Semiparametric EM-estimation of Censored Linear Regression Models for Durations PDF Download

Author: Alfred Hamerle
Publisher:
ISBN:
Category :
Languages : en
Pages : 11

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Author: Jianguo Sun
Publisher: Springer
ISBN: 0387371192
Category : Mathematics
Languages : en
Pages : 310

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This book collects and unifies statistical models and methods that have been proposed for analyzing interval-censored failure time data. It provides the first comprehensive coverage of the topic of interval-censored data and complements the books on right-censored data. The focus of the book is on nonparametric and semiparametric inferences, but it also describes parametric and imputation approaches. This book provides an up-to-date reference for people who are conducting research on the analysis of interval-censored failure time data as well as for those who need to analyze interval-censored data to answer substantive questions.

Author: Ding-Geng (Din) Chen
Publisher: CRC Press
ISBN: 1466504250
Category : Mathematics
Languages : en
Pages : 435

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Book Description
Interval-Censored Time-to-Event Data: Methods and Applications collects the most recent techniques, models, and computational tools for interval-censored time-to-event data. Top biostatisticians from academia, biopharmaceutical industries, and government agencies discuss how these advances are impacting clinical trials and biomedical research. Divided into three parts, the book begins with an overview of interval-censored data modeling, including nonparametric estimation, survival functions, regression analysis, multivariate data analysis, competing risks analysis, and other models for interval-censored data. The next part presents interval-censored methods for current status data, Bayesian semiparametric regression analysis of interval-censored data with monotone splines, Bayesian inferential models for interval-censored data, an estimator for identifying causal effect of treatment, and consistent variance estimation for interval-censored data. In the final part, the contributors use Monte Carlo simulation to assess biases in progression-free survival analysis as well as correct bias in interval-censored time-to-event applications. They also present adaptive decision making methods to optimize the rapid treatment of stroke, explore practical issues in using weighted logrank tests, and describe how to use two R packages. A practical guide for biomedical researchers, clinicians, biostatisticians, and graduate students in biostatistics, this volume covers the latest developments in the analysis and modeling of interval-censored time-to-event data. It shows how up-to-date statistical methods are used in biopharmaceutical and public health applications.

Author: Ling Ma
Publisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages :

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By interval-censored data, we mean that the failure time of interest is known only to lie within an interval instead of being observed exactly. Many clinical trials and longitudinal studies may generate interval-censored data. One common example occurs in medical or health studies that entail periodic follow-ups. An important special case of interval-censored data is the so called current status data when each subject is observed only once for the status of the occurrence of the event of interest. That is, instead of observing the survival endpoint directly, we only know the observation time and whether or not the event of interest has occurred at that time. Such data may occur in many fields, for example, cross-sectional studies and tumorigenicity experiments. Sometimes we also refer current status data to as case I interval-censored data and the general case as case II interval-censored data. In the following, for simplicity, we will refer current status data and interval-censored data to case I and case II interval-censored data, respectively. The statistical analysis of both case I and case II interval-censored failure time data has recently attracted a great deal of attention and especially, many procedures have been proposed for their regression analysis under various models. However, due to the strict restrictions of existing regression analysis procedures and practical demands, new methodologies for regression analysis need to be developed. For regression analysis of interval-censored data, many approaches have been proposed and for most of them, the inference is carried out based on the asymptotic normality. It's well known that the symmetric property implied by the normal distribution may not be appropriate sometimes and could underestimate the variance of estimated parameters. In the first part of this dissertation, we adopt the linear transformation models for regression analysis of interval-censored data and propose an empirical likelihood-based procedure to address the underestimating problem from using symmetric property implied by the normal distribution of the parameter estimates. Simulation and analysis of a real data set are conducted to assess the performance of the procedure. The second part of this dissertation discusses regression analysis of current status data under additive hazards models. In this part, we focus on the situation when some covariates could be missing or cannot be measured exactly due to various reasons. Furthermore, for missing covariates, there may exist some related information such as auxiliary covariates (Zhou and Pepe, 1995). We propose an estimated partial likelihood approach for estimation of regression parameters that make use of the available auxiliary information. To assess the finite sample performance of the proposed method, an extensive simulation study is conducted and indicates that the method works well in practical situations. Several semi-parametric and non-parametric methods have been proposed for the analysis of current status data. However, most of these methods deal only with the situation where observation time is independent of the underlying survival time completely or given covariates. The third part of this dissertation discusses regression analysis of current status data when the observation time may be related to survival time. The correlation between observation time and survival time and the covariate effects are described by a copula model and the proportional hazards model, respectively. For estimation, a sieve maximum likelihood procedure with the use of monotone I-spline functions is proposed and the proposed method is examined through a simulation study and illustrated with a real data set. In the fourth part of this dissertation, we discuss the regression analysis of interval- censored data where the censoring mechanism could be related to the failure time. We consider a situation where the failure time depend on the censoring mechanism only through the length of the observed interval. The copula model and monotone I-splines are used and the asymptotic properties of the resulting estimates are established. In particular, the estimated regression parameters are shown to be semiparametrically efficient. An extensive simulation study and an illustrative example is provided. Finally, we will talk about the directions for future research. One topic related the fourth part of this dissertation for future research could be to allow the failure time to depend on both the lower and upper bounds of the observation interval. Another possible future research topic could be to consider a cure rate model for interval-censored data with informative censoring.

