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Panel count data occur in studies that concern recurrent events, or event history studies, when study subjects are observed only at discrete time points. By recurrent events, we mean the event that can occur or happen multiple times or repeatedly. Examples of recurrent events include disease infections, hospitalizations in medical studies, warranty claims of automobiles or system break-downs in reliability studies. In fact, many other fields yield event history data too such as demographic studies, economic studies and social sciences. For the cases where the study subjects are observed continuously, the resulting data are usually referred to as recurrent event data.

This book collects and unifies statistical models and methods that have been developed for analyzing panel count data. It provides the first comprehensive coverage of the topic. The main focus is on methodology, but for the benefit of the reader, the applications of the methods to real data are also discussed along with numerical calculations. There exists a great deal of literature on the analysis of recurrent event data. This book fills the void in the literature on the analysis of panel count data.

This book provides an up-to-date reference for scientists who are conducting research on the analysis of panel count data. It will also be instructional for those who need to analyze panel count data to answer substantive research questions. In addition, it can be used as a text for a graduate course in statistics or biostatistics that assumes a basic knowledge of probability and statistics.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract
The event history study refers to the study concerning the patterns of the occurrences of certain events and is often seen in many fields. Among them, two that have seen or used such studies most are probably medical research and social sciences (Allison, 1984; Kalbfleisch and Prentice, 2002; Klein and Moeschberger, 2003; Nelson, 2003; Vermunt, 1997; Yamaguchi, 1991). In medical research, the event under study can be the occurrence of a disease or death, the hospitalization of certain patient, or the occurrence of some infection. In social sciences, examples of the subjects for event history studies include occurrence rates of births, deaths, marriages and divorces in demographic studies, and the employment or unemployment history of certain populations in social studies. In addition to these two, other fields that often see event history studies include reliability studies and tumorigenicity experiments.
Jianguo Sun, Xingqiu Zhao

2. Poisson Models and Parametric Inference

Abstract
It is well-known that for the analysis of count data, Poisson model is perhaps the most commonly used model or assumption (Breslow, 1984, 1990; Cameron and Trivedi, 1998). Thus for the analysis of panel count data, it is helpful to first consider Poisson-based approaches for the motivation of more general inference procedures and their comparison. As mentioned before, the focus of this chapter is on parametric approaches, which also can be seen as a motivation to many semiparametric inference procedures discussed later.
Jianguo Sun, Xingqiu Zhao

3. Nonparametric Estimation

Abstract
This chapter discusses one-sample analysis of panel count data with the focus on nonparametric estimation of the mean function of the underlying recurrent event process. As discussed above, one main objective of recurrent event studies is to investigate the recurrence pattern or shape of the recurrent event of interest. Although not completely determining the underlying process, the mean function does provide some insights about the recurrence patterns or shapes. Also it can be used for a graphical presentation of the underlying process as survival functions for failure time processes. Of course, it would be ideal to estimate the corresponding intensity process, but as discussed before, this is not possible for panel count data in general without some restrictive assumptions.
Jianguo Sun, Xingqiu Zhao

4. Nonparametric Comparison of Point Processes

Abstract
This chapter discusses nonparametric or distribution-free comparison of several point or recurrent event processes when one observes only panel count data. As commented above, in the case of panel count data, it is very difficult or impossible to estimate the intensity process and in consequence, one usually focuses on the rate or mean functions of the underlying recurrent event processes of interest. For the same reason, with respect to the comparison of the processes, it is common and also convenient to formulate the null hypothesis using the mean functions.
Jianguo Sun, Xingqiu Zhao

5. Regression Analysis of Panel Count Data I

Abstract
This chapter discusses regression analysis of panel count data. As discussed before, unlike recurrent event data, panel count data involve an extra observation process and this observation process may be independent of or could be related to the underlying recurrent event process of interest. In this chapter, we consider the situation where the two processes are independent of each other completely or conditionally given covariates. The situation where the two processes are related is investigated in the next chapter.
Jianguo Sun, Xingqiu Zhao

6. Regression Analysis of Panel Count Data II

Abstract
This chapter discusses the same problem as in the previous chapter, but under different situations. A basic assumption behind the methods described in the last chapter is that the underlying recurrent event process of interest and the observation process are independent of each other conditional on covariates. As pointed out before, sometimes this assumption may not hold. In other words, the observation process may depend on or contain relevant information about the recurrent event process. In a study on the occurrence of asthma attacks, for example, the observations on or clinical visits of asthma patients may be related to or driven by the numbers of the asthma attacks before the visits. The same can occur for similar recurrent event studies such as these on some disease infections or tumor development. In these situations, it is clear that the methods given in Chap. 5 are not valid as they would lead to biased estimation or wrong conclusions. The data arising from these cases are often referred to as panel count data with informative or dependent observation processes.
Jianguo Sun, Xingqiu Zhao

7. Analysis of Multivariate Panel Count Data

Abstract
This chapter discusses statistical analysis of multivariate panel count data, which arise when there exist several related types of recurrent events and study subjects are observed only at discrete time points. As remarked before, in this case, an issue that does not exist for univariate panel count data is the correlation between different types of events. To deal with it, two approaches are commonly used as with multivariate failure time data (Hougaard, 2000). One is the marginal model approach that leaves the correlation arbitrary, and the other is the joint model approach that characterizes the correlation through the use of some latent or random variables. In this chapter, we mainly adopt the marginal model approach and consider two problems, nonparametric comparison of treatments in terms of mean functions and regression analysis.
Jianguo Sun, Xingqiu Zhao

8. Other Topics

Abstract
In addition to what discussed in the previous chapters, there exist some other issues or topics about the analysis of panel count data that have been investigated in the literature or could occur in practice. In conducting regression analysis, for example, one can always ask which or if all covariate variables are important or significant enough to be included in the final model for the response variable of interest. That is, one faces a variable selection problem. For the problem, two situations usually occur. One is that the number of covariate variables is fixed and smaller than the sample size as in usual linear or nonlinear regression analysis (Johnson and Wichern, 2002). The other is that the number of covariate or predictor variables is much larger than the sample size and could be over several thousands or hundred thousands. The latter has become a huge and important topic in statistical genetic analysis as well as some other related areas (Beebe et al., 1998; Lee, 2004).
Jianguo Sun, Xingqiu Zhao

9. Some Sets of Data

Abstract
The following sets of data are used for the examples and discussion at various places of the book.
Jianguo Sun, Xingqiu Zhao

Backmatter

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