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and Hughes (2011) have proposed new inference schemes for F(t 0 ). They ob-
serve that the model of McKeown and Jewell (2010) is a monotone response
model in the sense of Banerjee (2007) and therefore likelihood ratio inversion
using the quantiles ofDcan be used to set confidence intervals for F(t 0 ). Sal y
Rosas and Hughes (2011) extend this model to cover situations where the cur-
rent status of an individual may be determined using any one of k available
laboratory tests with differing sensitivities and specificities. This introduces
complications in the structure of the likelihood and the MLE must now be
computed via the modified ICM of Jongbloed (1998). Confidence intervals for
F(t 0 ) in this model can be constructed via likelihood ratio inversion as before
because this model is also, essentially, a monotone response model. McKeown
and Jewell (2010) also consider time-varying misclassification as well as ver-
sions of these models in a regression setting while Sal y Rosas and Hughes
(2011) deal with extensions to two-sample problems and a semiparametric re-
gression version of the misclassification problem using the Cox proportional
hazards model.
3.8
Semiparametric Models and Other Work
The previous sections in this chapter have dealt, by and large, with fully
nonparametric models. There has, of course, been significant progress in semi-
parametric modeling of current status data over the past 10 years. One of the
earliest papers is that of Shen (2000), who considers linear regression with
current status data.
The general linear regression model is of the form Yi i = T X i + i (an in-
tercept term is included in the vector of regressors) and Shen deals with a sit-
uation where one observes i = 1fY i C i g, C i being an inspection time. The
error i is assumed independent of Ci i and X i while Ci i and Y i are assumed con-
 
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