On Some Inferential Problems with Recurrent Event Models PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download On Some Inferential Problems with Recurrent Event Models PDF full book. Access full book title On Some Inferential Problems with Recurrent Event Models by Withanage Ajith Raveendra De Mel. Download full books in PDF and EPUB format.
Author: Withanage Ajith Raveendra De Mel
Publisher:
ISBN:
Category : Goodness-of-fit tests
Languages : en
Pages : 79
Get Book Here
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: Withanage Ajith Raveendra De Mel
Publisher:
ISBN:
Category : Goodness-of-fit tests
Languages : en
Pages : 79
Get Book Here
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: Luc Duchateau
Publisher: Springer Science & Business Media
ISBN: 038772835X
Category : Mathematics
Languages : en
Pages : 329
Get Book Here
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: Richard J. Cook
Publisher: Springer Science & Business Media
ISBN: 0387698094
Category : Medical
Languages : en
Pages : 415
Get Book Here
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: Kunasekaran Nirmalkanna
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
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: Muna Mohamed Hammuda
Publisher:
ISBN:
Category :
Languages : en
Pages : 75
Get Book Here
Book Description
"Recurrent event data occurs in many disciplines such as actuarial science, biomedical studies, sociology, and environment to name a few. It is therefore important to develop models that describe the dynamic evolution of the event occurrences. One major problem of interest to researchers with these types of data is models for the distribution function of the time between events occurrences, especially in the presence of covariates that play a major role in having a better understanding of time to events. This work pertains to statistical inference of the regression parameter and the baseline hazard function in a Cox-type model for recurrent events that accounts for the effective age and time varying covariates. Estimators of the regression parameters as well as baseline hazard function are obtained using the counting processes and martingales machinery techniques. Asymptotic properties of the proposed estimators and how they can be used to construct confidence intervals are investigated. The results of the simulation studies assessing the performance of the estimators and an application to a biomedical dataset illustrating the models are presented. The impact of unit effective age is also assessed. To check the validity of the models used, many decision rules are developed for checking the validity of the various components of Cox-type model. Specifically, using martingales residuals, we proposed test statistics for checking the link function and the covariates functional form. Asymptotic properties of test statistics and simulation studies are presented as well"--Abstract, page iii.
Author: Deborah G. Mayo
Publisher: Cambridge University Press
ISBN: 1108563309
Category : Mathematics
Languages : en
Pages : 503
Get Book Here
Book Description
Mounting failures of replication in social and biological sciences give a new urgency to critically appraising proposed reforms. This book pulls back the cover on disagreements between experts charged with restoring integrity to science. It denies two pervasive views of the role of probability in inference: to assign degrees of belief, and to control error rates in a long run. If statistical consumers are unaware of assumptions behind rival evidence reforms, they can't scrutinize the consequences that affect them (in personalized medicine, psychology, etc.). The book sets sail with a simple tool: if little has been done to rule out flaws in inferring a claim, then it has not passed a severe test. Many methods advocated by data experts do not stand up to severe scrutiny and are in tension with successful strategies for blocking or accounting for cherry picking and selective reporting. Through a series of excursions and exhibits, the philosophy and history of inductive inference come alive. Philosophical tools are put to work to solve problems about science and pseudoscience, induction and falsification.
Author: Odd Aalen
Publisher: Springer Science & Business Media
ISBN: 038768560X
Category : Mathematics
Languages : en
Pages : 550
Get Book Here
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: Andreas Wienke
Publisher: CRC Press
ISBN: 9781420073911
Category : Mathematics
Languages : en
Pages : 324
Get Book Here
Book Description
The concept of frailty offers a convenient way to introduce unobserved heterogeneity and associations into models for survival data. In its simplest form, frailty is an unobserved random proportionality factor that modifies the hazard function of an individual or a group of related individuals. Frailty Models in Survival Analysis presents a comprehensive overview of the fundamental approaches in the area of frailty models. The book extensively explores how univariate frailty models can represent unobserved heterogeneity. It also emphasizes correlated frailty models as extensions of univariate and shared frailty models. The author analyzes similarities and differences between frailty and copula models; discusses problems related to frailty models, such as tests for homogeneity; and describes parametric and semiparametric models using both frequentist and Bayesian approaches. He also shows how to apply the models to real data using the statistical packages of R, SAS, and Stata. The appendix provides the technical mathematical results used throughout. Written in nontechnical terms accessible to nonspecialists, this book explains the basic ideas in frailty modeling and statistical techniques, with a focus on real-world data application and interpretation of the results. By applying several models to the same data, it allows for the comparison of their advantages and limitations under varying model assumptions. The book also employs simulations to analyze the finite sample size performance of the models.
