# Methodological insights on building and evaluating models for early warning of hypotension during surgery

Bob Aubouin-Pairault, Kaouther Moussa, Mazen Alamir, Benjamin Meyer, Rémi Wolf

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Bob Aubouin-Pairault, Kaouther Moussa, Mazen Alamir, Benjamin Meyer, Rémi Wolf. Methodological insights on building and evaluating models for early warning of hypotension during surgery. 2025. hal-05419169

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# Methodological insights on building and evaluating models for early warning of hypotension during surgery

Bob Aubouin-Pairault, Kaouther Moussa, Mazen Alamir, Benjamin Meyer, Remi Wolf

**Warning:** Submitted to Anesthesiology. Copyright may be transferred without notice.

**Abstract:**

**Background:** Early warning of hypotension could help prevent severe complications during surgery. Several data-driven models have been proposed, but framing, data selection, and evaluation metrics differ widely in the literature.

**Methods:** Using datasets from non-cardiac and cardiac surgery, we assess how data selection affects model performance. We compare models trained and tested with or without segments containing ongoing hypotension at prediction time or medical interventions, and evaluate both standard metrics and an operational metric proposed in recent studies.

**Results:** Across both datasets, data selection strongly influenced performance under a sliding window framing, particularly during testing, where model rankings changed with the selection strategy. Excluding interventions and ongoing hypotension better reflected the intended clinical use-case. The operational metric highlighted differences more clearly than ROC or precision-recall curves. In training, removing intervention on training data improve performances while exclusion of ongoing hypotension do not change the performances.

**Conclusion:** Data selection is critical when building and evaluating hypotension prediction models. We recommend training models on datasets excluding interventions, testing on datasets excluding interventions and ongoing hypotension, and evaluating with operational metrics and calibration curves.

**Keywords:** Online risk prediction; Hypotension; Machine learning; Problem framing; Data selection; Performance metric
# 1 Introduction

Since the introduction of the hypotension prediction index (HPI) algorithm in 2018¹ and its subsequent commercialization by Edwards Lifesciences, hypotension prediction has gained significant attention in both the data science and clinical communities. Hypotension, a common intraoperative complication, is associated with increased postoperative risk when the mean arterial pressure (MAP) falls below 80 mmHg for more than 10 minutes or below 70 mmHg for shorter periods²,³. Predicting its onset is challenging because of variable patient responses and limited understanding of the underlying mechanisms⁴.

To address this problem, data-driven methods have been proposed in numerous studies over the past seven years¹,⁵⁻¹⁸. Although a systematic review¹⁹ discussed most of the methods in the literature, it focused only on performance evaluation using the area under the receiver operating characteristic curve (AUROC). According to editorials²⁰,²¹, the AUROC may not be an appropriate indicator of model performance as it often hide a poor precision value. Moreover, the definition of the prediction problem is a critical consideration when evaluating a model²²,²³, which the review did not address.

Previous studies on hypotension prediction differ substantially in methodology, making comparisons difficult (see Supplementary Material 1 for a table classifying earlier work). Despite this diversity, methodological details are often underreported, and preprocessing code is rarely shared (only in⁵,¹⁶,¹⁸,²³). While the choice of framing structure has sparked multiple controversies regarding possible selection bias²¹⁻²⁴, data preprocessing has received less attention. The exclusion of segments with abnormal values, ongoing hypotension, or medical interventions is inconsistently applied and frequently lacks justification. Yet such choices can strongly influence metrics and bias models toward predicting interventions rather than true hypotension risk⁵,¹³,¹⁶⁻¹⁸,²⁵. Only a few studies explicitly attempted to remove intervention effects¹,²⁵,²⁶, and their strategies relied on simple thresholds for MAP variation. Consequently, reported model performance across studies is not directly comparable, as small changes in framing or preprocessing can lead to large differences in outcomes¹⁹,²².

In this paper, based on the framework proposed in our previous work¹⁸, we present a study of
the impact of data selection on model performance, assessed using a medically relevant metric. In
particular, we address two questions:

* Q1: How does removing segments with *ongoing hypotension* at prediction time affect model performance?

