A semiparametric pseudolikelihood estimation method for panel count data

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} = {Lambda}0 (t) exp ((beta)ʹ0Z). 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 ((beta)0, {Lambda}0). The algorithm appears to be attractive, especially when (beta)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.