Biomedical Engineering Reference
In-Depth Information
problems from multivariate current status data arise when two or more events
are of interest and all of them are Case I interval-censored. The development
of statistical methods for this type of data is still very limited despite increas-
ing interest. One challenge is how to measure the association among different
events. Section 4.5 introduces the maximum likelihood approach for bivariate
current status data. The two failure times are assumed to follow the propor-
tional odds model marginally, and the joint distribution is given by copula
models. Section 4.6 provides two animal studies to illustrate the approaches
discussed in the previous sections. In Section 4.7, bibliographic notes are pro-
vided. General discussion about the regression analysis for current status data
can also be found in the last section.
To make the notations consistent throughout this chapter, we make the
following definitions. Suppose in a survival study with n independent subjects
that T
i
and C
i
denote the failure time and the observation time for the i-
th subject, respectively, i = 1;:::;n. Then for current status data, the only
information available is given by the form (Ci,
i
;
i
;Z
i
); i = 1;:::;n, where
i
=
I(T
i
C
i
), denoting whether the failure occurs before or after the observation
time and Zi
i
is the vector of covariates for subject i.
4.2
Regression
Analysis
with
Proportional
Hazards
Model
In this section we focus on regression analysis for current status data with the
proportional hazards model. The proportional hazards (PH) model, which is
also known as the Cox model (Cox (1972)), is the most widely used regression
model in failure time data analysis. The PH model specifies that
(t; Z
i
) =
0
(t) exp(Z
0
i
);i = 1;:::;n
(4.1)
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