# External Validation of Accelerometry-Based Mechanical Loading Prediction Equations
## 3 Results
### Bland-Altman Plot Analysis  
A Bland-Altman plot of measurements that show high agreement would depict data points scattered randomly around the bias line, with most points falling within the limits of agreement, indicating no systematic bias between the actual and predicted values. In this study, Bland-Altman plots for pGRF prediction using [PERSON] et al., 2022 [20] showed systematic biases for both walking and running activities (Figure 1). The points for walking clustered more tightly around the mean difference line, while running data displayed a larger spread, particularly for higher values of ground reaction force. Similar trends were observed in pLR prediction equations using [PERSON] et al., 2022 [20] (Figure 2), where larger deviations were noted for running compared to walking. Regarding the Bland-Altman plot for walking and running \begin{table}
\begin{tabular}{l l r r r} \hline \hline
**Vector** & **Accelerometer Placement** & **MAE** & **MAPE** & **RMSE** \\ \hline \hline \multicolumn{2}{l}{**pGRF prediction**} & & & \\ \hline Resultant & Ankle & 646.2 & 27.2\% & 786.2 \\  & Lower back & 405.3 & 16.7\% & 518.9 \\  & Hip & 380.6 & 15.2\% & 499.2 \\ Vertical & Ankle & 633.6 & 28.1\% & 762.9 \\  & Lower back & 433.1 & 18.8\% & 542.0 \\  & Hip & 378.6 & 15.5\% & 500.8 \\ \hline \hline \multicolumn{2}{l}{**pLR prediction**} & & & \\ \hline Resultant & Ankle & 42,578.0 & 260.3\% & 46,675.9 \\  & Lower back & 30,446.0 & 171.4\% & 33,924.7 \\  & Hip & 25,233.5 & 149.0\% & 28,840.3 \\ Vertical & Ankle & 39,082.2 & 257.2\% & 43,130.8 \\  & Lower back & 36,628.7 & 213.6\% & 39,823.7 \\  & Hip & 28,880.9 & 161.5\% & 32,443.4 \\ \hline \hline \end{tabular} Abbreviations: MAE, mean absolute error; MAPE, mean absolute percent error; pGRF, peak ground reaction force; pLR, peak loading rate; RMSE, root mean square error.  
\end{table} 
Table 4: Accuracy indices for pGRF and pLR prediction for jumping based on the [PERSON] et al., (2023) [21] equations. The pLR predictions for jumping activities show particularly high error rates, with MAPE values exceeding 200%. These errors highlight the difficulty in capturing the rapid, high-magnitude forces involved in jumping, and the difficulty in reflecting measurement sensitivity in pLR predictions. \begin{table}
\begin{tabular}{l l r r r r} \hline \hline
**Vector** & **Activity** & **Accelerometer Placement** & **MAE** & **MAPE** & **RMSE** \\ \hline \hline \multicolumn{2}{l}{**pGRF Prediction**} & & & & \\ \hline Vertical & Walking & Hip & 75.0 & 9.7\% & 104.9 \\  & Running & Hip & 168.7 & 11.1\% & 213.5 \\ \hline \hline \end{tabular} Abbreviations: MAE, mean absolute error; MAPE, mean absolute percent error; pGRF, peak ground reaction force; RMSE, root mean square error.  
\end{table} 
Table 3: Accuracy indices for pGRF for walking and running based on the [PERSON] et al. (2014) [17] equation. pGRF prediction using the [PERSON] et al., 2014 [17] equation (Figure 3), the data points are much more evenly distributed around the bias, which is very close to zero, showing no signs of systematic bias. For jumping activities (Figures 4 and 5), Bland-Altman plots indicated substantial biases and wide limits of agreement, especially for pLR prediction (Figure 5). Figure 1: Bland–Altman plots displaying the level of agreement between actual and predicted pGRF 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 pGRF during walking and running were calculated using the equations from [PERSON] et al. (2022) [20]. 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: pGRF, peak ground reaction force.