Semiparametric analysis of multivariate panel count data with nonlinear interactions

Multivariate panel count data frequently arise in follow up studies involving several related types of recurrent events. For univariate panel count data, several varying coefficient models have been developed. However, varying coefficient models for multivariate panel count data remain to be studied. In this paper, we propose a varying coefficient mean model for multivariate panel count data to describe the possible nonlinear interact effects between the covariates and the local logarithm partial likelihood procedure is considered to estimate the unknown covariate effects. Furthermore, a Breslow-type estimator is constructed for the baseline mean functions. The consistency and asymptotic normality of the proposed estimators are established under some mild conditions. The utility of the proposed approach is evaluated by some numerical simulations and an application to a dataset of skin cancer study.