Penalized estimation of panel count data using generalized estimating equation

Abstract

This manuscript discusses the regression analysis of a semiparametric proportional mean model for panel count data. A spline-based generalized estimating estimation (GEE) approach is applied to account for the correlation among cumulative counts. To avoid the potential issue of overfitting, a penalization technique is applied to regularize the spline estimation. An easy-to-implement and computationally efficient two-stage iterative algorithm is developed to accomplish the penalized estimation. The proposed methodology does not specify the stochastic model of the underlying counting process and hence provides great flexibility for model fitting. Theoretically, the uniform convergence and the optimal rate of convergence for the functional estimator are established, and the asymptotic normality for regression parameter estimators is shown to be valid even if the working covariance matrix is misspecified. The semiparametric efficiency for regression parameter estimators can be achieved if the working matrix is correctly specified. Further, to address the issue of the underestimation of the variance-covariance matrix of regression parameter estimators for small sample sizes, which is brought up by GEE methodology, we propose a novel approach based on the modified sandwich estimator to compensate for the deficiency in variance-covariance estimation. Numerically, an extensive Monte Carlo study was conducted to evaluate the finite-sample performance of penalized spline estimators and the impact of the selection of the working matrix on the estimation, along with the robustness of the methodology to the underlying counting process. The proposed penalized approach was further applied to analyze data from a non-melanoma skin cancer chemoprevention study.