Sieve Estimation of Semiparametric Accelerated Mean Models with Panel Count Data

A widely adopted semiparametric model for analyzing panel count data is a proportional mean model, which may be deemed inappropriate when the proportionality assumption is violated. Motivated by the popular accelerated failure time model that relaxes such assumption, we investigate accelerated mean models for semiparametric regression analysis of panel count data. For estimation of bundled parameters, we develop a sieve least squares estimation procedure, which is robust in the sense that no distributional assumption is required for the underlying recurrent event process. Overcoming the theoretical challenges from bundled parameters, we establish the consistency and convergence rate of the proposed estimators, and derive the asymptotic normality of both the finite-dimensional estimator and the functionals of the infinite-dimensional estimator. Simulation studies demonstrate promising performances of the proposed approach, and an application to a skin cancer chemoprevention trial yields some new findings. MSC2020 subject classifications: Primary 62N01, 62N02; secondary 62F12.