Estimation of the mean function with panel count data using monotone polynomial splines

We study nonparametric likelihood-based estimators of the mean function of counting processes with panel count data using monotone polynomial splines. The generalized Rosen algorithm, proposed by Zhang & Jamshidian (2004), is used to compute the estimators. We show that the proposed spline likelihood-based estimators are consistent and that their rate of convergence can be faster than n1/3. Simulation studies with moderate samples show that the estimators have smaller variances and mean squared errors than their alternatives proposed by Wellner & Zhang (2000). A real example from a bladder tumour clinical trial is used to illustrate this method.