In randomized clinical trials, treatment effects are usually evaluated based only on current study data. However, in many cases, data of previous trials for the control treatment are available. Here we focus on how to use the historical information effectively with negligible bias which leads to the control of type I error. It is important to reduce the risk of bias using the methods that borrows historical information most when the current data are consistent with historical data and borrows least when the current data are inconsistent. This kind of idea is sometimes called as dynamic borrowing. In this study, we explicitly derive the approximated bias formula in a simple hierarchical model with the prior mean fixed. Using the derived bias formula, we propose two approaches for bias and type I error control. Simulation studies showed our proposed estimators were performed reasonably well compared to other approaches. We illustrate our method for a randomized clinical trial data with historical control information.