* Q2: How does removing segments followed by *interventions* that affect hypotension status affect model performance?

# 2 Materials and Methods

In this section, we describe the methodology used to answer the two questions introduced earlier,
following the TRIPOD guidelines²⁷. First, we present the data processing, then the model used to
predict hypotension, and finally the evaluation procedure. The data and model architecture are the
same as in our previous work¹⁸; however, we include new preprocessing steps and metric evaluations
to address the methodological questions.

## 2.1 Data Processing

Details of the data processing are provided in Supplementary Material 2. Briefly, data were extracted
from two sources: the VitalDB database²⁸ and the HG database (a non-public database from the
Hospital of Grenoble, France²⁹). Acquisition and release of the VitalDB data were approved by
the Institutional Review Board of Seoul National University Hospital (H-1408-101-605). For the
HG dataset, extracted from the PREDIMED data warehouse, ethical approval was obtained on
15 November 2022 by the regional ethics committee (CECIC Rhône-Alpes-Auvergne, Clermont-
Ferrand, IRB 5891).

Hypotension is defined as a mean arterial pressure (MAP) below 65 mmHg for more than 1 minute. The data are segmented using the sliding-window framing previously described¹⁸, also referred to as forward²⁵ or unbiased²³ framing in the literature. We used a 30 s sampling time, a 10 min observation length, a 2 min leading time, an 8 min prediction time, and a 30 s window shift, as illustrated in Figure 1.
<figure><img src="image_2.png" /><figcaption>Figure 1: Illustration of the sliding window used to segment the data.</figcaption></figure>

Patients in the VitalDB database are split into a training set and a test set. The training set is used to train the model, and the test set serves as an **internal test set**. The model is then validated on the HG database, which serves as an **external test set**. While the VitalDB dataset includes general surgery cases, the HG dataset mainly covers cardiac surgery and has a higher prevalence of hypotensive events (see Supplementary Material 2 for details).

To answer **Q1**, all segments with ongoing hypotension at prediction time or during the leading time are labeled accordingly, and two different training and test sets are created: one including these segments and one excluding them. We denote these sets as *full* and *no_hypo* train and test sets.

To address **Q2**, a definition of unobservable intervention that could change the outcome of the prediction is required. In this study, because surgical actions and bolus injections are not recorded in the VitalDB dataset, we selected only patients with low blood loss (less than 200 mL for the entire surgery) and low total bolus volume (see Supplementary Material 1 for details). We then examined continuous injection rates and volatile drug concentrations to identify the following types of interventions:

* **Causes of hypotension:** Any decrease in drugs known to increase MAP or any increase in drugs known to decrease MAP is considered a possible cause of hypotension.

* **Prevention of hypotension:** Any increase in drugs known to increase MAP or any decrease
in drugs known to decrease MAP is considered a possible preventive action.

Drugs considered to increase MAP are norepinephrine, epinephrine, phenylephrine, vasopressin, dopamine, dobutamine, and nitroprusside. Drugs considered to decrease MAP are propofol, remifentanil, sevoflurane, desflurane, diltiazem, and nitroglycerin.

Unobservable interventions are defined as drug adjustments that occur after the observation window ends but before either a hypotensive event begins or the prediction window closes. Figure 2 illustrates this idea using two mean arterial pressure (MAP) trendsrising (MAP+) and falling (MAP-)together with two norepinephrine infusion patternsincreasing (NOR+) and decreasing (NOR-). Because norepinephrine is a vasopressor:

* A segment is marked as having an unobservable intervention if the MAP change and norepinephrine change move in the same direction (MAP+ with NOR+ or MAP- with NOR-), since the drug adjustment could have influenced the blood-pressure outcome.

* A segment is considered free of intervention if the directions differ (MAP+ with NOR- or MAP- with NOR+), because the norepinephrine change could not explain the MAP trend.

* If the norepinephrine rate remains unchanged (not shown in Figure 2), the segment is also retained, as no intervention is present.

