# External Validation of Accelerometry-Based Mechanical Loading Prediction Equations
## 4 Discussion  
The objective of this study was to validate mechanical loading prediction equations previously developed using different sample and testing conditions than the ones used in their original validation studies in order to determine their external validity. This was accomplished by testing the mechanical loading prediction equations developed by [PERSON] et al., 2022 [20], [PERSON] et al., 2014 [17], and [PERSON] et al., 2023 [21] on a new sample performing walking, running, and several jumping activities. The main results indicated varying degrees of prediction accuracy, with discrepancies observed in the prediction errors for different activities and accelerometer placements. As far as we know, this is the first study to investigate the external validity of mechanical loading prediction equations. External validation is crucial for several reasons [27, 28, 29]. Firstly, it ensures that the prediction models are not overfitted to the specific sample and conditions of the original study, thus confirming their robustness and generalizability to other populations and settings. Secondly, this type of validation helps to identify the potential limitations and biases inherent in the original models. For example, models developed with a homogeneous sample may not perform well with a more diverse population, including variations in age, gender, body composition, and physical activity levels, which are all factors that can influence the prediction accuracy [24]. Thirdly, by testing these models in a variety of activity contexts we can better understand their practical applicability in real-world scenarios. This is particularly important for public health and clinical applications [30, 31], where accurate and reliable assessments of mechanical loading are needed to prescribe appropriate physical activities, monitor rehabilitation progress, and prevent injury. When comparing the results of this external validation study with the results of the original studies, some differences emerge. For walking and running, pGRF and pLR predictions using the [PERSON] et al., 2022 [20] equations, the original study reported lower prediction errors, with MAPE ranging from 6.8% to 7.3% for pGRF and 17.7% to 19.1% for pLR. In contrast, our current study found higher MAPE values, especially for walking,  
Figure 5: Bland–Altman plots displaying the level of agreement between actual and predicted pL for accelerometers worn at the ankle (panels **A,D**), lower back (panels **B,E**), and hip (panels **C,F**). These plots cover both the resultant vector (panels **A–C**) and its vertical component (panels **D–F**). Predictions of pLR during jumping were calculated using the equations from [PERSON] et al. (2023) [21]. The solid lines represent the bias (the mean difference between actual and predicted values), while the dashed lines mark the limits of agreement (bias \(\pm\)1.96 standard deviations). Abbreviations: pLR, peak loading rate. with MAPE exceeding 100% for pLR, indicating less accurate predictions in our external validation sample. Similarly, [PERSON] et al., 2014 [17] reported a MAPE of 8.3% for walking and running pGRF predictions, which is slightly better than the 9.7% and 11.1% MAPE observed in our study. For jumping activities, [PERSON] et al., 2023 [21] reported MAPE values between 12.3% and 14.5% for pGRF and 20.7% to 24.7% for pLR. Our current external validation study found significantly higher errors, particularly for pLR predictions during jumping, with MAPE values reaching up to 260.3%. These greater errors were, to some degree, expected because external validation involves testing the models on different populations and conditions than those used in the original studies, for which the models were optimized. When applied to new, more variable datasets, the models are likely to encounter variations that they were not initially exposed to, which usually leads to higher prediction errors [24; 27; 28]. The high errors observed in pLR predictions stem from several factors.