# Machine Learning Method for Prediction of Hearing Improvement After Stapedotomy
## 4 Discussion  
While it is difficult to assess the obtained results due to the shortage of hearing recovery prediction methods after slapedotomy, it is possible to compare the findings with hearing recovery prediction approaches of other surgeries or illnesses. Most of the existing approaches are classification-based--the models are trained to predict whether hearing recovery will be achieved or not. The existing approaches evaluate hearing recovery either by [PERSON]'s criteria [4; 5; 6; 7] or thresholding based on PTA or ABG [8; 9]. In our case, we aimed to accurately predict each postoperative hearing intensity. The hearing recovery level can be extracted from the audiogram estimate. It is hypothesized that estimating an entire postoperative audiogram provides more informativeness for slapedotomy prognosis. Since the single hold-out method has been shown to have low statistical power and high bias [27], regression results from training the models in nested cross-validation will be given higher importance when discussing regression results. The single hold-out method has provided value as an independent benchmark for model evaluation and further in the process for feature importance estimation. Considering the nested CV setup, the regression results indicate that the hearing intensities at border frequencies (8000 Hz AC, 4000 Hz BC) are notably more difficult to predict, given the superior performance of the naive model, which predicts no change from preoperative hearing. Furthermore, the models demonstrated mediocre quality for predicting values at high frequencies of 6000 Hz AC and 3000 Hz BC with MAE values below, but in close proximity to, the naive predictions. Initial hearing intensities at given frequencies have the highest variance, which could result in challenging prediction. Prediction of low-frequency AC hearing levels (125 Hz, 250 Hz, 500 Hz) also proved to be difficult with models achieving MAE values of around 8 dB. A lower MAE was observed for BC hearing targets, as the targets rarely deviated significantly from the preoperative values. The best prediction accuracy was achieved for the most crucial AC hearing frequencies 1000, 1500, 2000, and 3000 Hz. Among the models trained during the nested CV, Lasso performed best overall, considering the limitations of all models discussed in the previous paragraph. It should be noted that naive methods achieved best results at border frequencies (8000 Hz AC, 4000 Hz BC), indicating a poor prediction quality of all machine learning methods at these frequencies. The efficiency of feature selection and regularization approaches was demonstrated in the results, as Lasso and Ridge outperformed LR_all with all features for 13 out of 16 targets. Ridge and RF methods provided prediction accuracy comparable to Lasso. The success of linear models can be attributed to the linear relationship between preoperative and postoperative data. The superiority of Lasso and Ridge can also be due to the previous usage of Lasso in the feature selection. However, RF with all features did not achieve better results than other methods for any frequency, which further implies the feature selection benefits. KNNs was consistently the worst prediction model. This may indicate that the audiogram data are not well separated and, therefore, prediction based on feature proximity is not suitable. Feature importance based on the selection frequency for the prediction of different targets indicates an overall significance of high-frequency AC hearing at 8000 Hz. Based on the four closely analyzed targets, AC hearing at 8000 Hz consistently delivers value in the prediction of both AC and BC targets. The number of feature occurrences can be misleading for feature importance evaluation. For example, AC hearing intensity at 500 Hz was selected seven times. However, randomly permuting it in two analyzed cases only led to minimal MAE score decrease. Further insight into feature importance was provided by PFI and SHAP analyses.