Regression Analysis for Current Status Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 108

Another example is the accelerated failure time model, which is given by
log T = Z 0 + g(S) + W:
In this model, g(S) is an unknown smooth function for some covariates S
that may have a nonlinear effect on T and W and has a distribution known
up to a scale parameter. Shen (2000) and Xue et al. (2004) have discussed
the application of this model on current status data in detail. In addtion to
regression analysis, nonparametric methods are also very intuitive and useful
in analyzing current status data. However, it is beyond the scope of this chap-
ter, and so we do not introduce it here in this chapter; but for those who are
interested in these topics, you can refer to Sun (1999) and Sun (2006).
In all the approaches introduced in this chapter, the main ideas are the
same. That is, use a finite-dimensional parameter to approximate the infinite-
dimensional nuisance parameter. However, in the calculation procedure, one
may face the unstable estimation problem for some data sets. How to choose
the most appropriate method to estimate the baseline functions is challenging.
For the sieve estimator, the choice of the number of knots and the bandwidth
is another possible problem. And in the methods discussed, we only considered
the situation where covariates are time independent. In some cases, this may
not be true, and it would be useful to develop approaches that can handle
time-dependent covariates.
In the estimation procedures of bivariate current status data, for simplicity,
we assumed that the two related failure variables of interest have the same
monitoring time. This is true for many situations such that the two variables
represent two different events on the same subject. It is straightforward to
generalize the methodology to situations where the two variables may have
different monitoring times. For high-dimensional current status data, only a
few studies have been done, owing to the complicated structure. It may be of
interest in the near future.