Complex diseases often aggregate within families and using the history of family members' disease can potentially increase the accuracy of the risk assessment and allow clinicians to better target on high risk individuals. However, available family risk scores do not reflect the age of disease onset, gender and family structures simultaneously. In this paper, we propose an alternative approach for a family risk score, the stratified log-rank family score (SLFS), which incorporates the age of disease onset of family members, gender differences and the relationship among family members. Via simulation, we demonstrate that the new SLFS is more closely associated with the true family risk for the disease and more robust to family sizes than two existing methods. We apply our proposed method and the two existing methods to a study of stroke and heart disease. The results show that assessing family history can improve the prediction of disease risks and the SLFS has strongest positive associations with both myocardial infarction and stroke.