Background

Chest pain is among the most common chief complaints presenting to the emergency department (ED) [1,2,3]. The assessment of chest pain patients poses a diagnostic challenge in balancing risk and cost. Inadvertent discharge of acute coronary syndrome (ACS) patients is associated with higher mortality rates while inappropriate admission of patients with more benign conditions increases health service costs [4, 5]. Hence, the challenge lies in recognizing low-risk chest pain patients for safe and early discharge from the ED. There has been increasing focus on the development of risk stratification scores. Initially, risk scores such as the Thrombolysis in Myocardial Infarction (TIMI) score [6, 7] and the Global Registry of Acute Coronary Events (GRACE) score [8] were developed from post-ACS patients to estimate short-term mortality and recurrence of myocardial infarction. The History, Electrocardiogram (ECG), Age, Risk factors, and initial Troponin (HEART) score was subsequently designed for ED chest pain patients [9], which demonstrated superior performance in many comparative studies on the identification of low-risk chest pain patients [10,11,12,13,14,15,16,17]. Nonetheless, the HEART score has its disadvantages. Many potential factors can affect its diagnostic and prognostic accuracy, such as variation in patient populations, provider determination of low-risk heart score criteria, specific troponin reagent used, all of which contribute to clinical heterogeneity [18,19,20,21]. In addition, most risk scores still require variables that may not be available during the initial presentation of the patient to the ED such as troponin. There remains a need for a more efficient risk stratification tool.

We had previously developed a heart rate variability (HRV) prediction model using readily available variables at the ED, in an attempt to reduce both diagnostic time and subjective components [22]. HRV characterizes beat-to-beat variation using time, frequency domain, and nonlinear analysis [23] and has proven to be a good predictor of major adverse cardiac events (MACE) [22, 24, 25]. Most HRV-based scores were reported to be superior to TIMI and GRACE scores while achieving comparable performance with HEART score [17, 24, 26, 27]. Recently, we established a new representation of beat-to-beat variation in ECGs, the heart rate n-variability (HRnV) [28]. HRnV utilizes variation in sampling RR-intervals and overlapping RR-intervals to derive additional parameters from a single strip of ECG reading. As an extension to HRV, HRnV potentially supplements additional information about adverse cardiac events while reducing unwanted noise caused by abnormal heartbeats. Moreover, HRV is a special case of HRnV when n = 1. The HRnV prediction model, developed from multivariable stepwise logistic regression, outperformed the HEART, TIMI, and GRACE scores in predicting 30-day MACE [28]. Nevertheless, multicollinearity is a common problem in logistic regression models where supposedly independent predictor variables are correlated. They tend to overestimate the variance of regression parameters and hinder the determination of the exact effect of each parameter, which could potentially result in inaccurate identification of significant predictors [29, 30]. In the paper, 115 HRnV parameters were derived but only seven variables were left in the final prediction model, and this implies the possible elimination of relevant information [28].

Within the general medical literature, machine learning dimensionality reduction methods are uncommon and limited to a few specific areas, such as bioinformatics studies on genetics [31, 32] and diagnostic radiological imaging [33, 34]. Despite this, dimensionality reduction in HRV has been investigated and shown to effectively compress multidimensional HRV data for the assessment of cardiac autonomic neuropathy [35]. In this paper, we attempted to investigate several machine learning dimensionality reduction algorithms in building predictive models, hypothesizing that these algorithms could be useful in preserving useful information while improving prediction performance. We aimed to compare the performance of the dimensionality reduction models against the traditional stepwise logistic regression model [28] and conventional risk stratification tools such as the HEART, TIMI, and GRACE scores, in the prediction of 30-day MACE in chest pain patients presenting to the ED.

Methods

Study design and clinical setting

A retrospective analysis was conducted on data collected from patients > 20 years old who presented to Singapore General Hospital ED with chest pain between September 2010 to July 2015. These patients were triaged using the Patient Acuity Category Scale (PACS) and those with PACS 1 or 2 were included in the study. Patients were excluded if they were lost to the 30-day follow-up or if they presented with ST-elevation myocardial infarction (STEMI) or non-cardiac etiology chest pain such as pneumothorax, pneumonia, and trauma as diagnosed by the ED physician. Patients with ECG findings that precluded quality HRnV analysis such as artifacts, ectopic beats, paced or non-sinus rhythm were also excluded.