A third set of training and test sets is created by removing all segments followed by unobservable interventions. These are denoted *no_inter* training and test sets. In addition, a test set named *no_hypo no_inter*, excluding both hypotension at prediction time or during the leading period and unobservable interventions, is created. An illustration of all sets is provided in Figure 3.

## 2.2 Model

To illustrate the impact of data selection on machine learning procedures, we used the same model as in our previous work¹⁸, which outperformed a simple MAP-threshold baseline. In summary, features are extracted from each time series of interest using linear regression (with time as the predictor and the measured variable values over the observation window as the response). This feature-extraction procedure is performed on three different window lengths (1 minute, 3 minutes, and 10 minutes)
<figure><img src="image_3.png" /><figcaption>Figure 2: Illustration of the selection of medical interventions.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3: Illustration of the different sets and models used in this study.</figcaption></figure>
starting from the end of the observation window. The extracted features are the slope, intercept, and standard deviation of the residuals between the regression and the signal.

The time series considered are mean, systolic, and diastolic arterial pressure; heart rate; end-tidal $CO_2$ concentration; oxygen saturation; respiration rate; body temperature; minimum alveolar concentration of volatile anesthetics; remifentanil; and propofol target concentration. Additionally, age, BMI, and ASA score are included as static features. In total, 9 features are extracted per signal (3 per timescale), resulting in 102 features per segment.

All features are concatenated and input to an Extreme Gradient Boosting (XGBoost) model. The model is trained on a binary classification task to predict the occurrence of hypotension in the prediction window. Hyperparameters are optimized using a tree-structured Parzen estimator algorithm³⁰ with cross-validation. More details on feature extraction and model configuration are available in Supplementary Material 2.

Four models are compared in the results section, differing only in their training data: model *full*, model *no_hypo*, model *no_inter*, and model *no_hypo no_inter*, as illustrated in Figure 3.

Clinical baseline performance is also evaluated by predicting hypotension using only the last value of the mean arterial pressure (MAP). For each test set, the probability of hypotension based on this single value is calibrated using the corresponding training data (e.g., calibrated on *full* training data if tested on the *full* test set). The models performances are compared to this baseline.

## 2.3 Statistical Analysis

In addition to the standard receiver operating characteristic (ROC) and precision recall (PR) curves, we considered a more operational metric¹³. Because criticisms have been raised about the ROC curve for imbalanced datasets³¹, some studies have used the PR curve to better assess the clinical utility of predictive models²³,²⁶. The operational metric¹³ extends this idea by evaluating the model in the context of triggering alerts. An alert is defined as a predictive score exceeding a threshold when it was below that threshold in the previous segment, as illustrated in Figure 4. From this definition, precision and recall from an alert perspective can be computed. We refer to these metrics as operational precision and operational recall, defined as follows:
<figure><img src="image_5.png" /><figcaption>Figure 4: Illustration of the operational performance of the hypotension alert system.</figcaption></figure>

$$ \text{Operational Precision} = \frac{\text{Number of true alerts}}{\text{Total number of alerts}} $$

$$ \text{Operational Recall} = \frac{\text{Number of events predicted}}{\text{Total number of events}} $$

An event is considered predicted if at least one alert is triggered during the 8-minute prediction window.

Another useful method to evaluate the model is the calibration curve³². In addition to outputting a binary prediction (hypotension or not), most data-driven models can estimate the probability of each label given the inputs. A perfectly calibrated model outputs probabilities such that the observed frequency of labels for a given predicted probability matches that probability. The calibration curve therefore compares predicted probabilities with the observed frequencies and shows whether the model tends to over- or underestimate event probability. This provides information not captured by ROC or PR curves and assesses the quality of the predicted probabilities, while the other metrics evaluate only classification performance.

All tests are performed using the following metrics: standard ROC, standard PR, operational precision recall¹³, and calibration curves with integrated calibration index³³. Uncertainties in performance are estimated using a bootstrap method with 200 resampled datasets. Results are presented
as mean ± standard deviation for normally distributed data or as median [25th-75th percentiles] for non-normally distributed data. Normality is assessed using the Shapiro-Wilk statistic. Shaded areas around the curves represent twice the standard deviation.

