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Author: Qiang Zhao Publisher: ISBN: Category : Time-series analysis Languages : en Pages : 156
Book Description
Interval-censored failure time data commonly occur in follow-up studies. One of the main goals of such studies is to compare the distributions of the failure time among different treatment groups. By interval-censored data, we mean that the failure time of interest is not completely observed for some individuals. Instead, we only know that it belongs to a certain interval. This dissertation consists of three parts discussing the problem of comparing survival functions using nonparametric approaches based on two types of interval-censored data. First, Chapter 2 discusses the treatment comparison based on current status data, a special case of interval-censored data in which the failure time for each individual is either left- or right-censored. This part of research was motivated by comparing incidence rates of occult tumors, which is one of the main objectives of tumorigenicity experiments. For the problem, a common practice is to assume that tumors are either lethal or nonlethal (Hoel and Walburg, 1972; Sun, 1999), to fit incidence rate data to certain parametric or semiparametric models (Dewanji et al., 1993), or to treat tumors with intermediate, but known lethality (Lagakos and Louis, 1988). We propose a simple nonparametric test procedure for the incidence rate comparison that allows tumors to have intermediate and unknown lethality. This method also allows the distributions of death times to depend on treatments or doses. The proposed method is applied to a dataset arising from a tumorigenicity experiment. Chapters 3 and 4 consider the comparison of survival functions for case 2 interval-censored failure time data, which often occur in clinical trials and epidemiological studies. In Chapter 3, we generalize the most commonly used log-rank test (Mantel, 1966) for right-censored data to interval-censored data that may contain mixed types of observations: exactly observed, right-censored, left-censored, and interval-censored. Numerical studies are conducted to evaluate and compare the proposed test with existing methods, and the results indicate that the proposed test works well. We apply the method to a dataset arising from an AIDS cohort study, which motivated the study. A main drawback of most existing nonparametric test procedures for interval-censored data, including the one proposed in Chapter 3, is that they are ad-hoc and no asymptotic properties are established for the test statistics although they may be intuitive or simple. For those procedures, the derivation and calculation of the variance estimation are usually heuristical and complicated. In Chapter 4, we present a class of nonparametric tests for interval-censored data without exact observations and establish their asymptotics. These tests are generalizations of the log-rank test given in Peto and Peto (1972). Estimation of the variances of the test statistics is straightforward. The simulation results show that the proposed procedures perform satisfactorily. For illustration, we then apply the methods to a dataset from a cancer study.
Author: Qiang Zhao Publisher: ISBN: Category : Time-series analysis Languages : en Pages : 156
Book Description
Interval-censored failure time data commonly occur in follow-up studies. One of the main goals of such studies is to compare the distributions of the failure time among different treatment groups. By interval-censored data, we mean that the failure time of interest is not completely observed for some individuals. Instead, we only know that it belongs to a certain interval. This dissertation consists of three parts discussing the problem of comparing survival functions using nonparametric approaches based on two types of interval-censored data. First, Chapter 2 discusses the treatment comparison based on current status data, a special case of interval-censored data in which the failure time for each individual is either left- or right-censored. This part of research was motivated by comparing incidence rates of occult tumors, which is one of the main objectives of tumorigenicity experiments. For the problem, a common practice is to assume that tumors are either lethal or nonlethal (Hoel and Walburg, 1972; Sun, 1999), to fit incidence rate data to certain parametric or semiparametric models (Dewanji et al., 1993), or to treat tumors with intermediate, but known lethality (Lagakos and Louis, 1988). We propose a simple nonparametric test procedure for the incidence rate comparison that allows tumors to have intermediate and unknown lethality. This method also allows the distributions of death times to depend on treatments or doses. The proposed method is applied to a dataset arising from a tumorigenicity experiment. Chapters 3 and 4 consider the comparison of survival functions for case 2 interval-censored failure time data, which often occur in clinical trials and epidemiological studies. In Chapter 3, we generalize the most commonly used log-rank test (Mantel, 1966) for right-censored data to interval-censored data that may contain mixed types of observations: exactly observed, right-censored, left-censored, and interval-censored. Numerical studies are conducted to evaluate and compare the proposed test with existing methods, and the results indicate that the proposed test works well. We apply the method to a dataset arising from an AIDS cohort study, which motivated the study. A main drawback of most existing nonparametric test procedures for interval-censored data, including the one proposed in Chapter 3, is that they are ad-hoc and no asymptotic properties are established for the test statistics although they may be intuitive or simple. For those procedures, the derivation and calculation of the variance estimation are usually heuristical and complicated. In Chapter 4, we present a class of nonparametric tests for interval-censored data without exact observations and establish their asymptotics. These tests are generalizations of the log-rank test given in Peto and Peto (1972). Estimation of the variances of the test statistics is straightforward. The simulation results show that the proposed procedures perform satisfactorily. For illustration, we then apply the methods to a dataset from a cancer study.
