# Machine Learning Method for Prediction of Hearing Improvement After Stapedotomy
## 3 Results
### Feature Importance  
In this section, the feature importance results are discussed. If the type of hearing intensity is not specified in the text (preoperative/postoperative), it can be assumed to be preoperative. Only preoperative hearing intensities are part of feature sets and are therefore referenced frequently. To extract the features that are informative overall, Table 6 contains the top five most frequently selected features from the feature selection process on all targets. The high frequency AC value at 8000 Hz was chosen in the feature selection process in 10 out of 16 cases. AC hearing measurements at 500 Hz and ABG were selected for the prediction of seven targets. BC hearing intensities at 1000 and 4000 Hz were both selected five times. The following graphs show a comparison of feature importance analyses on four different targets. One high-frequency and middle-frequency target hearing intensity was compared for AC and BC, primarily to investigate the poorer prediction accuracy of high frequencies at the feature level. Feature importance graphs for predicting hearing at other frequencies are available in the Supplementary Files (PFI plots in S1 and SHAP plots in S2). PFI box plots show a decrease in MAE when randomly permuting each individual feature. If the model performs the same or better when a feature is randomly permuted, this indicates that the feature does not provide significant value to the prediction. Figure 5 contains a side-by-side comparison of the PFI for predicting AC hearing intensity at frequencies 2000 and 8000 Hz. The most significant features in the prediction of AC targets at 2000 Hz were the BC values at frequencies 2000 and 3000 Hz. A considerable impact was also observed for AC hearing intensities at frequencies 2000 and 8000 Hz, and age. Ear side and 125 Hz AC value had a negligible effect on prediction. When predicting the postoperative AC hearing intensity at 8000 Hz, the preoperative AC hearing intensity at 8000 Hz had the largest effect on successful prediction. Other relevant features were the combined BC hearing intensity at frequencies 3000 and 4000 Hz and age. AC value at the frequency 250 Hz was of limited predictive value, whereas random permutation of AC at 500 Hz mostly did not reduce the MAE. \begin{table}
\begin{tabular}{c c} \hline
**Feature** & **Number of Occurences** \\ \hline
8000 RefAir & 10 \\
500 RefAir & 7 \\ ABG & 7 \\
4000 BeffBone & 5 \\
1000 BeffBone & 5 \\ \hline \end{tabular}
\end{table} 
Table 6: Top 5 most frequently selected features. ABG = air–bone gap; xBefAir = preoperative air conduction hearing intensity at frequency x; xBefBone = preoperative bone conduction hearing intensity at frequency x. The SHAP feature directionality is shown in Figure 6. For the prediction of postoperative AC hearing at 2000 Hz, worse preoperative hearing at BC frequencies 2000 and 3000 Hz, as well as at AC frequencies 2000 and 8000 Hz, contributed to worse hearing prediction (higher dB values). Surgery on the right ear and young age were associated with better postoperative hearing. For the feature AC hearing at 250 Hz, the directionality cannot be clearly determined from the graph. Young age also had a better prognosis for the prediction of postoperative AC hearing at 8000 Hz. Higher feature values for AC hearing at 8000 Hz and combined BC hearing at 3000 and 4000 Hz had high SHAP values, causing worse postoperative hearing. Low values of AC hearing intensity at 8000 Hz show a significant impact on postoperative hearing. If low dB hearing intensities were observed preoperatively, they are likely to remain low postoperatively. Interestingly, for AC hearing at 250 and 500 Hz, the opposite influence can be observed--the model predicted lower (better) postoperative hearing intensity for individuals with worse preoperative hearing. However, the validity of this finding is questionable, as these two features have a limited impact on successful prediction (see Figure 5).