# 3 Results

Code to reproduce the results is available on GitHub<fnref n="1" />. Because the HG dataset cannot be shared, only the results on the internal test set can be reproduced.

A total of 1,017 patients were included in the internal set (711 for training and 306 for testing) and 563 in the external test set. Demographic characteristics of both cohorts are provided in Supplementary Material 2. The internal dataset primarily includes intermediate-risk general surgery cases, whereas the external dataset is composed mainly of cardiac surgery cases. Patients in the internal set are younger (61 years [52, 70] vs. 69 years [61, 74]) and generally healthier (ASA score 2 [2, 2] vs. 3 [3, 3]). Hypotension is less frequent internally, with only 9.39

Figure 5 shows the operational precision-recall curves for the different models on the internal test sets. Figure 6 shows the same metric on the external sets. Figures 7 and 8 present the various metrics for the different training sets on the *no_hypo no_inter* internal and external test sets. Curves for the other metrics on the remaining test sets are available in Supplementary Material Section 4.

## 3.1 Inclusion of segments with ongoing hypotension (Q1)

Including segments with ongoing hypotension in the test set increased both the prevalence of hypotensive segments (47% in the *full* set vs. 28% in the *no_hypo* set for the external test set) and the performance metrics of all models and baselines, as shown in Figures 5 and 6. For training, models trained without segments of ongoing hypotension (*no_hypo* and *no_hypo no_inter*) performed worse than models trained with them (*full* and *no_inter*) when evaluated on test sets that included such segments. However, their performance was similar when tested on sets excluding segments with ongoing hypotension.

<footnote n="1">¹https://github.com/BobAubouin/hypotension_pred</footnote>
## 3.2 Inclusion of segments with unobservable intervention (Q2)

Excluding segments with unobservable medical interventions from the test set improved all metrics, with the best results obtained on the *no_inter* test set for every model. For training, models built on data without interventions performed better than others when tested on sets that excluded segments with unobservable interventions. For example, the *no_inter* model achieved an area under the operational precision-recall curve of 0.42 (0.02) on the internal *no_hypo no_inter* test set, whereas the *full* model reached 0.38 (0.01).

# 4 Discussion

Methods proposed in previous hypotension prediction studies differ greatly. First, the target population and prediction horizon vary: most works focus on operating room (OR) data, while others use intensive care unit (ICU) recordings<sup>9-13</sup>. Because patients are more stable in the ICU, prediction horizons are typically longer (5-60 minutes) than in the OR (20 seconds-15 minutes). This difference in population also leads to different definitions of the hypotension label. In most studies, hypotension is defined as a MAP below 65 mmHg for one minute, as in this paper, but studies using ICU populations defined it over longer periods, from 5 minutes<sup>11,13</sup> to 27 minutes<sup>9,10</sup>. Second, two main framings are used: time-to-onset (backward), where the model predicts hypotension a fixed time before onset, and sliding-window (forward), where continuous segments are extracted to form the dataset<sup>21-24</sup>. Third, different training strategies are explored: direct binary classification versus regression of future MAP values followed by thresholding<sup>5,12,14,16</sup>. While classification generally outperforms regression<sup>5</sup>, predicting trajectories may provide more clinical flexibility. Model inputs are another source of heterogeneity: some studies use high-frequency arterial waveforms (100-500 Hz)<sup>1,5-8</sup>, whereas others rely on lower-frequency but more diverse monitoring signals (1-30 s)<sup>9-18</sup>. These choices determine the observation window (short patterns vs. long-term trends) and whether drug effects are implicitly included, affecting model usage.

