Semiparametric Estimation Methods for Panel Count Data Using Monotone B-Splines

We study semiparametric likelihood-based methods for panel count data with proportional mean model E[N(t)vertical bar Z] = Lambda(0)(t)exp(beta(T)(0)Z), where Z is a vector of covariates and Lambda(0)(t) is the baseline mean function. We propose to estimate Lambda(0)(t) and beta(0) jointly with Lambda(0)(t) approximated by monotone B-splines and to compute the estimators using generalized Rosen algorithm proposed by Jamshidian (2004). We show that the proposed spline-based likelihood estimators of Lambda(0)(t) are consistent with a possibly better than n(1/3) convergence rate if Lambda(0)(t) is sufficiently smooth. The normality of the estimators of beta(0) 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.