Low trauma fractures are amongst the most frequently encountered problems in the clinical assessment and treatment of bones, with dramatic health consequences for individuals and high financial costs for health systems. Consequently, significant research efforts have been dedicated to the development of accurate computational models of bone biomechanics and strength. However, the estimation of the fabric tensors, which describe the microarchitecture of the bone, has proven to be challenging using in vivo imaging. On the other hand, existing research has shown that isotropic models do not produce accurate predictions of stress states within the bone, as the material properties of the trabecular bone are anisotropic. In this paper, we present the first biomechanical study that uses statistically-derived fabric tensors for the estimation of bone strength in order to obtain patient-specific results. We integrate a statistical predictive model of trabecular bone microarchitecture previously constructed from a sample of ex vivo micro-CT datasets within a biomechanical simulation workflow. We assess the accuracy and flexibility of the statistical approach by estimating fracture load for two different databases and bone sites, i.e., for the femur and the T12 vertebra. The results obtained demonstrate good agreement between the statistically-driven and micro-CT-based estimates, with concordance coefficients of 98.6 and 95.5% for the femur and vertebra datasets, respectively.