Two Likelihood-based Semiparametric Estimation Methods for Panel Count Data with Covariates

We consider estimation in a particular semiparametric regression model for the mean of a counting process with “panel count” data. The basic model assumption is that the conditional mean function of the counting process is of the form E{N(t)|Z} = exp(β 0 Z)Λ0(t) where Z is a vector of covariates and Λ0 is the baseline mean function. The “panel count” observation scheme involves observation of the counting process N for an individual at a random number K of random time points; both the number and the locations of these time points may differ across individuals. We study semiparametric maximum pseudo-likelihood and maximum likelihood estimators (β̂ n , Λ̂ ps n ) and (β̂n, Λ̂n) of the unknown parameters (β0, Λ0). The pseudo-likelihood estimator is fairly easy to compute, while the maximum likelihood estimator poses more challenges from the computational perspective. We study asymptotic properties of both estimators under the proportional mean model and we also establish asymptotic normality for the estimators of the regression parameter β0. The methods are validated by some simulation studies and illustrated by an example.