Regarding data selection for training and evaluation, preprocessing also differs substantially between studies. Segments with ongoing hypotension were included in some works<sup>14,16,26</sup> but excluded
<figure><img src="image_6.png" /><figcaption>(a) Full test set</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(c) No\_inter test set</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(b) No\_hypo test set</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(d) No\_hypo no\_inter test set</figcaption></figure>

<caption>Figure 5: Operational precision-recall curves for the different training sets on the different **internal** test sets.</caption>
<figure><img src="image_10.png" /><figcaption>Figure 6: Operational precision-recall curves for the different training sets on the different external test sets.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure 7: Different metrics of the different training sets on the *no_hypo no_inter* internal test set.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 8: Different metrics of the different training sets on the *no_hypo no_inter* external test set.</figcaption></figure>
in others. Segments with medical interventions potentially affecting hypotension labels were filtered
in some studies¹,²⁵,²⁶ but only by removing segments with sudden MAP decreases.

In this study, we focused on sliding-window framing and investigated two questions to assess the impact of data selection and metric choice on model performance. Our results, consistent between internal and external sets, show that including segments with ongoing hypotension in the test set significantly improves metrics, as does excluding segments with medical interventions. For training, only the exclusion of segments with medical interventions significantly improved the metrics. From a clinical perspective, predicting hypotension while it is occurring is not useful and should not be considered. However, medical interventions bias the analysis, since the goal of the model is to answer: “Would the model predict hypotension if no intervention occurred?” We therefore **recommend** removing segments with ongoing hypotension at prediction time and excluding medical interventions in the prediction window when evaluating the model. For training, we **recommend** removing medical interventions that could change the hypotension label.

Finally, the choice of metric is important, as it can reveal differences between models. As noted previously²⁰,²¹,²⁶,³⁴, the ROC curve can overestimate model capability. For example, in Figure 7, AUROC is 0.86 for most models, but precision remains below 40% for recall above 50%. Thus, the precision-recall curve, especially the operational PRC coupled with baseline comparison, provides a more realistic evaluation because precision is easier to interpret. Calibration curves offer another perspective by showing model bias. As seen in Figure 8d, all models underestimate hypotension risk in the external test set, reflecting training on VitalDB where prevalence is lower than in HG. This bias is not visible in other metrics.

Future directions are numerous. Clinically, assessing causality between hypotension and patient outcomes is necessary, as it is unclear whether proactive hypotension management improves patient state. Results from ongoing trials are awaited³⁵,³⁶. Methodologically,⁵ showed that predicting MAP trajectories as an intermediate step may lower classification performance, though new deep-learning methods could offer opportunities to address this issue. Metric choice is also crucial; the operational metric seems most relevant, though alert evaluation metrics are not yet standardized and threshold selection is rarely discussed. Finally, different physiological mechanisms can cause hypotension.
Unsupervised clustering methods³⁷ could help predict hypotension types rather than only onset³⁸.

This study has several limitations:

* Prediction of hypotension for the next ten minutes with a two-minute lead time is arbitrary; consensus is needed, but transparency allows reproducibility.

* Only drug interventions were considered when filtering medical interventions, as surgical data were unavailable. Future work could include surgical interventions.

* Only an XGBoost model with linear regression-based features was evaluated; more sophisticated models or feature extraction could change results.

* Predicting MAP trajectories as an intermediate step was not studied; while potentially informative, binary evaluation remains relevant for alert systems.

In conclusion, we studied the framing of the hypotension prediction problem. We focused on different variations within the sliding-window framing to provide insights for future research. We conclude that the inner details of the framing have a significant impact on model performance, which prevents direct comparison of metrics across existing studies. Future research should clearly define the framing of the problem and compare results to a clinical baseline tested on the same data and pre-processing.

## Declaration of Competing Interest

The authors declare no conflict of interest.

## Declaration of Generative AI and AI-assisted technologies in the writing process

During the preparation of this work the authors used ChatGPT in order to improve readability and language. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.
Acknowledgment

This work was supported by the Clinical project, funded by the ANR (French National Research Agency) under grant ANR-24-CE45-4255.

