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)|Z] = Λ ₀(t) exp(β ^T ₀ Z), where Z is a vector of covariates and Λ ₀(t) is the baseline mean function. We propose to estimate Λ ₀(t) and β ₀ jointly with Λ 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 Λ ₀(t) are consistent with a possibly better than n ^1/3 convergence rate if Λ ₀(t) is sufficiently smooth. The normality of the estimators of β 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.