## 3 Results  
A flowchart illustrating this process is presented in Figure 3. Out of the 405 cases initially considered, 365 were analyzed in this study, with 40 excluded owing to missing data. The patient background data are detailed in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variables** & \\ \hline Age (years), mean (range) & 63.8 (18–95) \\ \hline Female sex, n (\%) & 209 (57.3) \\ \hline Height (cm), mean (95\% CI) & 160.4 (159.4–161.4) \\ \hline Weight (kg), mean (95\% CI) & 61.7 (60.4–63.1) \\ \hline ASA-PS, n (\%) & \\ \hline
1 & 54 (14.8) \\ \hline
2 & 265 (72.6) \\ \hline
3 & 45 (12.3) \\ \hline SBP before induction (mmHg), mean (range) & 139.5 (79–203) \\ \hline DBP before induction (mmHg), mean (range) & 76.8 (45–121) \\ \hline HR before induction (bpm), mean (range) & 73.5 (34–144) \\ \hline Induction propofol dose (mg), mean (range) & 98.5 (20–200) \\ \hline Induction fentanyl dose (mg), mean (range) & 93.4 (0–200) \\ \hline Induction remifentanil dose (mg/kg/min), mean (range) & 0.2 (0.0–0.5) \\ \hline \hline \end{tabular} Note: Continuous variables are presented as the mean (range) or mean (95\% confidence interval), as appropriate. Categorical variables are presented as the number (percentage). ASA-PS: American Society of Anesthesiologists physical status; SBP: Systolic blood pressure; DBP: Diastolic blood pressure; HR: Heart rate.  
\end{table} 
Table 1: Background characteristics of the patients. Figure 3: Flowchart of the participant selection and dataset splitting. A total of 405 participants were screened, and 365 were analyzed after excluding 40 with missing data. The dataset was randomly split into training (n = 234), validation (n = 58), and test (n = 73) sets. The term \"PIHF\" is a combined concept of post-induction hypertension and hypotension. In the data collected in this study, among the 157 patients with PIHF, only 1 had post-induction hypertension. Therefore, PIHFs in the present study are almost synonymous with post-induction hemodynamic hypotension. Histograms of the propofol doses per body weight and histograms of the age are shown in Figures 4 and 5. The patients were divided into two groups according to the presence or absence of PIHF: red indicates the group with PIHF and blue indicates the group without PIHF. The \(t\)-tests showed that an older age was a significant predictor of the occurrence of PIHF (\(p<0.001\)). However, the propofol dose did not predict the occurrence of PIHF in patients older than 65 years (\(p=0.67\)). Among the 365 cases, 80% (n = 292) were randomly allocated to the model building, while the remaining 20% (n = 73) constituted the testing data. The data for model building  
Figure 4: Histograms of the propofol dose and post-induction hemodynamic fluctuations (PIHFs) in the elderly. Blue bars represent patients who experienced PIHF (PIHF [+]); orange bars represent those who did not (PIHF [-]). The \(x\)-axis indicates the propofol dose per body weight [mg/kg], and the \(y\)-axis shows the number of patients. Figure 5: Histograms of the age and post-induction hemodynamic fluctuations (PIHFs). Blue bars represent patients who experienced PIHF (PIHF [+]); orange bars represent those who did not (PIHF [-]). The \(x\)-axis represents the age grouped in 5-year intervals, and the \(y\)-axis indicates the number of patients. was further split into the training (n = 233, 80%) and validation data (n = 58, 20%). Through manual hyperparameter tuning, the following values were determined: a batch size of 20, a learning rate of 0.08, and 26 epochs. Figure 6 plots the predictions made by the models on the horizontal axis and the residual errors on the vertical axis. Model P tended to have larger predictions than model N, and the residual errors are often positive. Model P exhibited RMSE and MAE values of 25.8 (95%CI: 21.3-30.7) and 16.7 (95%CI: 16.4-23.8), respectively, which were higher than those of model N, showing 17.6 (95%CI: 14.4-20.9) and 13.0 (95%CI: 10.3-15.9) (\(p<0.001\)).