Quantile regression for panel count data based on quadratic inference functions

Panel count data frequently arise in such areas as medical research and reliability studies, and various estimation methods have been developed for analyzing this type of data. In the literature, however, there are few methods incorporating the correlation within subjects. In this paper, on the basis of quadratic inference functions, we apply the quantile regression to analyze panel count data with time-varying coefficients. The proposed procedure can easily take into account the correlation within subjects and yields more efficient estimators even if the working correlation is misspecified. An efficient nonparametric hypothesis test is also proposed to determine whether coefficient functions are time varying or time invariant. Asymptotic results for the proposed estimators are established under some regularity conditions. Simulation studies are carried out to evaluate the finite-sample behavior of the method and to compare the estimation efficiency. Finally, an application of the method is demonstrated by re-analyzing a dataset from a bladder tumor study.