Author: William A. Barnett
Publisher: Cambridge University Press
ISBN: 9780521424318
Category : Business & Economics
Languages : en
Pages : 512

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Papers from a 1988 symposium on the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data.

Author: Jinqing Li
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 273

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Book Description
Interval-censored failure time data arise in many areas including demographical, financial, actuarial, medical and sociological studies. By interval censoring we mean that the failure time is not always exactly observed and we can only observe an interval within which the failure event has occurred. The goal of this dissertation is to develop maximum penalized likelihood (MPL) methods for ptoportional hazard (PH), additive hazard (AH) and accelerated failure time (AFT) models with partly interval-censored failure time data, which contains exactly observed, left-censored, finite interval-censored and right-censored data.

Author: Richard Breen
Publisher: SAGE
ISBN: 9780803957107
Category : Mathematics
Languages : en
Pages : 92

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This book provides an introduction to the regression models needed, where an outcome variable for a sample is not representative of the population from which a generalized result is sought.

Author: Han Zhang (Graduate of University of Missouri)
Publisher:
ISBN:
Category :
Languages : en
Pages : 135

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Book Description
Interval-censored failure time data arises when the failure time of interest is known only to lie within an interval or window instead of being observed exactly. Many clinical trials and longitudinal studies may generate interval-censored data. One common area that often produces such data is medical or health studies with periodic follow-ups, in which the medical condition of interest such as the onset of a disease is only known to occur between two adjacent examination times. An important special case of interval-censored data is the so-called current status data when each study subject is observed only once for the status of the event of interest. That is, instead of observing the survival endpoint directly, we will only know the observation time and whether or not the event of interest has occurred by that time. Such data may occur in many fields as cross-sectional studies and tumorigenicity experiments. Sometimes we also refer current status data as case I interval-censored data and the general case as case II interval-censored data. Recently the semi-parametric statistical analysis of both case I and case II intervalcensored failure time data has attracted a great deal of attention. Many procedures have been proposed for their regression analysis under various models. We will describe the structure of interval-censored data in Chapter 1 and provides two specific examples. Also some special situations like informative censoring and failure time data with missing covariates are discussed. Besides, a brief review of the literature on some important topics, including nonparametric estimation and regression analysis are performed. However, there are still a number of problems that remain unsolved or lack approaches that are simpler, more efficient and could apply to more general situations compared to the existing ones. For regression analysis of interval-censored data, many approaches have been proposed and more specifically most of them are developed for the widely used proportional hazards model. The research in this dissertation focuses on the statistical analysis on non-proportional hazards models. In Chapter 2 we will discuss the regression analysis of interval-censored failure time data with possibly crossing hazards. For the problem of crossing hazards, people assume that the hazard functions with two samples considered may cross each other where most of the existing approaches cannot deal with such situation. Many authors has provided some efficient methods on right-censored failure time data, but little articles could be found on interval-censored data. By applying the short-term and long-term hazard ratio model, we develop a spline-based maximum likelihood estimation procedure to deal with this specific situation. In the method, a splined-based sieve estimation are used to approximate the underlying unknown function. The proposed estimators are shown to be strongly consistent and the asymptotic normality of the estimators of regression parameters are also shown to be true. In addition, we also provided a Cramer-Raw type of criterion to do the model validation. Simulation study was conducted for the assessment of the finite sample properties of the presented procedure and suggests that the method seems to work well for practical situations. Also an