## 3 Results
### Predictive Ability and Logistic Regression Model Design  
The AUC values, with a 95% confidence interval (CI), of the variables that exhibited significant differences between the two groups and have a good predictive ability (>0.7) were as follows:  
1. Age = 0.712 (CI 95% 0.579-0.844)
2. SLS = 0.711 (CI 95% 0.569-0.853)
3. PSI = 0.725 (CI 95% 0.577-0.873)
4. APSI = 0.705 (CI 95% 0.555-0.856)
5. SRS error = 0.732 (CI 95% 0.585-0.879)  
The variables that are not included above displayed a low or non-significant AUC value.  
The aforementioned continuous variables and the categorical variable PSI < 0.75 were used to design logistic regression models. To avoid collinearity between the variables, the models were made to include combinations of one variable per function (gait, balance, and hearing). A dual sensory-gait model (Model 1) was found to be the best model, and was also adjusted for age (Model 2). The models include the following continuous variables: SRS error and SLS, as well as the categorical variable PSI < 0.75. Before proceeding with the analysis, some adjustments were made to the variables. Considering that it is practically impossible for a single limb stance to last 0% of the gait cycle, the SLS variable was adjusted to start from 35% instead of 0. This value was chosen as the starting point because the minimum value found in the dataset was 35.53%. A similar adjustment was made for the age variable, considering that the dataset contains only participants over the age of 65. The results of the analysis using the Wald \(\chi^{2}\) test and the odds ratio at a 95% CI for models 1 and 2 are presented in Table 6. Based on the calculated predictions of these two models, their respective ROC curves were obtained and used to determine the predictive ability of each model. To summarize, the predictive abilities of the function quantifiers used in the logistic regression models, SLS adjusted, PSI, and SRS error, are represented by their AUC values of: 0.712, 0.725, and 0.732, respectively. In comparison, the AUC values calculated for models 1 (0.832) and 2 (0.838) were greater, indicating a better predictive ability.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Variable**} & **HC (_n = 39_)** & **LC (_n = 18_)** & \multirow{2}{*}{_p-Value *_} \\  & **MEAN (SD)** & **MEAN (SD)** & \\ \hline PTA R & 23.5 (10.05) & 26.4 (10.50) & 0.290 \\ PTA L & 23.38 (10.84) & 32.3 (19.32) & 0.075 \\ SRT & 19.23 (8.61) & 25 (13.26) & 0.221 \\ WRS & 76.99 (12.14) & 71.61 (13.07) & 0.140 \\ WRS error & 11.05 (5.02) & 14.33 (6.62) & 0.223 \\ SRS & 98.27 (1.94) & 95.2 (4.85) & 0.063 \\ SRS error & 1.38 (1.55) & 4 (3.91) & 0.049 * \\ \hline HC, Healthy Control; LC, Lower Cognition; SD, Standard Deviation; PTA, Pure Tone Audiometry; SRT, Speech Recognition Threshold; WRS, Word Recognition Score; SRS, Sentence Recognition Score. * significance level \(p\)-value < 0.05. & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Auditory examination variables of LC and HC.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Variable**} & **HC (_n = 39_)** & **LC (_n = 18_)** & \multirow{2}{*}{_p-Value *_} \\  & **MEAN (SD)** & **MEAN (SD)** & \\ \hline PSI & 0.68 (0.37) & 1.16 (0.86) & 0.006 * \\ APSI & 0.54 (0.36) & 0.86 (0.64) & 0.012 * \\ MLSI & 0.27 (0.15) & 0.59 (0.62) & 0.017 * \\ \hline \hline \end{tabular}
\end{table}
Table 5: Postural stability variables of LC and HC.