Analysis of panel count data with measurement errors in the covariates

Panel count data often occurs in clinical, industrial, and demographic studies where the subjects may experience multiple recurrences of the event of interest over time. This paper considers the regression analysis of panel count data when covariates are measured with error. The simplest method to solve this problem is the complete case method, which only analyzes subjects with complete covariates. In the context of right-censored data, Zhou and Pepe [ Zhou, H. and Pepe, M. S., 1995, Auxiliary covariate data in failure time regression analysis. Biometrika, 82, 139 - 149] and Zhou and Wang [ Zhou, H. and Wang, C.- Y., 2000, Failure time regression with continuous covariates measured with error. Journal of Royal Statistical Society Series B, 62, 657 - 665] proposed the estimated partial likelihood methods using discrete auxiliary covariates and continuous auxiliary covariates, respectively. In this paper, these methods are extended to panel count data and an iterative algorithm is developed, in order to estimate the baseline mean function and regression parameters. In addition, simulation studies are conducted to evaluate the proposed method.