An efficient penalized estimation approach for a semi-parametric linear transformation model with interval-censored data

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.