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

Abstract

We study semiparametric likelihood-based methods for panel count data with proportional mean model E[ℕ(t)|Z]=Λ⁰(t)exp(β₀^TZ), 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 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 Λ₀(t) are consistent with a possibly better than n^1/3 convergence rate if Λ₀(t) is sufficiently smooth. The normality of the estimators of 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.

Keywords:  :

• B-splines
• Counting process
• Empirical process
• Generalized Rosen algorithm
• Maximum likelihood method
• Maximum pseudolikelihood method
• Monte Carlo