The Statistical Analysis of Interval-censored Failure Time Data

verfasst von: Jianguo Sun

Verlag: Springer New York

Buchreihe : Statistics for Biology and Health

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft" , Springer Professional "Technik"

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Über dieses Buch

Survival analysis, the analysis of failure time data, is a rapid developing area and a number of books on the topic have been published in last twenty-five years. However, all of these books deal with right-censored failure time data, not the analysis of interval-censored failure time data. Interval-censored data include right-censored data as a special case and occur in many fields. The analysis of interval-censored data is much more difficult than that of right-censored data because the censoring mechanism that yields interval censoring is more complicated than that for right censoring.

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. A number of inference approaches are discussed in the book, including the maximum likelihood, estimating equations, sieve maximum likelihood, and conditional likelihood. One major difference between the analyses of right- and interval-censored data is that the theory of counting processes, which is responsible for substantial advances in the theory and development of modern statistical methods for right-censored data, is not applicable to interval-censored data. The focus of the book is on nonparametric and semiparametric inferences, but it also describes parametric and imputation approaches. In addition, Bayesian methods and the analysis of interval-censored data with informative interval censoring are considered as well as the analysis of interval-censored recurrent event, or panel count, data.

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. It can also be used as a text for a graduate course in statistics or biostatistics that assume a basic knowledge of probability and statistics.

Jianguo (Tony) Sun is a professor at the Department of Statistics of the University of Missouri-Columbia. He has developed novel statistical methods for the analysis of interval-censored failure time data and panel count data over the last fifteen years.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract

By failure time data, we mean data that concern positive random variables representing times to certain events. Examples of the event, often referred to as the failure or survival event, include death, the onset of a disease or certain milestone, the failure of a mechanical component of a machine, or learning something. The occurrence of the event is usually referred to as a failure. Sometimes we also use the terminology survival data and refer to the variable of interest as survival time or the survival variable. Failure time data arise extensively in medical studies, but there are many other investigations that also produce failure time data. These include biological studies, demographical studies, economic and financial studies, epidemiological studies, psychological experiments, reliability experiments, and sociological studies.

2. Inference for Parametric Models and Imputation Approaches

Abstract

Although the main focus of this book is nonparametric and semiparametric inference procedures, it is helpful to first consider inference methods for parametric models and some imputation approaches. A main advantage of parametric approaches is that their implementation is straightforward in principle and in fact standard maximum likelihood theory generally applies. Imputation approaches are used to reduce the problem of analyzing interval-censored failure time data to that of analyzing right-censored failure time data. Thus one can avoid dealing with interval censoring and use existing inference procedures and statistical software developed for right-censored data.

3. Nonparametric Maximum Likelihood Estimation

Abstract

Estimation of a survival function is perhaps the first and most commonly required task in the analysis of failure time data. There can be many reasons or purposes for such a task. For example, an estimated survival function can be used to assess the validity of an assumption about a particular parametric model for the underlying survival variable of interest. Also, one may need to estimate survival functions to estimate certain survival probabilities, to graphically compare several different treatments, or to predict survival probabilities for future patients. In the case where a parametric model can be reasonably assumed for the underlying survival function, the estimation problem is relatively easy, and the maximum likelihood approach discussed in Section 2.3 is commonly used for the problem. In this chapter, attention is focused on nonparametric estimation of survival functions along with estimation of hazard functions.

4. Comparison of Survival Functions

Abstract

Comparison of treatments is one of the primary objectives in most medical studies such as clinical trials. In such cases, nonparametric or distributionfree methods are usually preferred if there does not exist strong evidence to support a particular parametric model. For right-censored failure time data, most of the existing nonparametric methods can be classified into two types: weighted log-rank tests and weighted Kaplan-Meier. In particular, the logrank test is perhaps the most commonly used nonparametric procedure in practice. Detailed discussions about these two types of statistics can be found in Fleming and Harrington (1991) and Kalbfleisch and Prentice (2002) among other books. This chapter deals with similar methods that are appropriate for interval-censored failure time data. Alternatives to these methods, which are discussed in Chapters 5 and 6, base the comparisons on the score tests derived under various regression models.

5. Regression Analysis of Current Status Data

Abstract

As commented before, current status data occur in many fields including animal carcinogenicity experiments, demographical studies, econometrics, epidemiological studies, and reliability studies. In some situations such as carcinogenicity experiments on occult tumors, current status data are the only information available about underlying survival variables of interest such as tumor onset time (Dinse and Lagakos, 1983). That is, the survival variables cannot be directly measured. In some other situations such as those arising from cross-sectional studies on some milestone event, current status data provide easier and more reliable information about the time to the event than complete data that give exact times to the event. An example of such situations is epidemiological studies where the event of interest is onset of certain chronic disease (Keiding, 1991; Keiding et al., 1996; Shiboski and Jewell, 1992). Another example is given by demographical studies where the event of interest can be, for instance, first pregnancy or marriage (Diamond and McDonald, 1991; Diamond et al., 1986).

6. Regression Analysis of Case II Interval-censored Data

Abstract

This chapter discusses regression analysis of general or case II intervalcensored failure time data. Compared with current status data, it is apparent that case II interval-censored data provide more information about the underlying survival time of interest. Thus intuitively, regression analysis of case II interval-censored data may seem to be simpler than that of current status data. On the other hand, for case II interval-censored data, one has to deal with two or more variables representing observation times rather than only one variable as in the case of current status data. As seen in Chapter 3 and the following, regression analysis of case II interval-censored data is more complicated and difficult than that of current status data in both computation and theory.

7. Analysis of Bivariate Interval-censored Data

Abstract

Bivariate failure time data occur in many situations. A standard example is studies on twins or eyes where one is interested in times to the occurrences in both twins or eyes of a certain event such as some diseases or disease-related symptoms. By bivariate failure time data, we usually mean that there exist two failure time variables of interest, and the two variables cannot be assumed to be independent. For example, in an eye study, the two variables could be times to the blindness for both left and right eyes, and the two are obviously related. A more general example of bivariate failure time data is times to two same or different types of events that happen on the same subject. It is apparent that bivariate failure time data are special cases of multivariate failure time data that concern information about several possibly related failure times. Sometimes, multivariate failure time data are also referred to as correlated failure time data. This chapter focuses on bivariate failure time data in the presence of interval censoring.

8. Analysis of Doubly Censored Data

Abstract

As discussed in Section 1.3, doubly censored data occur in studies that consist of two related events with one followed by the other. A typical example is given by a disease progression study in which the onset of the disease is caused or preceded by certain virus infection. In these situations, three variables are present, and they are time to infection, time between infection and the onset of the disease, and time to the onset of the disease. It is apparent that one only needs to know two of the three variables. If the variable of interest is the time to infection or the time to the onset of the disease, in general, one only needs to analyze the variable of interest without the need of dealing with the other two variables.

9. Analysis of Panel Count Data

Abstract

10. Other Topics

Abstract

In this chapter, we discuss several important topics about interval-censored failure time data that can occur in practice but were not discussed in the previous chapters. These include goodness-of-fit (GOF) tests or regression diagnostics, regression analysis of failure time data with interval-censored covariates, Bayesian analysis of interval-censored failure time data, and informative interval censoring.

Backmatter

Titel: The Statistical Analysis of Interval-censored Failure Time Data
verfasst von: Jianguo Sun
Verlag: Springer New York
Electronic ISBN: 978-0-387-37119-1
Print ISBN: 978-0-387-32905-5
DOI: https://doi.org/10.1007/0-387-37119-2