As far as radius is concerned, the distal radius fractures (DRFs) are the most common hazard. Epidemiological surveys indicate that DRFs are the most common upper limb fractures in patients over 65 years of age [14], and accounting for 26–46% of all skeletal fractures observed in primary care [15, 16]. Younger patients receive a DRF after an adequate trauma, and elderly patients suffer fractures through low-energy mechanisms. DRFs cause a decline in clinically important functions, which is an important reason for mortality or loss of independence in the elderly population [17, 18]. Low-energy fractures are hallmarks of low bone strength, and DRF patients had a 1.51-fold and 1.40-fold higher incidence of hip fracture and spinal fracture, respectively [10, 19]. Although a fall from a standing height is the most common cause of DRFs, sufficient bone strength can withstand this impact more and reduce the risk of DRFs [20]. Bone strength and quality is determined by bone architecture (including geometry and microarchitecture) and material properties (including mineralization and collagen cross-links) [2, 12]. BMD can provide insights regarding material properties and is a significant predictor of bone strength [1]. Nevertheless, the added value of bone architecture in estimating bone strength should not be ignored [3]. SOS may identify aspects of bone quality not completely captured by BMD, such as microarchitecture or material properties, and can be used for bone strength or integrity assessment [3, 8]. Therefore, identifying the low bone strength of radius through SOS can be used to screen high-risk groups of fractures, especially high-risk groups of DRFs, which can help us to intervene in advance and possibly reduce the incidence, associated morbidity, and health care costs of these injuries.

In this study, we constructed prognostic nomogram models based on age, gender, weight, height, and BMI. All these detected factors are closely related to low bone strength. We found patients with lower bone strength of radius were, on average, older, and had shorter height, lower body weight, and higher BMI than those with normal bone strength, and all SOS measurement was significantly lower in the low bone strength group than in the normal bone strength group. Furthermore, patients with low bone strength of radius had a higher proportion of women (7318 (85.7%) versus 6693 (59.2%), p < 0.001) than controls in gender distribution. The two prognostic models were created from the same data source using different statistical methods, and risk factors teased out from one method are not necessarily the same as in another. However, the difference in risk estimates from different models seemed to be minor of clinical concern, since both calibration plots and DCA of the two models aligned almost perfectly. Of note, a high area under the ROC curve (AUC) was noticed for both model 1 and model 2, respectively. The LASSO prognostic model 2 excluded weight and did not perform any better on predicting bone strength of radius. A possible reason for this is that weight was underestimated in the population studies used to develop the models. Additionally, weight might serve as a predictor operating along with other relevant risk factors such as BMI independently, producing a compounding effect on increasing the accuracy of prediction.

Recent studies have shown that age was a major determinant of SOS in both sexes. In females, SOS values had a much stronger correlation with age than male subjects [13]. Correspondingly, age and sex have a pronounced effect on the incidence rates of DRFs in the elderly population. Results of a large national registry of DRFs in adults showed that the vast majority of DRFs occurred in elderly women (≥ 50 years) [20]. Parallel to increasing age and decreasing estrogen, postmenopausal women experience loss and breakdown of bone mass [21]. The substantial increase in the number of fractures in postmenopausal women, and the ratio between women and men of 4:1, which could explain the lower bone strength of radius in women in our study [22]. Although it has been found in our research and similar studies that the SOS parameters of radius of men are more optimistic than women, it is worth noting that men over the age of 65 with DRFs are more likely to have post-fracture disability and fracture displacement and significantly associated with DRFs pattern complexity [23], indicating that there are also potential threats to the bone strength of the elderly male population [24]. Therefore, the assessment of future fracture risk among men with low radius SOS should not be neglected. Additionally, we found that the height of the low bone strength group significantly reduced compared with the normal group, which may be related to the damage of bone strength caused by osteoporosis [25, 26]. Height loss is a frequent manifestation of vertebral osteoporosis and is easy to measure in healthcare settings [27]. A significant association was observed between weight and bone strength which also corresponded to a previous study. It suggested that fat mass negatively correlated with BMD in young people [28]. Furthermore, integrating weight with age could modestly improve the prognosis of low bone strength in model 1 compared with the adjusted weight in model 2 because it is more sensitive and specific. Height and weight are also closely related to the range of BMI. A strong correlation between BMI and SOS parameters has been observed in diabetic patients [12]. Our findings are also indicated the correlation between BMI and SOS parameters; that is, higher BMI can predict lower bone strength of radius, an effect likely mediated by mechanical loading on bone [29]. In fact, fat mass and lean mass both cause mechanical loading on bone, and the relative effect of these two determinants of body composition on bone strength still remains controversial [29,30,31]. Logistic regression analysis showed that BMI was independent risk factors for DRFs [21], and a higher BMI increases the odds of a complex DRF [15]. However, others have shown that BMI does not affect the incidence of DRFs [32, 33], and other studies failed to detect the association between SOS or all three QUS measurements with BMI [34, 35]. In summary, we believe that changes in such indicators often cannot be understood separately, and the relation of SOS measures with BMI needs further investigation. Moreover, the nomograms as shown in this study are useful methods for communicating fractures risk to an individual patient, because they objectively incorporated many risk data of the individual patient.

The present findings should be interpreted within the context of some potential advantages and disadvantages. A major strength of the study is that the sample size was large, to allow for a reliable evaluation of relations between bone strength of radius and influencing factors. Moreover, this study includes both male and female populations across a broader age spectrum, which was quite rare in the same-topic study. In addition, SOS of radius provides relatively comprehensive bone strength information, while lower bone strength of radius is an independent risk factor for DRFs, which can provide a practical reference for clinical risk assessment of DRFs [6]. Nevertheless, our study has some limitations. First, SOS has some limitations due to the QUS device. For example, SOS results cannot be compared across devices, and the response to bone strength and ability to predict fractures of SOS is not as well studied as that of BMD. Additionally, this study was limited by its cross-sectional nature, with restriction of study cohort to only the Chinese population. However, the selection of grouping and modeling methods is fully based on the characteristics of the data, which provides a reference to other similar research. Although we used backward stepwise regression and LASSO regression to make models to compare which analysis method is better, there is only a slight difference between the two from the internal-verification effect of the model. Thus, external validation will be needed to clarify it further.