Osteoporosis is characterized by an abnormal loss of bone mineral content, which leads to a tendency to non-traumatic bone fractures or to structural deformations of bone. Thus, bone density measurement has been considered as a most reliable method to assess bone fracture risk due to osteoporosis. In past decades, x-ray images have been studied in connection with the bone mineral density estimation. However, the estimated bone mineral density from the x-ray image can undergo a relatively large accuracy or precision error. The most relevant origin of the accuracy or precision error may be unstable x-ray image acquisition condition. In the previous study, we presented a bone mineral density estimation method that uses the trabecular bone filling factor in the radius x-ray image and that is relatively insensitive to the x-ray image acquisition condition. In this paper, we investigate the method using larger patient data and point out a preliminary result related to the fracture risk prediction using the method.