In this study, we used data from the Microsoft Waveform Database, and we obtained data access permission from the Microsoft Data Access Committee [12]. Microsoft obtained institutional review board approval from WCG IRB (Puyallup, WA, United States). Individuals unable to consent in English, pregnant women, prisoners, institutionalized individuals, and individuals younger than 18 years were excluded from participation due to their vulnerable status. All the subjects voluntarily participated in the experiment and signed informed consent. The original informed consent and the institutional review board both allow for secondary analysis without additional consent. The dataset used in this study was de-identified to protect the privacy of the subjects.

The database that we obtained data from was developed for validating new methods for blood pressure measurement with noninvasive sensors. Noninvasive epidermal pressure signals, ECG signals, and PPG signals were acquired with tension, electrical, and optical sensors, respectively. Meanwhile, the reference blood pressure was measured with either the oscillometric method or the auscultatory method. In this study, we used noninvasive signals for hypertension detection. To validate our proposed method, we used data collected based on the oscillometric method. A total of 614 subjects participated in the oscillometric protocol scheme, with ages ranging from 18-85 years. After excluding data anomalies during the collection process, including miswear, malfunction, data file failure, participant opt-out, alignment failure, and quality failure, relevant measurement information from 483 subjects was retained [12]. In a further waveform preprocessing step, poor waveform segments and subjects with less than 4 qualified waveform segments were removed, which led to the final retention of measurement data from 405 participants, comprising 183 hypertensive patients and 222 healthy individuals. The ages of the 405 participants ranged from 18-60 years, with an average age of 45 years. In addition, the 405 participants comprised 199 females and 206 males.

Moreover, measurements in this protocol were obtained during controlled laboratory visits spaced at least 24 hours apart. Additionally, dynamic measurements were collected during the 24-hour interval between laboratory visits. Automatic measurements were taken every 30 minutes in the morning and every 60 minutes in the evening. Each patient typically had 24-36 waveform segments, with each acquired for 15-30 seconds. Our feature extraction primarily relied on data from dynamic measurements.

We extracted 205 features from the filtered ECG and PPG signals with the extraction method defined in our previous study [13]. The features mainly include pulse transit time (PTT), time duration (TD), amplitude (AM), intensity of PPG, the first derivative of PPG (dPPG), the second derivative of PPG (sdPPG), area under the PPG curve (AR), and physiological meaningful relative index (RI). The mathematical expression and definition of these features are as follows and are also described in Table 1. The fiducial points of ECG, PPG, dPPG, and sdPPG signals of each cardiac cycle were identified to calculate the features. The identified fiducial points are illustrated in Figure 3.

Feature Point (FP, 1∼10) = [PPG valley, sdPPG a, dPPG peak, sdPPG a, PPG peak, sdPPG c, sdPPG d, dPPG valley, sdPPG e, sdPPG f, PPG valley next]

PTT = FP(i) - R peak, i=1∼10

TD = [RRI, (FP(j) - FP(i)), i,j=1∼10, and j>i]

AM = PPG(FP(j)) - PPG(FP(i)), i=1∼10, and j>i

AIPPG = PPG(FP(i)), i=1∼10

AIdPPG = dPPG(FP(i)), i=1∼10

AIsdPPG = sdPPG(FP(i)), i=2,4,7∼10

AR = Area between (FP(j) – FP(i)), i,j=1∼10

RI: relative rising time, dicrotic diastolic ratio, augmentation index, inflection point area point, slope transit time, ratio of sdPPG (b/a, c/a, (c+d–b)/a, etc), PPG intensity ratio, perfusion index [13].

After obtaining the above features, we can perform feature selection and build a causal graph based on the causal inference algorithm.

We used the greedy equivalence search (GES) algorithm to learn the causal graph. The GES algorithm is based on the theoretical basis of Meek’s conjecture [14]. The Meek’s conjecture is: if direct acyclic graph (DAG) M is an independent map of another DAG F, then there exists a finite set of edges in DAG F that can be added or reversed, after each modifiable edge is added or reversed direction, DAG M is still an independent graph of DAG F. After all modifications are done, M = F. Underlying the Meek’s conjecture, we can use generalized score functions [15] and the GES algorithm to get the final causal graph. Figure 4 shows the implementation steps of the GES algorithm. In addition, we also provide the pseudo code to illustrate the detailed steps of the GES algorithm as shown in Textbox 1.

