<p>In familial or multi-center studies, comparisons of outcomes across different centers are of interest. An extensive body of statistical models has been developed for various outcomes. However, most existing models apply only to simple data types. In this article, a fixed center effect proportional mean model is suggested to quantify center effects with respect to panel count data. When the number of centers is large, the traditional estimation methods that treat these center effects as categorical variables have many parameters to be estimated and thus may not be feasible to implement. In order to avoid including so many unknown variables, a new estimation procedure is proposed, where the center effects can be easily estimated by the center-specific ratio of observed to expected cumulative numbers of panel count data. The dimension of the estimated parameter space of the proposed procedure is only dependent on the number of covariates, and it is computationally more efficient. Given some regularity conditions, the asymptotic properties of the proposed estimators are established. Extensive simulation studies are conducted to assess the finite-sample properties of the proposed estimators. Finally, the proposed method is applied to a real dataset from the China Health and Nutrition Study.</p>