Author: Jeremy Gorelick Publisher: ISBN: Category : Electronic dissertations Languages : en Pages : 122
Book Description
This thesis considers the problem of treatment comparisons when only interval-censored failure time data are available. This type of data occurs frequently in clinical trials and other follow-up studies. We study several nonparametric procedures developed previously and compare them under different situations. In particular, we study the situation where the difference between the groups occurs at an early or late time period. For this problem, we generalize the log-rank tests developed for interval-censored data in Zhao and Sun (2004) and the weighted log-rank test presented in Kalbfleisch (2002). Numerical studies are conducted to evaluate the proposed test and compare it with the unweighted log-rank test, which indicate that the proposed method works well. This thesis also considerers the problem of finding an appropriate sample size to achieve a desired power. We present a simple-to-use formula to find the sample size for a prespecified power and level of significance for the case of interval-censored data. Since many researchers use missing data techniques such as imputation along with right-censored methods to analyze interval-censored data, we also compare an imputed Kaplan-Meier Estimate of the survival function to Turnbull's Self Consistent Estimate. We present a large numerical study to show that these estimates often disagree at late time points when the mean survival time is large.
Author: Chao Zhu Publisher: ISBN: Category : Languages : en Pages : 91
Book Description
Interval-censored failure time data commonly arise in follow-up studies such as clinical trials and epidemiology studies. For their analysis, what interests researcher most includes comparisons of survival functions for different groups and regression analysis. This dissertation, which consists of three parts, consider these problems on two types of interval-censored data by using nonparametric and semiparametric methods.
Author: Jianguo Sun Publisher: Springer ISBN: 0387371192 Category : Mathematics Languages : en Pages : 310
Book Description
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: Ran Duan Publisher: ISBN: Category : Clinical trials Languages : en Pages : 109
Book Description
By interval-censored failure time data, we mean that the failure time of interest is observed to belong to some windows or intervals, instead of being known exactly. One would get an interval-censored observation for a survival event if a subject has not experienced the event at one follow-up time but had experienced the event at the next follow-up time. Interval-censored data include right-censored data (Kalbfleisch and Prentice, 2002) as a special case. Nonparametric comparison of survival functions is one of the main tasks in failure time studies such as clinical trials. For interval-censored failure time data, a few nonparametric test procedures have been developed. However, due to the strict restrictions of existing nonparametric tests and practical demands, some new nonparametric tests need to be developed. This dissertation consists of four parts. In the first part, we propose a new class of test procedures whose asymptotic distributions are established under both null and alternative hypotheses, since all of the existing test procedures cannot be used if one intends to perform some power or sample size calculation under the alternative hypothesis. Some numerical results have been obtained from a simulation study for assessing the finite sample performance of the proposed test procedure. Also we applied the proposed method to a real data set arising from an AIDS clinical trial concerning the opportunistic infection cytomegalovirus (CMV). The second part of this dissertation will focus on the nonparametric test for intervalcensored data with unequal censoring. As we know, one common drawback or restriction of the nonparametric test procedures given in the literature is that they can only apply to situations where the observation processes follow the same distribution among different treatment groups. To remove the restriction, a test procedure is proposed, which takes into account the difference between the distributions of the censoring variables. Also the asymptotic distribution of the test statistics is developed by counting process and martingale theory. For the assessment of the performance of the procedure, a simulation study is conducted and suggested that it works well for practical situations. An illustrative example from a study aiming to investigate the HIV -1 infection risk among hemophilia patients is provided. The third part of this dissertation deals with the regression analysis of multivariate interval-censored data with informative censoring. Multivariate interval-censored failure time data often occur in the clinical trial that involves several related event times of interest and all the event times suffer interval censoring. Different types of models have been proposed for the regression analysis ( Zhang et al. (2008); Tong et al. (2008); Chen et al. (2009); Sun (2006)). However, most of these methods only deal with the situation where observation time is independent of the underlying survival time completely or given covariates. In this chapter, we discuss regression analysis of multivariate interval-censored data when the observation time may be related to the underlying survival time. An estimating equation based approach is proposed for regression coefficient estimate with the additive hazards frailty model and the asymptotic properties of the proposed estimates are established by using counting processes. A major advantage of the proposed method is that it does not involve estimation of any baseline hazard function. Simulation results suggest that the proposed method works well for practical situations. Finally, we will talk about the directions for future research. One is about the nonparametric test for interval-censored data with informative censoring. The other is about multiple generalized log-rank test for interval censored data.
