# Machine Learning Method for Prediction of Hearing Improvement After Stapedotomy
## 3 Results
### Regression Evaluation: Nested CV  
In Table 5, the accuracy scores (MAE \(\pm\) SD) of the five different models trained by nested CV are presented along with the RF without feature selection and best naive predictions column.  
For the naive predictions in nested CV, in the first eight rows (including the 4000 Hz frequency), the naive approach y_average performed best. In all other rows, the naive method x was best performing. Their MAE values are given in the rightmost column of Table 5.  
[PERSON] attained the highest MAE scores in a total of seven frequencies. For AC frequencies 250 Hz, 500 Hz, and 3000 Hz, MAEs of 8.08, 7.34, and 6.92 were recorded. In predicting BC frequencies, [PERSON] was most successful at frequencies 1000 Hz, 1500 Hz, 2000 Hz, and 3000 Hz with MAE scores of 3.87, 5.41, 5.62, and 5.30. [PERSON] had the highest prediction accuracy for AC hearing at 125 Hz, 1500 Hz, and 4000 Hz with MAEs 8.86, 5.69, and 8.41. RF demonstrated the lowest MAE scores among all considered models at AC frequencies 1000 and 2000 HZ and a BC frequency of 500 Hz. MAE values of 6.90, 5.61, and 3.23 were achieved at these frequencies. LR_all model achieved the lowest MAE value (10.90) at an AC frequency of 6000 Hz. Naive prediction approaches performed best for two of the highest AC and BC frequency targets. Specifically, an MAE of 12.26 was observed for AC frequency 8000 Hz, and an MAE of 5.21 was observed for BC hearing at 4000 Hz.  
Higher dB values were observed for SD than MAE in all occurrences. No significant differences between SDs were observed, with the most accurate models in terms of MAE typically achieving lower standard deviation values. However, some target frequencies can be found where SD was lower for models that did not achieve the highest MAE. For example, Ridge (6.95 \(\pm\) 8.00) had lower SD than RF (6.90 \(\pm\) 8.11) for AC hearing at 1000 Hz. Lasso (8.55 \(\pm\) 11.12, 11.26 \(\pm\) 14.15) achieved lower SD values than Ridge (8.41 \(\pm\) 11.17) and LR_all (10.90 \(\pm\) 14.94) for high frequency AC hearing at 4000 and 6000 Hz. Similarly, Lasso (12.46 \(\pm\) 16.03) had lower SD than the naive method x (12.26 \(\pm\) 16.36) for predicting AC  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Frequency** & **LR\_all** & **Lasso** & **Ridge** & **KNNs** & **RF** & **RF\_all** & **Naive** \\ \hline \multicolumn{6}{c}{AC} \\ \hline
125 & 10.25 \(\pm\) 12.55 & 8.90 \(\pm\) 10.95 & **8.86 \(\pm\) 10.92** & 9.54 \(\pm\) 11.58 & 9.48 \(\pm\) 11.40 & 9.48 \(\pm\) 11.20 & 10.51 \(\pm\) 12.65 \\  
hearing intensity at 8000 Hz. For bone conduction, a lower SD was observed for LR_all (3.61 \(\pm\) 4.85) than for RF (3.23 \(\pm\) 5.17) at frequency 500 Hz.  
Comparing results of the two training methods used, namely, the hold-out method (Table 4) and nested CV (Table 5), several differences were observed. Overall better accuracy scores were achieved with nested CV at AC frequencies 125 Hz, 250 Hz, 500 Hz, 3000 Hz, and 4000 Hz, as well as at BC frequencies of 500 and 3000 Hz. Worse scores were observed at other frequencies. The model performance also differed significantly. While the LR_all model was the best performing in the hold-out context, with best scores at six frequencies, it was ranked among the worst models during nested CV training. The model that demonstrated the best performance in the nested CV setting was Lasso.