Author: John D. Kalbfleisch
Publisher: John Wiley & Sons
ISBN: 1118031237
Category : Mathematics
Languages : en
Pages : 462
Get Book Here
Book Description
Contains additional discussion and examples on left truncationas well as material on more general censoring and truncationpatterns. Introduces the martingale and counting process formulation swillbe in a new chapter. Develops multivariate failure time data in a separate chapterand extends the material on Markov and semi Markovformulations. Presents new examples and applications of data analysis.
Author: Guanglei Yu
Publisher:
ISBN:
Category :
Languages : en
Pages : 108
Get Book Here
Book Description
Recurrent event data and panel count data are two common types of data that have been studied extensively in event history studies in literature. By recurrent event data, we mean that subjects are observed continuously in the follow-up study and thus occurrence times of recurrent events of interest are available. For panel count data, subjects are monitored periodically at discrete observation times and thus only numbers of recurrent events between two subsequent observations are recorded. In addition, one may face mixed panel count data in practice, which are the mixture of recurrent event data and panel count data. They arise when each study subject may be observed continuously during the whole study period, continuously over some study periods and at some time points otherwise, or only at some discrete time points. That is, these mixed data provide complete or incomplete information on the recurrent event process over different time periods for different subjects. It is well-known that in panel count data, the observation process may carry information on the underlying recurrent event process and the censoring may also be dependent in practice. Under such circumstance, the first part of this dissertation will discuss regression analysis of panel count data with informative observations and drop-outs. For the problem, a general means model is presented that can allow both additive and multiplicative effects of covariates on the underlying recurrent event process. In addition, the proportional rates model and the accelerated failure time model are employed to describe the covariate effects on the observation process and the dropout or follow-up process, respectively. For estimation of regression parameters, some estimating equation-based procedures are developed and the asymptotic properties of the proposed estimators are established. In addition, a resampling approach is proposed for the estimation of the covariance matrix of the proposed estimator and a model checking procedure is also provided. The results from an extensive simulation study indicate that the proposed methodology works well for practical situations and it is applied to a motivated set of real data from the Childhood Cancer Survivor Study (CCSS) given in Section 1.1.2.2. In the second part of this dissertation, we will consider regression analysis of mixed panel count data. One major problem in the statistical inference on the mixed data is to combine these two different types of data structures. Since panel count data can be viewed as interval-censored recurrent event data with exact occurrence times of events of interest unobserved or missing, they may be augmented by filling in those missing data by imputation. Then the mixed data can be converted to recurrent event data on which the existing statistical inference method can be easily implemented. Motivated by this, a multiple imputation-based estimation approach is proposed. A simulation study is conducted to study the finite-sample properties of the proposed methodology and it shows that the proposed method is more efficient than the existing method. Also, an illustrative example from the CCSS is provided. The third part of this dissertation still considers regression analysis of mixed panel count data but in the presence of a dependent terminal event, which precludes further occurrence of either recurrent events of interest or observations. For this problem, we present a marginal modeling approach which acknowledges the fact that there will be no more recurrent events after the terminal event and leaves the correlation structure unspecified. To estimate the parameters of interest, an estimating equation-based procedure is developed and the inverse probability of survival weighting technique is used. Asymptotic properties of proposed estimators are also established and finite-sample properties are assessed in a simulation study. We again apply this proposed methodology to the CCSS. In the last part of this dissertation, we will discuss some work directions of the future research.
