A Varying-Coefficient Additive Hazard Model for Recurrent Events Data

The additive hazard model, which focuses on risk differences rather than risk ratios, has been widely applied in practice. In this paper, we consider an additive hazard model with varying coefficients to analyze recurrent events data. The model allows for both varying and constant coefficients. We first propose an estimating equation-based approach with spline basis smoothing for all functional coefficients. Then, we provide theoretical justifications for the resulting estimates, including consistency, rate of convergence, and asymptotic distribution. Furthermore, we construct a Cramér-von Mises test procedure to investigate whether the functional coefficients should be treated as constant, and its asymptotic null distribution is also derived. Extensive simulation experiments are conducted to evaluate the finite-sample performance of the proposed approaches. A Chronic Granulotamous Disease data set was analyzed to illustrate our methodology.