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# Supplementary Material for: Methodological insights on building and evaluating models for early warning of hypotension during surgery

Bob Aubouin-Pairault, Kaouther Moussa, Mazen Alamir, Benjamin Meyer, Remi Wolf

December 16, 2025

# 1 Classification of previous works

# 2 Data processing

The data used for this study is extracted from the VitalDB database [19] and a specific dataset extracted from the clinical data warehouse PREDIMED [20], referred to as the HG dataset. VitalDB contains high-fidelity multiparameter physiological data from 6389 patients undergoing general anesthesia for non-cardiac surgery in Seoul (Korea) between 2016 and 2017. In this database, the physiological signals are recorded at fixed intervals of one to seven seconds, depending on the signal. The HG dataset contains data from 589 patients undergoing general anesthesia for cardiac and major surgery registered in Grenoble (France) between 2016 and 2022. The physiological signals are recorded at intervals of 30 seconds.

To follow the guidelines of [21], the model is trained on a subset of the VitalDB dataset and tested separately on the other subset. Then, the model is tested on the external HG dataset. This process is illustrated in Figure 1.

First, the patients are selected using the following criteria in each database:

* Arterial blood pressure is invasively measured;

* The patient age is over 18 years old;

* The operation is not a transplantation;

* The clinical intervention is not an emergency;

* The total duration of the operation is over one hour;

* The total estimated blood loss is under 200 ml.

* The total weight of bolus injected during the whole surgery is less than:

- 9 mg for ephedrine,

- 500 mcg for phenylephrine,
<figure><img src="image_13.png" /><figcaption>Figure 1: Illustration of the training and test process of the model. The model is trained on the VitalDB dataset and tested on a subset of the VitalDB dataset. The model is then validated on the HG dataset.</figcaption></figure>
<table><caption>Table 1: Table 1: Summary of the development of online hypotension prediction model. SW stands for Sliding window, TTO for time to onset, ROC for Receiver Operating Characteristic, SAT for Score At Threshold, PR for Precision-Recall, AUPRC for Area Under Precision-Recall Curve, and AUROC for Area Under ROC curve.</caption><thead><tr><th>Paper</th><th>Framing</th><th>Metric</th><th>Intervention curation</th><th>Model comparison</th><th>Hypotension at prediction</th></tr></thead><tbody><tr><td>Hatib et al. (2018) [1]</td><td>TTO with gray zone</td><td>ROC + SAT</td><td>Yes</td><td>with ΔMAP</td><td>No</td></tr><tr><td>Moghadam et al. (2020) [2]</td><td>TTO + SW with gray zone</td><td>ROC + SAT</td><td>No</td><td>No</td><td>No</td></tr><tr><td>Cherifa et al. (2020) [3]</td><td>SW</td><td>SAT</td><td>No</td><td>With last MAP value</td><td>Yes</td></tr><tr><td>Yoon et al. (2020) [4]</td><td>SW</td><td>ROC + Calibration + PR<br>Operationnal metric</td><td>No</td><td>With other model</td><td>No</td></tr><tr><td>Moghadam et al. (2021) [5]</td><td>SW with gray zone</td><td>SAT</td><td>No</td><td>No</td><td>No</td></tr><tr><td>Lee et al. (2021) [6]</td><td>TTO with gray zone</td><td>ROC + SAT</td><td>No</td><td>With other model</td><td>No</td></tr><tr><td>Choe et al. (2021) [7]</td><td>TTO with gray zone</td><td>PR + AUPRC + AUROC</td><td>No</td><td>With other models</td><td>No</td></tr><tr><td>Cherifa et al. (2021) [8]</td><td>SW</td><td>Agreement plots</td><td>No</td><td>With other models</td><td>Yes</td></tr><tr><td>Lee et al. (2022) [9]</td><td>SW</td><td>AUROC</td><td>No</td><td>No</td><td>No</td></tr><tr><td>Jo et al. (2022) [10]</td><td>TTO</td><td>AUROC, AUPRC, Calibration</td><td>No</td><td>No</td><td>No</td></tr><tr><td>Feld et al. (2023) [11]</td><td>SW</td><td>ROC + PR</td><td>No</td><td>With other model</td><td>No</td></tr><tr><td>Hwang et al. (2023) [12]</td><td>SW with gray zone</td><td>AUROC</td><td>No</td><td>With ablation study</td><td>No</td></tr><tr><td>Lu et al. (2023) [13]</td><td>SW</td><td>AUROC + SAT</td><td>No</td><td>Not on same data</td><td>No</td></tr><tr><td>Shi et al. (2023) [14]</td><td>SW</td><td>SAT</td><td>No</td><td>With other models</td><td>No</td></tr><tr><td>Kapral et al. (2024) [15]</td><td>SW</td><td>ROC + Calibration</td><td>No</td><td>With other model</td><td>Yes</td></tr><tr><td>Jeong et al. (2024) [16]</td><td>SW</td><td>AUROC + SAT</td><td>No</td><td>No</td><td>No</td></tr><tr><td>Cheng et al. (2024) [17]</td><td>SW</td><td>AUROC + SAT</td><td>No</td><td>With other models</td><td>Yes</td></tr><tr><td>Aubouin-Pairault et al. (2025) [18]</td><td>SW</td><td>Custom PR</td><td>No</td><td>With last MAP value</td><td>No</td></tr></tbody></table>

