Efficient estimation of partially linear additive Cox model under monotonicity constraint

We provide a simple and practical, yet flexible spline estimation method for partially linear additive Cox model with monotonicity constraint. We propose to approximate the unknown monotone function by monotone B-splines, and employ a hybrid numerical approach based on the Newton-Raphson algorithm and the isotonic regression to compute the spline estimates. We show that the spline estimators of the nonparametric components achieve the optimal rate of convergence under the smooth condition, and that the estimators of the regression parameters are asymptotically normal and efficient. Moreover, a direct variance estimation method based on the least-squares estimation is proposed. The finite-sample performance of the spline estimates is evaluated by a Monte Carlo study. The methodology is illustrated with a synovial sarcoma dataset.