A semiparametric pseudolikelihood estimation method for panel count data

Abstract

In this paper, we study panel count data with covariates. A semiparametric pseudolikelihood estimation method is proposed based on the assumption that, given a covariate vector Z , the underlying counting process is a nonhomogeneous Poisson process with the conditional mean function given by E { N ( t ) | Z } = Λ 0 ( t ) exp (β′ 0 Z ). The proposed estimation method is shown to be robust in the sense that the estimator converges to its true value regardless of whether or not N ( t ) is a conditional Poisson process, given Z . An iterative numerical algorithm is devised to compute the semiparametric maximum pseudolikelihood estimator of (β 0 , Λ 0 ). The algorithm appears to be attractive, especially when β 0 is a high‐dimensional regression parameter. Some simulation studies are conducted to validate the method. Finally, the method is applied to a real dataset from a bladder tumour study.