Many cancer studies are conducted in multiple centers. While they have the advantage of more patients and larger population, center-to-center heterogeneity could be significant such that it cannot be ignored in analysis. In this paper, we propose semiparametric additive risk models with a general link function to estimate risk effects while accounting for center-specific baseline function. We propose an estimating equation for inference and show that the derived estimators are consistent and asymptotically normal. Simulation studies demonstrate good small-sample performance of the proposed method. We apply the method to analyze data from the Study of Left Ventricular Dysfunction (SOLVD) in 1990 and discuss application to one-to-one matched design.