An efficient penalized estimation approach for semiparametric linear transformation models with interval-censored data

We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semiparametric models, the unknown monotone function is approximated via a monotone B-spline. A penalization technique is used to provide computationally efficient estimation of all parameters. To accomplish model fitting and inference, an easy to implement nested iterative expectation-maximization (EM) algorithm is developed for estimation, and a simple variance-covariance estimation approach is proposed which makes large-sample inference for the regression parameters possible. Theoretically, we show that the estimator of the unknown monotone increasing function achieves the optimal rate of convergence, and the estimators of the regression parameters are asymptotically normal and efficient under the appropriate selection of the order of the smoothing parameter and the knots of the spline space. The proposed penalized procedure is assessed through extensive numerical experiments and implemented in R package PenIC. The proposed methodology is further illustrated via a signal tandmobiel study.

Automated summary

Efficient estimation of flexible transformation models with interval-censored data is studied in this paper. To reduce the dimension of semiparametric models, the unknown monotone function is approximated using a monotone B-spline. A penalization technique is used to computationally efficiently estimate all parameters. An easy-to-implement nested iterative expectation-maximization (EM) algorithm is developed for estimation and a simple variance-covariance estimation approach is proposed for large-sample inference of the regression parameters. Theoretical results show that the estimator achieves the optimal convergence rate for the unknown monotone increasing function, and the estimators of the regression parameters are asymptotically normal and efficient under appropriate selection of the smoothing parameter order and the spline space knots. Extensive numerical experiments and implementation in the R package PenIC assess the proposed penalized procedure. The methodology is further illustrated through a signal transduction study.