Partially linear single-index proportional hazards model with current status data

A partially linear single-index proportional hazards model with current status data is introduced, where the cumulative hazard function is assumed to be nonparametric and a nonlinear link function is assumed to take a parametric spline function. Efficient estimation and effective algorithm are established. Polynomial spline smoothing is invoked for the estimation of the cumulative baseline hazard function with monotonicity constraint on the functional, while a simultaneous sieve maximum likelihood (SML) estimation is proposed to estimate regression parameters. The proposed SML estimator for the parameter vector is shown to be asymptotically normal and semiparametric efficient. The spline estimator of the functional of the cumulative hazard function is shown to achieve the optimal nonparametric rate of convergence. A simulation study is conducted to examine the finite sample performance of the proposed estimators and algorithm, and an analysis of renal function recovery data is presented.