illustrative example using a data set from a tumor study is provided. As we discussed in Chapter 1, several semi-parametric and non-parametric methods have been proposed for the analysis of current status data. However, most of them only deal with the situation where observation time is independent of the underlying survival time. In Chapter 3, we consider regression analysis of current status data with informative observation times in additive hazards model. In many studies, the observation time may be correlated to the underlying failure time of interest, which is often referred to as informative censoring. Several authors have discussed the problem and in particular, an estimating equation-based approach for fitting current status data to additive hazards model has been proposed previously when informative censoring occurs. However, it is well known that such procedure may not be efficient and to address this, we propose a sieve maximum likelihood procedure. In particular, an EM algorithm is developed and the resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study was conducted for the assessment of the finite sample properties of the presented procedure and suggests that it seems to work well for practical situations. An application to a tumorigenicity experiment is also provided. In Chapter 4, we considered another special case under the additive hazards model, case II interval-censored data with possibly missing covariates. In many areas like demographical, epidemiological, medical and sociological studies, a number of nonparametric or semi-parametric methods have been developed for interval-censored data when the covariates are complete. However, it is well-known that in reality some covariates may suffer missingness due to various reasons, data with missing covariates could be very common in these areas. In the case of missing covariates, a naive method is clearly the complete-case analysis, which deletes the cases or subjects with missing covariates. However, it's apparent that such analysis could result in loss of efficiency and furthermore may lead to biased estimation. To address this, we propose the inverse probability weighted method and reweighting approach to estimate the regression parameters under the additive hazards model when some of the covariates are missing at random. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal. Several numerical results suggest that the proposed method works well in practical situations. Also an application to a health survey is provided. Several directions for future research are discussed in Chapter 5.

Author: Yonggang Zhao
Publisher:
ISBN:
Category : Regression analysis
Languages : en
Pages :

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Abstract: In survival analysis, a linear model often provides an adequate approximation to the survival times and covariates after a suitable transformation. This dissertation is devoted to a systematic investigation of semiparametric regression methods for estimating the regression parameter in the context of linear regression without specifying the error distribution, where the response is right-censored. The method uses the random-sieve likelihood, which combines the benefits of semiparametric likelihood with estimating equations and constraints. A method of estimating the parameters is developed and inferential procedures based on the asymptotic distributions of the estimated regression parameters and of the profile likelihood ratios are derived. The small sample operating characteristics of the proposed method are examined via simulations and illustrated on a data set from a study of ganglioside of primary brain tumors and a data set from bone marrow transplant study. This dissertation proposes an estimation method as well as an inference procedure, for a general linear model, allowing for right-censoring and an unspecified error distribution. The proposed methodology yields an easily interpreted regression estimate, and is especially useful when the proportionality assumption doesn't hold for Cox regression models. However, how to determine the best transformation of the response or how to select the best model from the class studied are left for future work.

Author: Mark J. van der Laan
Publisher: Springer Science & Business Media
ISBN: 0387217002
Category : Mathematics
Languages : en
Pages : 412

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Book Description
A fundamental statistical framework for the analysis of complex longitudinal data is provided in this book. It provides the first comprehensive description of optimal estimation techniques based on time-dependent data structures. The techniques go beyond standard statistical approaches and can be used to teach masters and Ph.D. students. The text is ideally suitable for researchers in statistics with a strong interest in the analysis of complex longitudinal data.