ABSTRACT
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