Then, the GES algorithm has 2 stages. In the first stage, it starts from an equivalence class (empty graph) with no dependencies and keeps adding possible edges to search for the largest equivalence class of generalized scoring functions until the scoring functions’ local maximum is reached. Then, in the second stage, the greedy principle is used to gradually delete the directed edges until the generalized scoring function reaches the local maximum again, and the final causal graph is obtained.

Considering that hypertension is a discrete variable while the feature variables are continuous, we are essentially dealing with mixed data. Traditional scoring functions such as Bayesian information criterion and Bayesian Dirichlet equivalent uniform do not take into account the issue of mixed data; for example, it discretizes continuous data and process it uniformly, resulting in a loss of valuable information. Therefore, we introduce a generalized scoring function to replace traditional scoring functions. The generalized function is primarily based on kernels and handles linear causal relationships, nonlinear causal relationships, continuous variables, discrete variables, and mixed data in a uniform manner, maximizing information retention. Finally, this scoring function addresses the issue of Markov equivalence classes, to some extent, overcoming the limitation of equivalence greedy search algorithms in distinguishing Markov equivalence classes.

Finally, we needed to organize a feature matrix in which each row represents a sample and each column represents a kind of feature, then input this matrix into the equivalent greedy search algorithm to obtain the causal graph. Prior to this, feature selection is a necessary step to construct the feature matrix.

This section mainly explains the specific process of feature selection in this study, which is mainly divided into the following 3 parts. After completing feature selection, we will perform causal strategy and causal graph construction.

In order to mitigate the potential issues of bidirectional causality and cyclic graphs, we conducted the analysis of the causal relationships between respective feature variables and hypertension under each indicator, culminating in the derivation of corresponding causal subgraphs, so as to obtain the causal graph.

In conjunction with a 10-fold cross-validation approach to partition the dataset into training and testing sets, our predictive modeling of hypertension risk primarily leverages 4 classification algorithms: random forest, logistic regression, decision trees, and naive Bayes. These algorithms are selected for their effectiveness in capturing diverse patterns in the data. Moreover, the evaluation of our models is based on a comprehensive set of performance metrics, encompassing accuracy, precision, recall, F₁-score, and the AUC, which are defined later on. Following the derivation of the final causal diagram, we proceeded to select an equal number of feature variables with the strongest correlation to hypertension, based on the point-biserial correlation coefficient. These selected features were then used in the prediction of hypertension risk. Subsequently, we compared the predictive performance of this model with the one based on causal feature variables.

We found that there are 24 feature variables directly causally related to hypertension under 6 indicators. These can be abstracted into 10 representative feature variables in the causal graph. Then, we used the point-biserial correlation coefficient to select the 24 feature variables with the strongest correlation to hypertension. After conducting data analysis, we discovered that there are 5 feature variables that overlap between the causal feature variables and the correlated feature variables. These variables are as follows and 4 of them are shown in Figure 5.

Furthermore, we selected the representative samples from the groups of hypertensive patients and healthy people for comparative analysis. The PPG waveform analysis diagrams of hypertensive patients and healthy people are shown in Figure 6, and the scatter plots of feature 52 are shown in Figure 7. Then, based on the analysis of feature 52’s position in PPG signals, we observed that in hypertensive patients, the peak of the c-point on sdPPG may occur earlier compared to healthy individuals. This could be a possible reason as to why feature 52 is strongly correlated with hypertension and is considered to have a strong causal relationship with hypertension.

Finally, it is important to note that further research and validation are necessary to confirm the relationship between feature 52, the c-point on sdPPG, and hypertension. These findings may provide valuable insights into potential markers for hypertension and contribute to the understanding of its pathophysiology.

In this study, considering the potential disturbance to the causal graph caused by randomly partitioning the data into training and testing sets, we used the idea of 10-fold cross-validation and causal strategy I to mitigate such interference. After applying the aforementioned procedures, we obtained a total of 6 causal subgraphs under different metrics. In addition, due to space constraints, this paper only presents the causal subgraphs under the standard deviation and range indicators, as shown in Figures 8 and 9, respectively. It is observed that the feature variables directly causally associated with the risk of hypertension vary across different indicators. Based on the principle of majority rule, we applied causal strategy II to obtain the final causal graph, as depicted in Figure 10.