Data collection

For each patient, HRV and HRnV parameters were calculated using HRnV-Calc software suite [28, 36] from a five to six-minute single-lead (lead II) ECG performed via the X-series Monitor (ZOLL Medical, Corporation, Chelmsford, MA). Table 1 shows the full list of HRV and HRnV parameters used in this study. Besides, the first 12-lead ECGs taken during patients’ presentation to the ED were interpreted by two independent clinical reviewers and any pathological ST changes, T wave inversions, and Q-waves were noted. Patients’ demographics, medical history, first set of vital signs, and troponin-T values were obtained from the hospital’s electronic health records (EHR). In this study, high-sensitivity troponin-T was selected as the cardiac biomarker and an abnormal value was defined as > 0.03 ng/mL.

Table 1 List of traditional heart rate variability (HRV) and novel heart rate n-variability (HRnV) parameters used in this study. HRnV is a new representation of beat-to-beat variation in ECGs and parameter “n” controls the formation of new RR-intervals that are used for parameter calculation. Details of HRnV definition can be found in [28]
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The primary outcome measured was any MACE within 30 days, including acute myocardial infarction, emergent revascularization procedures such as percutaneous coronary intervention (PCI) or coronary artery bypass graft (CABG), or death. The primary outcome was captured through a retrospective review of patients’ EHR.

Machine learning dimensionality reduction

Dimensionality reduction in machine learning and data mining [37] refers to the process of transforming high-dimensional data into lower dimensions such that fewer features are selected or extracted while preserving essential information of the original data. Two types of dimensionality reduction approaches are available, namely variable selection and feature extraction. Variable selection methods generally reduce data dimensionality by choosing a subset of variables, while feature extraction methods transform the original feature space into lower-dimensional space through linear or nonlinear feature projection. In clinical predictive modeling, variable selection techniques such as stepwise logistic regression are popular for constructing prediction models [38]. In contrast, feature extraction approaches [39] are less commonly used in medical research, although they have been widely used in computational biology [40], image analysis [41, 42], physiological signal analysis [43], among others. In this study, we investigated the implementation of eight feature extraction algorithms and evaluated their contributions to prediction performance in risk stratification of ED chest pain patients. We also compared them with a prediction model that was built using conventional stepwise variable selection [28]. Henceforth, we use the terms “dimensionality reduction” and “feature extraction” interchangeably.

Given that there were n samples (xi, yi), i = 1, 2, …, n, in the dataset (X, y), where each sample xi had original D features and its label yi = 1 or 0, with 1 indicating a positive primary outcome, i.e., MACE within 30 days. We applied dimensionality reduction algorithms to project xi into a d-dimensional space (d < D). As a result, the original dataset X ∈ ℝn × D became \( \hat{\boldsymbol{X}}\boldsymbol{\in}{\mathbb{R}}^{n\times d} \). There was a total of D = 174 candidate variables in this study. As suggested in Liu et al. [28], some variables were less statistically significant in terms of contributions to the prediction performance. Thus, we conducted univariable analysis and preselected a subset of \( \overset{\sim }{D} \) variables if their \( p<\overset{\sim }{P} \). In this study, we determined \( \overset{\sim }{P} \) by running principal component analysis (PCA) [44] and logistic regression through 5-fold cross-validation; we plotted a curve to visualize the choice of a threshold and its impact on predictive performance. PCA was used for demonstration because of its simplicity and fast running speed. Other than PCA, we also implemented seven dimensionality reduction algorithms, including kernel PCA (KPCA) [45] with polynomial kernel function, latent semantic analysis (LSA) [46], Gaussian random projection (GRP) [47], sparse random projection (SRP) [48], multidimensional scaling (MDS) [49], Isomap [50], and locally linear embedding (LLE) [51]. All these algorithms are unsupervised learning methods, meaning the transformation of feature space does not rely on sample labels y. Among the eight methods, MDS, Isomap, and LLE are manifold learning-based techniques for nonlinear dimensionality reduction. Table 2 gives a brief introduction to these eight methods.

Table 2 Summary of machine learning dimensionality reduction methods used in this study
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Predictive and statistical analysis

In this study, we chose logistic regression as the classification algorithm to predict the MACE outcome. As described earlier, we determined the threshold \( \overset{\sim }{P} \) to preselect a subset of \( \overset{\sim }{D} \) variables, ensuring the removal of less significant variables as indicated by univariable analysis, after which X ∈ ℝn × D became \( \overset{\sim }{X}\in {\mathbb{R}}^{n\times \overset{\sim }{D}} \). In summary, the inputs to all dimensionality reduction algorithms were in \( \overset{\sim }{D} \)-dimensional space. Subsequently, conventional logistic regression was implemented to take d-dimensional \( \hat{\boldsymbol{X}} \) to predict y, where 5-fold cross-validation was used.

