A robust approach for regression analysis of panel count data with time-varying covariates

Abstract

The validity of statistical inference for panel count data with time-varying covariates depends on the correct specification of within-subject correlation structures; misspecification often leads to questionable inference. To alleviate, robust inference has been proposed for mean models, which implicitly assume monotone mean functions. When covariate values fluctuate with time, however, the assumed monotonicity becomes unrealistic. In this research, we propose a robust inference based on rate models that are free of such constraints. Since the asymptotic variance has no closed form under the rate model, we further develop computationally efficient robust variance estimators using the Expectation-Maximization (EM) algorithm, thus sidestepping the need for computationally intensive numerical methods, which could undermine the robustness. Rigorous theoretical development is provided in support of parameter estimation and inference. Extensive simulation studies demonstrate the superiority of the proposed method. We present a real clinical application to illustrate the use of the proposed method.