In this subsection, we used multiple classifier algorithms for hypertension classification prediction. First, we primarily utilized logistic regression and other classification algorithms based on causal feature variables for hypertension classification. The classification performance is presented in Table 2. We found that the logistic regression algorithm exhibited the best predictive performance with an accuracy of 0.89, precision of 0.92, recall of 0.82, and F₁-score of 0.87. Both the accuracy and accuracy rate are relatively high, which means that our classification prediction model can accurately predict hypertensive patients and healthy people, and the probability of making errors in the judgment of hypertensive patients is low; the F₁-score further proves the above conclusion. In addition, a higher recall rate indicates that most patients with high blood pressure can be correctly predicted.

Subsequently, Figure 11 illustrates the receiver operating characteristic curve and precision-recall curve of the classifier algorithms. The purple line represents the logistic regression classification algorithm. It can be observed that the area under the curve of this logistic regression classification algorithm is higher than that of other classification algorithms in both receiver operating characteristic and precision-recall curves.

Finally, we compared the classification performance based on causal feature variables with that based on correlated feature variables, as shown in Table 3. We found that the best performance in terms of the 4 evaluation metrics was consistently achieved by the classification algorithm based on causal feature variables. This finding is also consistent with the results presented in Figures 12 and 13. These findings imply that the causal characteristics we screened have certain mining value in the field of hypertension prediction.

This study primarily explored the relationship between feature variables extracted from ECG and PPG signals and hypertension from a causal perspective, using causal inference methods to construct causal graphs. Simultaneously, to preserve the temporal information of time series signals to the maximum extent, causal graphs were constructed separately for 6 metrics, including standard deviation, mean, range, coefficient of variation, median, and quartiles. These causal graphs were derived based on specific causal strategies, ensuring a certain degree of reliability and accuracy in the resulting causal graphs. By assessing the performance of feature variables based on causality in hypertension risk classification prediction against those based on correlation, we validated the reliability of causality-based feature variables compared to correlation-based ones.

Specifically, when selecting feature variables strongly associated with hypertension, both causal inference and correlation coefficient–based methods performed similarly. However, when the association between feature variables and hypertension was weak, causal inference methods tended to select more reliable feature variables compared to correlation-based methods. This is the reason why feature variables based on causality outperformed those based on correlation in hypertension risk prediction. Additionally, we found that feature 52’s derived variables exhibited significant differences in distribution between the hypertensive and healthy subject groups under multiple metrics. This may provide potential value and insights for subsequent pathological mechanism analysis.

This study conducted exploratory analysis, initially focusing on the correlation analysis between hypertension and blood pressure based on the medical information mart for intensive care (MIMIC) database. Typically, the gold standard for diagnosing hypertension is SBP and DBP, where subjects are considered hypertensive when SBP exceeds 140 mm Hg or DBP exceeds 90 mm Hg. Nevertheless, when clustering analysis was performed on 24-hour dynamic blood pressure data collected from patients, we observed that the blood pressure distribution of hypertensive and nonhypertensive subjects did not exhibit significant differentiation or stratification; instead, they appeared mixed. After analysis, we attributed this phenomenon to factors such as patients taking antihypertensive medications, being in specific states, or incorrect device wear, which indirectly reflects the limitations of blood pressure measurement. Second, we previously conducted causal analysis [16] using data collected from a self-generated database of 30 individuals. Causal analysis was primarily carried out under the mean metric, resulting in limited preservation of temporal information. However, it still revealed significant differences in the distribution of feature 52 between the hypertensive and healthy subject groups, consistent with the findings of this paper.

There were some limitations to this study. First, our work primarily focused on binary classification to distinguish hypertensive patients from healthy individuals. However, hypertension can be categorized into different stages, such as stage 1, stage 2, and stage 3, based on blood pressure level and disease condition. Second, the population used could have been more diverse in terms of race and ethnicity. In our future work, we will consider conducting clustering of the features to distinguish different stages of hypertension, and we will validate the work on larger and more diverse subject populations to be able to draw more general conclusions.

In this study, we explored the feasibility of predicting the risk of hypertension using causal inference methods. First, we constructed causal graphs using the GES algorithm and 10-fold cross-validation approach under each indicator. We then applied corresponding causal strategies to obtain the optimal causal graphs for each indicator. Finally, we merged the causal graphs from different indicators into a final causal graph based on the majority rule. After selecting the feature variables, we used classifiers including random forests, decision trees, naive Bayes, and logistic regression to predict hypertension. Overall, combining various indicators, we found that most classifiers based on causal features have better classification performance than classifiers based on correlation features. To the best of our knowledge, this study represents the first attempt to introduce causal inference methods in hypertension prediction, providing a new perspective for understanding the physiological mechanisms of hypertension.