We compared the models built with machine learning dimensionality reduction with our previous stepwise model [28], in which the following 16 variables were used: age, diastolic blood pressure, pain score, ST-elevation, ST-depression, Q wave, cardiac history (the “History” component in the HEART score), troponin, HRV NN50, HR2V skewness, HR2V SampEn, HR2V ApEn, HR2V1 ApEn, HR3V RMSSD, HR3V skewness, and HR3V2 HF power. As described in [28], we selected candidate variables with p < 0.2 in univariable analysis and subsequently conducted multivariable analysis using backward stepwise logistic regression. In the current study, we further built eight dimensionality reduction models without using the cardiac troponin and compared them with the stepwise model without the troponin component. This analysis enabled us to check the feasibility of avoiding the use of laboratory results for quick risk stratification.

In evaluating the modeling performance, we performed the receiver operating characteristic (ROC) curve analysis and reported the corresponding area under the curve (AUC), sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) measures. Moreover, we generated the calibration plots for prediction models. In describing the data, we reported continuous variables as the median and interquartile range (IQR) and statistical significance using two-sample t-test. We reported categorical variables as frequency and percentage and statistical significance using chi-square test. All analyses were conducted in Python version 3.8.0 (Python Software Foundation, Delaware, USA).

Results

We included 795 chest pain patients in this study, of which 247 (31%) patients had MACE within 30 days of presentation to the ED. Table 3 presents the baseline characteristics of the patient cohort. Patients with MACE were older (median age 61 years vs. 59 years, p = 0.035) and more likely to be male (76.1% vs. 64.6%, p = 0.002). History of diabetes, current smoking status, and pathological ECG changes such as ST elevation, ST depression, T wave inversion, pathological Q waves, and QTc prolongation were significantly more prevalent in patients with the primary outcome. Troponin-T and creatine kinase-MB levels were also significantly elevated in patients with the primary outcome. There was no statistically significant difference in patient ethnicity between MACE and non-MACE groups.

Table 3 Baseline characteristics of patient cohorts
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Figure 1a depicts the PCA-based predictive performance versus the threshold \( \overset{\sim }{P} \) (for preselection of variables) and Fig. 1b shows the number of preselected variables versus threshold \( \overset{\sim }{P} \). The predictive performance peaked at \( \overset{\sim }{P}=0.02 \), where a total of 30 variables were preselected, including gender, diastolic blood pressure, pain score, ST-elevation, ST-depression, T-wave inversion, Q wave, cardiac history, EKG, and risk factor components of the HEART score, troponin, HRV RMSSD, HRV NN50, HRV pNN50, HRV HF power, HRV Poincaré SD1, HR2V RMSSD, HR2V NN50, HR2V pNN50, HR2V HF power, HR2V Poincaré SD1, HR2V1 RMSSD, HR2V1 NN50, HR2V1 HF power, HR2V1 Poincaré SD1, HR3V1 RMSSD, HR3V1 HF power, HR3V1 Poincaré SD1, HR3V2 RMSSD, and HR3V2 Poincaré SD1. These were used as inputs to all dimensionality reduction algorithms whose outputs were linear or nonlinear combinations of these 30 variables.

Fig. 1
figure 1

Variable preselection using p-value in univariable analysis for dimensionality reduction: a prediction area under the curve versus the p-value, and (b) the number of preselected variables versus the p-value

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Figure 2 shows the predictive performance (in terms of AUC value) versus feature dimension (i.e., number of “principal components”) for all eight dimensionality reduction algorithms. The AUC values of GRP, SRP, and KPCA gradually increased with the increment of feature dimension, while the AUC values of PCA, LSA, MDS, Isomap, and LLE drastically jumped to more than 0.8 when feature dimension d ≥ 3 and plateaued in the curves when d ≥ 15. The highest AUC values of PCA, KPCA, LSA, GRP, SRP, MDS, Isomap, and LLE were 0.899, 0.896, 0.899, 0.896, 0.898, 0.901, 0.888, and 0.898, achieved with feature dimensions of 15, 30, 15, 22, 20, 27, 23, and 30, respectively.

