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

摘要

We study semiparametric likelihood-based methods for panel count data with proportional mean model E[N(t)|Z] = Λ_0(t)exp(β_0~TZ), 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.