  We consider partly linear transformation models applied to current status
data. The unknown quantities are the transformation function, a linear
regression parameter and a nonparametric regression effect. It is shown that
the penalized MLE for the regression parameter is asymptotically normal and
efficient and converges at the parametric rate, although the penalized MLE for
the transformation function and nonparametric regression effect are only
$n^{1/3}$ consistent. Inference for the regression parameter based on a block
jackknife is investigated. We also study computational issues and demonstrate
the proposed methodology with a simulation study. The transformation models and
partly linear regression terms, coupled with new estimation and inference
techniques, provide flexible alternatives to the Cox model for current status
data analysis.