Fig. 2
figure 2

Prediction performance based on the eight dimensionality reduction algorithms versus the number of feature dimensions after reduction

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Figure 3 shows the ROC curves of the eight dimensionality reduction algorithms, the stepwise logistic regression [28], and three clinical scores. All eight dimensionality reduction methods performed comparably with the stepwise variable selection, and MDS achieved the highest AUC of 0.901. Table 4 presents ROC analysis results of all 12 methods/scores where sensitivity, specificity, PPV, and NPV are reported with 95% confidence intervals (CIs), noting that the performance of the stepwise model in this paper was slightly different from that reported in [28] due to the choice of cross-validation scheme, i.e., 5-fold (AUC of 0.887) versus leave-one-out (AUC of 0.888). Figure 4 presents the calibration curves of predictions by all methods/scores. The stepwise model and seven dimensionality reduction models (PCA, KPCA, LSA, GRP, SRP, MDS, and Isomap) showed reasonable model calibrations, in which their curves fluctuated along the diagonal line, meaning these models only slightly overestimated or underestimated the predicted probability of 30-day MACE. The LLE model was unable to achieve good calibration. In comparison, all three clinical scores (HEART, TIMI, and GRACE) generally underpredicted the probability of 30-day MACE.

Fig. 3
figure 3

ROC curves (based on the optimal number of dimensions) generated by the stepwise model, eight dimensionality reduction models, and three clinical scores

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Table 4 Comparison of performance of the HRnV models (based on 5-fold cross-validation), HEART, TIMI, and GRACE scores in predicting 30-day major adverse cardiac events (MACE). The cut-off values were defined as the points nearest to the upper-left corner on the ROC curves
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Fig. 4
figure 4

Calibration curves (based on the optimal number of dimensions) generated by the stepwise model, eight dimensionality reduction models, and three clinical scores

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Figure 5 shows the ROC curves of prediction models without using cardiac troponin. At feature dimensions of 13, 21, 13, 29, 24, 17, 18, and 18, the highest AUC values of PCA, KPCA, LSA, GRP, SRP, MDS, Isomap, and LLE were 0.852, 0.852, 0.852, 0.852, 0.851, 0.852, 0.845, and 0.849, respectively. The stepwise model without troponin yielded an AUC of 0.834 compared to 0.887 with troponin. All prediction models outperformed both the TIMI and GRACE scores while achieving comparable results with the HEART score.

Fig. 5
figure 5

ROC curves (based on the optimal number of dimensions) generated by the stepwise model, eight dimensionality reduction models, and three clinical scores, where the prediction models were built without using cardiac troponin.s

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Discussion

In this study, we showed that machine learning dimensionality reduction yielded only marginal, non-significant improvements compared to stepwise model in predicting the risk of 30-day MACE among chest pain patients in the ED. This corroborates with similar observations that traditional statistical methods can perform comparably to machine learning algorithms [52, 53]. Among the dimensionality reduction models integrated with cardiac troponin, the MDS model had the highest discriminative performance (AUC of 0.901, 95% CI 0.874–0.928) but did not significantly outperformed the traditional stepwise model (AUC of 0.887, 95% CI 0.859–0.916). Among the models without using troponin, PCA, KPCA, LSA, GRP, and MDS performed equally well, achieving an AUC of 0.852, compared with the stepwise model without troponin which had an AUC of 0.834. In general, the traditional stepwise approach was proved to be comparable to machine learning dimensionality reduction methods in risk prediction, while benefiting from model simplicity, transparency, and interpretability that are desired in real-world clinical practice.

High-dimensional data suffers from the curse of dimensionality, which refers to the exponentially increasing sparsity of data and sample size required to estimate a function to a given accuracy as dimensionality increases [54]. Dimensionality reduction has successfully mitigated the curse of dimensionality in the analysis of high-dimensional data in various domains such as computational biology and bioinformatics [31, 32]. However, clinical predictive modeling typically considers relatively few features, limiting the effects of the curse of dimensionality. This may account for the relatively limited benefit of dimensionality reduction in our analysis.

Additionally, with comparable performance to the traditional stepwise model, transparency and interpretability of machine learning dimensionality reduction models are constrained by complex algorithmic transformations of variables, leading to obstacles in the adoption of such models in real-world clinical settings. In contrast, traditional biostatistical approaches like logistic regression with stepwise variable selection deliver a simple and transparent model, in which the absolute and relative importance of each variable can be easily interpreted and explained from the odds ratio. Marginal performance improvements should be weighed against these limitations in interpretability, which is an important consideration in clinical predictive modeling.

