# External Validation of Accelerometry-Based Mechanical Loading Prediction Equations
## 3 Results  
Table 1 shows the characteristics of the participants from the studies by [PERSON] et al., 2022 [20], [PERSON] et al., 2014 [17], and [PERSON] et al., 2023 [21]. The studies by [PERSON] et al., 2022 [20] and [PERSON] et al., 2023 [21] involved a larger and older population compared to the study by [PERSON] et al., 2014 [17], which had a younger sample with a lower average body mass index. The diversity in sample characteristics across these studies shows the variability in the populations used to validate mechanical loading prediction equations. Accuracy of pGRF and pLR Predictions for Walking and Running Using the [PERSON] et al., 2022 [20] Equations  
The accuracy of mechanical loading predictions for walking and running using the [PERSON] et al., 2022 [20] equations is summarized in Table 2. The pGRF prediction for walking showed MAE ranging from 557.0 N to 621.7 N across different accelerometer placements, with MAPE values between 74.1% and 83.3%, which can be considered as very large prediction errors. The RMSE values ranged from 567.2 N to 632.5 N, indicating substantial discrepancies between predicted and actual values. For running, the pGRF prediction demonstrated improved accuracy, with MAE values ranging from 189.9 N to 247.5 N, \begin{table}
\begin{tabular}{l c c c} \hline  & **[PERSON] et al. (2022) [20]** & **[PERSON] et al. (2014) [17]** & **[PERSON] et al. (2023) [21]** \\ \hline  & (52 females, 79 males) & (20 females, 19 males) & (51 females, 27 males) \\ \hline Age (years) & 32.0 \(\pm\) 11.2 & 21.2 \(\pm\) 1.3 & 35.6 \(\pm\) 11.6 \\ Height (m) & 1.65 \(\pm\) 0.09 & 1.73 \(\pm\) 0.12 & 1.63 \(\pm\) 0.09 \\ Mass (kg) & 76.9 \(\pm\) 19.6 & 67.6 \(\pm\) 11.5 & 82.4 \(\pm\) 20.6 \\ BMI (kg\(\cdot\)m\({}^{-2}\)) & 28.5 \(\pm\) 81 & 22.5 \(\pm\) 2.3 & 31.3 \(\pm\) 8.7 \\ \hline \end{tabular} Data presented as mean \(\pm\) standard deviation. Abbreviations: BMI, body mass index.  
\end{table} 
Table 1: Sample characteristics of the [PERSON] et al. (2022) [20], [PERSON] et al. (2014) [17], and [PERSON] et al. (2023) [21] studies. MAPE between 11.6% and 14.4%, and RMSE from 240.9 N to 314.8 N. The pLR predictions for walking had high MAE values, ranging from 8042.0 N\(\cdot\)s\({}^{-1}\) to 10,328.2 N\(\cdot\)s\({}^{-1}\) and MAPE between 106.5% and 147.6%. In contrast, running pLR predictions showed MAE values from 14,198.7 N\(\cdot\)s\({}^{-1}\) to 22,334.3 N\(\cdot\)s\({}^{-1}\), MAPE between 35.2% and 56.6%, and RMSE from 17,408.8 N\(\cdot\)s\({}^{-1}\) to 26,363.9 N\(\cdot\)s\({}^{-1}\). With these results, particularly MAPE values over 100%, the pLR prediction can be regarded as unacceptable. Supplemental Table S1 describes the pGRF and pLR prediction errors for each separate walking and running speed using the [PERSON] et al., 2022 [20] equation. The results for walking and running pGRF predictions using the [PERSON] et al., 2014 [17] equation are presented in Table 3. For walking, the pGRF prediction using hip accelerometers had an MAE of 75.0 N, MAPE of 9.7%, and RMSE of 104.9 N. Running predictions showed higher errors, with an MAE of 168.7 N, MAPE of 11.1%, and RMSE of 213.5 N. Compared to [PERSON] et al., 2022 [20], the [PERSON] et al., 2014 [17] equation generally showed a much better accuracy for walking but comparable errors for running. The pGRF prediction errors for each walking and running speed using the [PERSON] 2014 [17] equation are shown in Supplemental Table S2.