# Machine Learning Method for Prediction of Hearing Improvement After Stapedotomy
## 2 Materials and Methods  
### Dataset  
Stapedotomies were performed by a single surgeon under general anaesthesia through the transcanal approach. The stapedotomy and removal of the stapes suprastructure were performed with an argon laser (manufactured by A.R.C. Laser GmbH, Nurnberg, Germany) in all cases. A titanium MatriX stapes prosthesis (produced by Heinz Kurz GmbH, Dusslingen, Germany) was inserted into the stapedotomy and fixed on the long process of the incus. Patient data were collected from tertiary medical center over a four-year period from 2019 to 2023. Pure-tone audiometry was performed one day before and two months after stapedotomy. Air conduction (AC) intensities were measured at 10 frequencies, 125 Hz, 250 Hz, 500 Hz, 1000 Hz, 1500 Hz, 2000 Hz, 3000 Hz, 4000 Hz, 6000 Hz, and 8000 Hz, which are presented in increasing order on the x-axis of the audiograms. For bone conduction (BC), 6 frequency categories were analyzed (500 Hz, 1000 Hz, 1500 Hz, 2000 Hz, 3000 Hz, and 4000 Hz). The audiograms were collected on paper and the measurements manually copied into a computer. Ambiguous samples containing more than 3 illegible hearing intensities were excluded from further analysis.  
A total of 123 ear measurements were included in the final dataset from 79 female subjects (approximately 64%) and 44 male subjects (approximately 36%), reflecting the slight female predominance in the affection of otosclerosis [10]. Missing values, which occurred in rare cases at individual border frequencies (approximately 0.5% of all data), were interpolated using the nearest neighbor technique. The use of neighbor hearing intensity was chosen because the border hearing intensities had only one neighbor, typically within a narrow range--in our dataset, around 86% of the values at neighboring frequencies differed by 10 dB or less. The preoperative air conduction pure-tone average--PTA (500 Hz, 1k Hz, 2k Hz, 3k Hz) [10]--decreased from 55.8 dB to 32.3 dB after stapedotomy.  
The features are presented in two groups for clarity. The base features in Table 1 include known patient data at the time of the surgery and the operated ear side, whereas the preoperative hearing intensity features (Table 2) are audiogram-based.  
The target values of our prediction are postoperative hearing intensities made at the same frequencies as the preoperative hearing intensities, as pure-tone audiometry is typically performed before and after the surgery at the same standard frequencies. Both BC and AC hearing intensities were predicted to allow an estimation of the full postoperative audiogram. An example of the hearing improvement reflected in the audiogram measurements is shown in Figure 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Features** & **Frequency (N = 123) 1** \\ \hline Age & 50.28 \(\pm\) 11.40 \\ Gender & \\ Female & 79 (64.2) \\ Male & 44 (35.8) \\ Ear side & \\ Left & 67 (54.5) \\ Right & 56 (45.5) \\ \hline \hline \end{tabular} \({}^{1}\) Total number of samples.  
\end{table}
Table 1: Base dataset features. Values are presented as mean \(\pm\) standard deviation (numerical) or number (%) (categorical).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Frequency in Hz** & **Intensity in dB 1** \\ \hline Air conduction readings & \\ 125 & 52.64 \(\pm\) 15.15 \\ 250 & 54.88 \(\pm\) 14.28 \\ 500 & 57.24 \(\pm\) 14.89 \\ 1000 & 56.87 \(\pm\) 14.49 \\ 1500 & 54.51 \(\pm\) 15.73 \\ 2000 & 53.54 \(\pm\) 17.97 \\ 3000 & 55.57 \(\pm\) 19.98 \\ 4000 & 58.09 \(\pm\) 21.56 \\ 6000 & 59.23 \(\pm\) 21.60 \\
8000 & 62.93 \(\pm\) 22.19 \\ Bone conduction readings & \\ 500 & 17.60 \(\pm\) 9.31 \\ 1000 & 21.42 \(\pm\) 10.80 \\ 1500 & 28.50 \(\pm\) 13.21 \\ 2000 & 29.31 \(\pm\) 14.85 \\ 3000 & 31.10 \(\pm\) 16.15 \\ 4000 & 32.24 \(\pm\) 16.24 \\ \hline \hline \end{tabular} \({}^{1}\) Mean \(\pm\) standard deviation.  
\end{table}
Table 2: Hearing intensity features. Before the surgery, for each singular frequency, a hearing intensity in decibels was measured.