- 0 mg epinephrine,

- 50mcg for fentanyl,

- three times the patient weight for propofol (corresponding to induction bolus).

These criteria are chosen in order to focus on adult patients while minimizing the risk of unpredictable hypotension due to surgery intervention as it might be the case in transplantation, emergency, and bleeding operations. Moreover, the extracorporeal circulation phase of cardiac surgeries in the HG data is removed as it is out of the scope of this study. Finally, to have a coherent external test of the model on the HG dataset, the VitalDB dataset is resampled with a sampling time of 30 seconds.

For all cases, the periods at the beginning and the end of the procedure, where arterial pressure is not monitored, are removed. Then, each procedure is divided into 20-minute segments and a 30-second shift between them, 10 minutes for observation, 2 minutes for leading time, and 8 minutes for prediction. Segments including abnormal MAP values (MAP<40mmHg or MAP>150mmHg), where more than 10 % of the data is missing or including hypotension events during the observation window or leading time period are removed. A segment is labeled as hypotensive if a hypotension event occurs during its prediction window. Finally, for the VitalDB dataset, the patients are split into a training set and a test set, with particular attention paid to obtaining an equivalent distribution of labeled segments in both sets.

Regarding the VitalDB dataset, 1,017 patients are included for a total of 285,703 segments. Demographic data of the patients are presented in Table 2. Among the selected procedures in
VitalDB, 54.6 % of the patients experienced at least one hypotensive event. However, 9.4 % of the segments are labeled as hypotensive in the full dataset, leading to an unbalanced dataset. For the HG dataset, 563 patients are included for a total of 156,069 segments. The demographic data of the patients are presented in Table 3. Among the procedures in HG, 94.8 % of the patients experienced at least one hypotensive event, and 47.4 % of the segments are labeled as hypotensive. The difference in prevalence between the two datasets might be explained by the fact that the patients in HG are in a more critical condition (mean ASA score of 3.0 in HG and 1.9 in VitalDB). The difference might also come from the type of surgery, the HG data mainly comes from cardiac surgery, which is known to be more subject to hypotension [22]. This difference in arterial pressure can be observed in Figure 2, where the raw MAP of the two datasets are compared.

