Augmented Estimating Equations for Semiparametric Panel Count Regression with Informative Observation times and Censoring Time

We propose an augmented estimating equation (AEE) approach for a semiparametric mean regression model with panel count data under possibly informative observation schemes and censoring. On a grid of time points, counts in all the subintervals of each observation window are treated as missing values, and are imputed with a robust working model given the observed count in the window. The observation scheme and the event process are allowed to be dependent through covariates and an unobserved frailty, which enters the mean function multiplicatively. Conditional on covariates, the censoring time and the event process can be dependent through the frailty. Regression coefficients and the unspecified baseline mean function are estimated with an Expectation-Solving (ES) algorithm. Distributions of the observation times, censoring time, and frailty are all considered as nuisance and unspecified. With empirical process theory, estimators for both the parametric and nonparametric component are shown to be consistent. The regression coefficient estimator is shown to be asymptotically normal. The cumulative baseline estimator is self-consistent in that the estimator is automatically non-decreasing. In simulation studies, the estimator performs well for moderate sample sizes and appears to be competitive in comparison with existing estimators under a wide range of practical settings. The utility of the proposed methods is illustrated with a bladder tumor study.