Semiparametric Estimation Methods for Panel Count Data Using Monotone Polynomial Splines

We study semiparametric likelihood-based methods for panel count data with proportional mean model E[N(t)|Z] = Λ0(t) exp(β 0 Z), where Z is a vector of covariates and Λ0(t) is the baseline mean function. We propose to estimate Λ0(t) and β0 jointly with Λ0(t) approximated by monotone polynomial B -splines and to compute the estimators using the generalized Rosen algorithm utilized in Zhang and Jamshidian (2004) for nonparametric maximum likelihood estimation problems. We show that the proposed spline-based likelihood estimators of Λ0(t) are consistent with a possibly better than n 1/3 convergence rate. The normality of estimators of the β0 is also established. Comparisons between the proposed estimators and their alternatives studied in Wellner and Zhang (2007) are made through simulations studies, regarding their finite sample performance and computational complexity. A real example from a bladder tumor clinical trial is used to illustrate the methods.