<table><caption>Table 2: Demographic characteristics of the VitalDB subset used for the prediction of hypotension.</caption><thead><tr><th></th><th>Median [25th, 75th percentiles]</th></tr></thead><tbody><tr><td>Age (years)</td><td>59 [50, 68]</td></tr><tr><td>Weight (kg)</td><td>61 [53.6, 68.4]</td></tr><tr><td>Height (cm)</td><td>162 [156.1, 168.4]</td></tr><tr><td>Duration (h:min)</td><td>3:14 [2:17, 4:15]</td></tr><tr><td>ASA</td><td>2 [2, 2]</td></tr><tr><td>Female/Male</td><td>51% / 49% (517 / 500)</td></tr><tr><td>Preoperative hypertension</td><td>28.71%</td></tr><tr><td>Preoperative diabetes mellitus</td><td>9.83%</td></tr><tr><td>Preoperative kidney disease</td><td>2.06%</td></tr><tr><td><strong>Surgery type</strong></td><td></td></tr><tr><td>Thoracic</td><td>613</td></tr><tr><td>Digestive</td><td>253</td></tr><tr><td>Gynecologic</td><td>38</td></tr><tr><td>Urologic</td><td>12</td></tr><tr><td>Vascular</td><td>4</td></tr><tr><td>Other, not cardiac</td><td>135</td></tr><tr><td><strong>Surgery risk</strong></td><td></td></tr><tr><td>Low</td><td>441</td></tr><tr><td>Intermediate</td><td>499</td></tr><tr><td>High</td><td>77</td></tr></tbody></table>
<figure><img src="image_14.png" /><figcaption>Figure 2: Comparison of the raw mean arterial pressure of the VitalDB and the HG raw data.</figcaption></figure>

<table><caption>Table 3: Demographic characteristics of the HG data subset used for prediction of hypotension.</caption><thead><tr><th></th><th>Median [25th, 75th percentiles]</th></tr></thead><tbody><tr><td>Age (years)</td><td>69 [61, 74]</td></tr><tr><td>Weight (kg)</td><td>76 [67, 86]</td></tr><tr><td>Height (cm)</td><td>170 [164, 175]</td></tr><tr><td>Duration (h:min)</td><td>2:48 [2:20, 3:35]</td></tr><tr><td>ASA</td><td>3 [3, 3]</td></tr><tr><td>Female/Male</td><td>26 % / 74% (145 / 418)</td></tr><tr><td><strong>Surgery type</strong></td><td></td></tr><tr><td>Cardiac</td><td>525</td></tr><tr><td>Vascular</td><td>24</td></tr><tr><td>Digestive</td><td>9</td></tr><tr><td>Thoracic</td><td>4</td></tr><tr><td>Orthopedic</td><td>1</td></tr><tr><td><strong>Surgery risk</strong></td><td></td></tr><tr><td>High</td><td>563</td></tr></tbody></table>

# 3 Features Extraction

The features used in the proposed model are either extracted from time series data or patient information. The time series considered include the following:

* Mean, systolic, and diastolic arterial pressure;

* Heart rate;
<figure><img src="image_15.png" /><figcaption>Figure 3: Illustration of the feature extraction process using linear regression on different timescales.</figcaption></figure>

* End-tidal CO₂ concentration;

* Oxygen saturation;

* Respiration rate;

* Body temperature;

* Minimum alveolar concentration of volatile anesthetics;

* Remifentanil and propofol target concentration.

To extract features from the signals, linear regression is applied to obtain the slope and the intercept at the end of the observation window, as proposed in [3]. This feature extraction method is used as it is simple to implement and easy to interpret. The linear regression process is applied on three different timescales: the last minute, the last 3 minutes, and the last 10 minutes. Moreover, the standard deviation of the error between the linear regression and the signal is computed. The feature extraction process is illustrated in Figure 3.

For the patient information, the age, the body mass index (BMI), and the ASA score are used as features. This information is readily available and denotes the patient's general health.

Thus, the total number of features is 102: 9 features extracted from each time series (3 by timescale) and 3 features from the patient information. We do not use any feature selection process as tree decision methods like XGBoost are known to be robust to irrelevant features.
4 Additionnal results

<figure><img src="image_16.png" /><figcaption>Figure 4: Receiver operator characteristic curves for the different models on the different **internal** test sets.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Figure 5: Calibration curves for the different models on the different **internal** test sets.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Figure 6: Standard precision-recall curves for the different models on the different **internal** test sets.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Figure 7: Receiver operator characteristic curves for the different models on the different external test sets.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Figure 8: Calibration curves for the different models on the different **external** test sets.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Figure 9: Standard precision-recall curves for the different models on the different **external** test sets.</figcaption></figure>

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