  We consider efficient estimation of flexible transformation models with
interval-censored data. To reduce the dimension of semi-parametric models, the
unknown monotone transformation function is approximated via monotone splines.
A penalization technique is used to provide more computationally efficient
estimation of all parameters. To accomplish model fitting, a computationally
efficient nested iterative expectation-maximization (EM) based algorithm is
developed for estimation, and an easily implemented variance-covariance
approach is proposed for inference on regression parameters. Theoretically, we
show that the estimator of the transformation function achieves the optimal
rate of convergence and the estimators of regression parameters are
asymptotically normal and efficient. The penalized procedure is assessed
through extensive numerical experiments and further illustrated via two real
applications.
