated asthma attacks in children. Finally, we propose some goodness-of-fit procedures as future research.
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.
Author: Odd Aalen
Publisher: Springer Science & Business Media
ISBN: 038768560X
Category : Mathematics
Languages : en
Pages : 550
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Book Description
The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.
Author: Zheng Li
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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: Germán Aneiros
Publisher: Springer Nature
ISBN: 3030477568
Category : Mathematics
Languages : en
Pages : 254
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Book Description
This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.
Author: Menglu Liang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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: Withanage Ajith Raveendra De Mel
Publisher:
ISBN:
Category : Goodness-of-fit tests
Languages : en
Pages : 79
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Book Description
"Recurrent events (RE) occur in many disciplines, such as biomedical, engineering, actuarial science, sociology, economy to name a few. It is then important to develop dynamic models for their modeling and analysis. Of interest with data collected in a RE monitoring are inferential problems pertaining to the distribution function F of the time between occurrences, or that of the distribution function G of the monitoring window, and their functionals such as quantiles, mean. These problems include, but not limited to: estimating F parametrically or nonparametrically; goodness of fit tests on an hypothesized family of distributions; efficient of tests; regression-type models, or validation of models that arise in the modeling and analysis of RE. This dissertation work focuses on several inferential problems of significant importance with these types of data. The first one we dealt with is the problem of informative monitoring. Informative monitoring occurs when G contains information about F, and the information is accounted for in the inferential process through a Lehman-type model, 1-G=(1-F)[superscript beta], so called generalized Koziol-Green model in the literature. We propose a class of inferential procedures for validating the model. The research work proceeds with the development of a flexible, random cells based chi-square goodness of fit test for an hypothesized family of distributions with unknown parameter. The cells are random in the sense that they are cut free, are function of the data, and are not predetermined in advance as is done in standard chi-square type tests. A minimum chi-square estimator is used to construct the test statistic whose power is assessed against a sequence of Pitman-like alternatives. The last problem we considered is that of an efficiency, optimality, and comparison of various statistical tests on RE that are derived in this work and existed in the literature. The efficiency and optimality are obtained by extending the theory of Bahadur and Wieand to RE. Asymptotic properties of the different estimators and or statistics are presented via empirical processes tools. Small sample results using intensive simulation study of the various procedures are presented, and these show good approximation of the truth. Real recurrent event data from the engineering and biomedical studies are utilized to illustrate the various methods"--Abstract, page iv.
Author: Richard J. Cook
Publisher: Springer Science & Business Media
ISBN: 0387698108
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: Dimitris Rizopoulos
Publisher: CRC Press
ISBN: 1439872864
Category : Mathematics
Languages : en
Pages : 279
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Book Description
In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest, e.g., prostate cancer studies where longitudinal PSA level measurements are collected in conjunction with the time-to-recurrence. Joint Models for Longitudinal and Time-to-Event Data: With Applications in R provides a full treatment of random effects joint models for longitudinal and time-to-event outcomes that can be utilized to analyze such data. The content is primarily explanatory, focusing on applications of joint modeling, but sufficient mathematical details are provided to facilitate understanding of the key features of these models. All illustrations put forward can be implemented in the R programming language via the freely available package JM written by the author. All the R code used in the book is available at: http://jmr.r-forge.r-project.org/
Author: John P. Klein
Publisher: Springer Science & Business Media
ISBN: 9401579830
Category : Mathematics
Languages : en
Pages : 446
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Book Description
Survival analysis is a highly active area of research with applications spanning the physical, engineering, biological, and social sciences. In addition to statisticians and biostatisticians, researchers in this area include epidemiologists, reliability engineers, demographers and economists. The economists survival analysis by the name of duration analysis and the analysis of transition data. We attempted to bring together leading researchers, with a common interest in developing methodology in survival analysis, at the NATO Advanced Research Workshop. The research works collected in this volume are based on the presentations at the Workshop. Analysis of survival experiments is complicated by issues of censoring, where only partial observation of an individual's life length is available and left truncation, where individuals enter the study group if their life lengths exceed a given threshold time. Application of the theory of counting processes to survival analysis, as developed by the Scandinavian School, has allowed for substantial advances in the procedures for analyzing such experiments. The increased use of computer intensive solutions to inference problems in survival analysis~ in both the classical and Bayesian settings, is also evident throughout the volume. Several areas of research have received special attention in the volume.
