chapter  5
Statistical Analysis of Dependent Current Status Data
Pages 36

Department of Statistics, Sookmyung Women’s University, Seoul, South Korea

Jinheum Kim

Department of Applied Statistics, University of Suwon, Gyenggi, South Korea

Chung Mo Nam

Department of Preventive Medicine, Yonsei University College of Medicine,

Seoul, South Korea

Youn Nam Kim

Department of Preventive Medicine, Yonsei University College of Medicine,

Seoul, South Korea

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.4 Software: R Package CSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.5 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

114 Interval-Censored Time-to-Event Data: Methods and Applications

R Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Current status data are commonly found in observational studies. One typical

example is a tumorigenicity experiment where the estimation of the distribu-

tion and covariate effect on tumor onset is a main interest. In some animal

tumorigenicity data, the occurrence time of the tumor is not observed because

the existence of the tumor is examined only at either death time or sacrifice

time of the animal. Thus, we observed only the states subjects stay at the

observation times instead of exact state transition times. Such an incomplete

data structure makes it difficult to investigate the impact of treatment on the

occurrence of tumor. The problem is more serious according to the lethality of

tumor. Most existing methods assume that tumor onset time and observation

time are independent. However, this assumption is sometimes not enough. In

particular, in a tumorigenicity study, the observation time occurs either at

death or at sacrifice. When observation is made with a naturally dead animal,

this death may be related to both tumor onset and treatment. Lindsey and

Ryan (1994) constructed the likelihoods of four possible outcomes consider-

ing two different cases of censoring time. Lagakos and Louis (1988) suggested

methods for several possible cases with respect to the lethality of the tumor.

If the tumor is not lethal, that is, the tumor cannot cause death, censoring

time would be independent of tumor onset time. For the lethal tumor case,

two cases can be considered. One is a rapidly lethal tumor and the other is an

intermediate lethal tumor. In the former case, the death time follows the onset

of tumor and the logrank test is used to compare treatments on tumor onset

times. However, most tumors are intermediate lethal tumors and do not pro-

vide any evidence about the correlation between tumor onset time and death

time. Therefore, two events of interest are tumor onset and death, and the