Current Status Data in the Twenty-First Century: Some Interesting Developments - Interval-Censored-Time-to-Event Data: Methods and Applications - page 82

X = (V; ;Z;W), where = 1(U V ). It is easily seen that this extends the
models in Shen (2000) to incorporate a nonparametric covariate effect. Note
however that in the more restricted setup of Shen (2000), the distribution of e
is not assumed known. Ma and Kosorok (2005) develop a maximum penalized
log-likelihood estimation method for the parameters of interest and demon-
strate, in particular, the asymptotic normality and eciency of their estimate
of . A later paper, Ma and Kosorok (2006), studies adaptive penalized M-
estimation with current status data. More recently, Cheng and Wang (2012)
have generalized the approach of Ma and Kosorok (2005) to cover additive
transformation models. In their model, H(U) = T Z + P j=1 h j (W j ) + ,
where the h j 's are smooth and can have varying degrees of smoothness and
U is subjected to current status censoring by a random examination time V .
In contrast to the approach adopted in Ma and Kosorok (2005), Cheng and
Wang (2012) consider a B-spline-based estimation framework and establish
asymptotic normality and eciency of their estimate of . Banerjee et al.
(2006) study the Cox PH regression model with current status data. They de-
velop an asymptotically pivotal likelihood ratio method to construct pointwise
confidence sets for the conditional survival function of the event time T given
time-independent covariates Z. In related work, Banerjee et al. (2009) study
binary regression models under a monotone shape constraint on the nonpara-
metric component of the regression function using a variety of link functions
and develop asymptotically pivotal methods for constructing confidence sets
for the regression function. Through the connection of these models to the
linear transformation models with current status data as in Shen (2000), the
techniques of Banerjee et al. (2009) can be used to prescribe confidence sets
for the conditional survival function of T given X for a number of different
error distributions which correspond to the link functions in the latter paper.
Semiparametric models for current status data in the presence of a \cured"
proportion in the population has also attracted interest. Lam and Xue (2005)
use a mixture model that combines a logistic regression formulation for the