Spline-Based Semiparametric Sieve Maximum Likeli- hood Method for Over-dispersed Panel Count Data

In this article we propose to analyze over-dispersed panel count data using a Gamma-Frailty nonhomogeneous Poisson process model. Conditional on a Gamma distributed frailty variable, the cumulative count, N (t), is assumed to follow a nonhomogeneous Poisson process. Cubic B-spline functions are used to approximate the logarithm of the baseline mean function Λ0 (t) in the semiparametric proportional mean model E (N (t) |Z) = Λ0 (t) e T 0 Z . The regression parameters and spline coefficients are estimated by maximizing a likelihood with the nuisance over-dispersion parameter, σ, replaced by a method of moment estimate. The asymptotic properties of the proposed maximum likelihood estimator, including its consistency, convergence rate and the asymptotic normality of the estimated regression parameters, are studied using modern empirical process theory. A spline-based least-squares standard error estimator is developed to facilitate a robust inference of the regression parameters. Simulation studies are conducted to investigate finite sample performance of the proposed method. Finally, the proposed method is applied to the data from a bladder tumor clinical trial.