Author: Ding-Geng (Din) Chen Publisher: CRC Press ISBN: 1466504250 Category : Mathematics Languages : en Pages : 435
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: Qingning Zhou Publisher: ISBN: Category : Languages : en Pages : 135
Book Description
This dissertation deals with various issues in the statistical analysis of bivariate interval-censored failure time data, including regression analysis, model selection and estimation of the association between failure times. In particular, it includes three projects. The first project discusses regression analysis of bivariate current status data under the marginal proportional hazards model. For the problem, by using Bernstein polynomials and an unspecified copula model, we develop a sieve maximum likelihood estimation approach that applies to very general situations. In particular, it allows one to estimate the underlying copula model and can be easily implemented. The strong consistency, asymptotic normality and efficiency of the estimators of regression parameters are established. In the second project, we consider regression analysis of bivariate case II interval-censored data. For this problem, we present a class of semiparametric transformation models which is very flexible and in particular includes the commonly used proportional hazards model as a special case. Also, for inference, we develop a sieve maximum likelihood approach based on Bernstein polynomials. The strong consistency, asymptotic normality and efficiency of the resulting estimators of the regression parameters are established. In the third project, we consider the class of semiparametric copula-based models, in which multivariate survival functions are characterized by parametric copulas and nonparametric marginal survival functions. One important issue in applying this class of models to a given data set is how to choose an appropriate parametric copula. We propose two model selection procedures for Archimedean copulas with bivariate interval-censored data. The first procedure is based on a comparison of the nonparametric and model-based estimators of the probability integral transformation K, while the second procedure is based on a pseudo-likelihood function.
Author: Clifford Isaac Anderson-Bergman Publisher: ISBN: 9781303810138 Category : Languages : en Pages : 213
Book Description
Interval censoring occurs when event times are known to have occurred within an interval, rather than observing the exact time of event. This includes observations that are right censored, left censored and contained in intervals such that the left side is greater than the origin and the right side is finite (i.e. neither right censored or left censored). For interval censored data, the most common survival estimator used is the non-parametric maximum likelihood estimator (NPMLE), a generalization of the Kaplan-Meier curve which does not require any uncensored event times. The popularity of this estimator is due in part to the fact that assessing model fit for interval censored data can be very difficult. However, the extreme flexibility of the estimator comes at the cost of high variance, often providing an n^(1/3) convergence rate rather than the more typical n^(1/2). In a compromise between a highly constrained parametric estimator and the overly flexible NPMLE, we apply the popular log-concave density constraint to the NPMLE. By constraining a non-parametric estimator to have a log-concave density, an inves- tigator can improve the performance without needing to select a parametric family or smoothing parameter. We describe a fast algorithm we have developed for finding the log-concave NPMLE for interval censored data. We demonstrate that using the constraint significantly reduces the variance of the survival estimates in comparison to the unconstrained NPMLE via simulations. Next, we present three inference methods for our new estimator. This includes a goodness of fit test, two methods of confidence interval construction and a Cox PH model which incorporates a baseline log-concave distribution. We evaluate the power of the goodness of fit test and compare the other inference methods with the unconstrained counterparts via simulation. We apply these methods to a study on the effects of different environments on the rates of lung cancer among mice and another study investigating age at menopause. While our work demonstrates that the application of the shape constraints can be very helpful in the context of interval censored data, in some situations the log- concave constraint may not allow for as heavy tailed distributions as the investigator would like. To address this, we propose a new, more flexible "inverse convex" shape constraint, examine its behavior via simulation and show that it provides a better fit than the log-concave estimator when applied to real income data, which is well known to be heavy tailed. We are very optimistic about applying this new estimator to censored data, although we have yet to implement an algorithm to do so. We end this work with an algorithm for finding the (unconstrained) bivariate NPMLE for interval censored data. The bivariate NPMLE is used when each subject has two censored outcomes and the investigator is interested in modeling the relation between the two outcomes. Quickly finding the NPMLE has proven to be a challenging computational problem, as the number of parameters to consider is of order O(n^2). We present an efficient EM algorithm to find the bivariate NPMLE. We note that this is not related to shape constrained estimation.
Author: Qiang Zhao
Author: Qiang Zhao
Author: Jeremy Gorelick
Author: Chao Zhu
Author: Jianguo Sun
Author: Ran Duan
Author: Ding-Geng (Din) Chen
Author: 黃進龍
Author: Qingning Zhou
Author: Clifford Isaac Anderson-Bergman
Author: Li Ding