Recurrent event data and panel count data are often encountered in longitudinal follow-up studies. The main difference between the two types of data is the observation process. Continuous observations will result in recurrent event data; and discrete observations will lead to panel count data. In statistical literature, regression analysis of the two types of data have been well studied; and a typical assumption of those studies is that all covariates are accurately recorded. However, in many applications, it is common to have measurement errors in some of the covariates. For example, in a clinical trial, a medical index might have been measured multiple times. Then dealing with the differences among those measurements is an essential topic for statisticians.

For recurrent event data, we present a class of semiparametric regression models that allow correlations between censoring time and recurrent event process via frailty. An estimating equation based approach is developed to account for the presence of measurement errors in some of the covariates. Both large and finite sample properties of the proposed estimators are established. An example from the study of gamma interferon in chronic granulomatous disease is provided.

For panel count data, we consider two situations in which the observation process is independent or dependent of covariates. Estimating equations are developed for the estimation of the regression parameters for both cases. Simulation studies indicate that the proposed inference procedures perform well for practical situations. An example of bladder cancer study is used to demonstrate the value of the proposed method.