Efficient estimation of a linear transformation model for current status data via penalized splines

We propose a flexible and computationally efficient penalized estimation method for a semi-parametric linear transformation model with current status data. To facilitate model fitting, the unknown monotone function is approximated by monotone B-splines, and a computationally efficient hybrid algorithm involving the Fisher scoring algorithm and the isotonic regression is developed. A goodness-of-fit test and model diagnostics are also considered. The asymptotic properties of the penalized estimators are established, including the optimal rate of convergence for the function estimator and the semi-parametric efficiency for the regression parameter estimators. An extensive numerical experiment is conducted to evaluate the finite-sample properties of the penalized estimators, and the methodology is further illustrated with two real studies.