Comparing the eight dimensionality reduction algorithms, PCA and LSA use common linear algebra techniques to learn to create principal components in a compressed data space, while MDS, Isomap, and LLE are nonlinear, manifold learning-based dimensionality reduction methods. As observed from our results, complex nonlinear algorithms did not show an obvious advantage over simple PCA and LSA methods in enhancing the predictive performance. Yet, nonlinear algorithms are more computationally complex and require more computing memory. For example, KPCA and Isomap have computational complexity of O(n3) and memory complexity of O(n2), while PCA has computational complexity of \( O\left({\overset{\sim }{D}}^3\right) \) and memory complexity of \( O\left({\overset{\sim }{D}}^2\right) \) [39]. In applications of clinical predictive modeling, n ⁠— the number of patients ⁠— is usually larger than \( \overset{\sim }{D} \) ⁠ — the number of variables; in our study, n is 795 and \( \overset{\sim }{D} \) is 29 or 30, depending on the inclusion of troponin. This suggests that linear algorithms may be preferred due to reduced computational complexity and memory while retaining comparable performance. Another observation in this study was that the impact of preselection (as shown in Fig. 1) on predictive performance was more substantial than that of dimensionality reduction, indicating the importance of choosing statistically significant candidate variables.

Our study also reiterates the value of HRnV-based prediction models for chest pain risk stratification. Among chest pain risk stratification tools in the ED, clinical scores like HEART, TIMI, and GRACE are currently the most widely adopted and validated [55, 56]. However, a common barrier to quick risk prediction using these traditional clinical scores is the requirement of cardiac troponin, which can take hours to obtain. To address these difficulties, machine learning-based predictive models that integrate HRV measures and clinical parameters have been proposed [17, 22, 25, 26], including our development of HRnV, a novel alternative measure to HRV that has shown promising results in predicting 30-day MACE [28], which was the stepwise model in this paper. Both the dimensionality reduction-based predictive models and the stepwise model with troponin presented superior performance than HEART, TIMI, and GRACE scores. When troponin was not used, several dimensionality reduction-based models such as PCA, KPCA, and MDS still yielded marginally better performance than the original HEART score, while benefiting from generating the predictive scores in merely 5 to 6 min.

Additionally, Table 4 shows that all HRnV-based predictive models had higher specificities than the HEART score while all HRnV-based models except Isomap also improved on the already high sensitivity of the HEART score [21, 57]. The specificities of KPCA, Isomap, and MDS were significantly higher by an absolute value of almost 10%. Substantial improvements to the specificity of MACE predictive models may reduce unnecessary admission and thus minimize costs and resource usage [5]. This is particularly relevant in low-resource settings, for example, the overburdened EDs in the current coronavirus disease 2019 (COVID-19) pandemic, where novel methods in resource allocation and risk stratification could alleviate the strain on healthcare resources [58].

There remains a need for further investigation into methods that utilize information from the full set of HRV and HRnV variables. From 174 variables in the initial data set, dimensionality reduction performed the best with a preselection of 30 variables, of which 19 were HRV and HRnV parameters. That is, the majority of the newly constructed HRnV parameters were removed based on the strict significance threshold of p < 0.02 on univariable analysis. Therefore, novel HRnV measures were not fully used in prediction models of 30-day MACE, leaving room for further investigation of alternative ways of using them. Moving forward, it may be valuable to develop and evaluate deep learning frameworks [59] to synthesize novel low-dimensional representations of multidimensional information. Alternatively, building point-based, interpretable risk scores [60] can also be beneficial to implementation and adoption in real-world clinical settings, since designing inherently interpretable models is more favorable than explaining black box models [61].

We acknowledge the following limitations of this study. First, the clinical application (i.e., risk stratification of ED chest pain patients) was only one example of clinical predictive modeling, thus our conclusion on the effectiveness of machine learning dimensionality reduction algorithms may not be generalizable to other applications, particularly those with a larger number of variables. Second, only eight dimensionality reduction algorithms were investigated, while many other methods are available. Third, given the small sample size, we were unable to determine the threshold \( \overset{\sim }{P} \) and build predictive models with a separate training set; this also limited the stability check [62] for both logistic regression and machine learning models. Last, we did not build a workable predictive model for risk stratification of ED chest pain patients, although several models built in this study showed promising results compared to existing clinical scores. We aim to conduct further investigations.

Conclusions

In this study we found that machine learning dimensionality reduction models showed marginal value in improving the prediction of 30-day MACE for ED chest pain patients. Being black box models, they are further constrained in clinical practice due to low interpretability. Whereas traditional stepwise prediction model showed simplicity and transparency, making it feasible for clinical use. To fully utilize the available information in building high-performing predictive models, we suggest additional investigations such as exploring deep representations of the input variables and creating interpretable machine learning models to facilitate real-world clinical implementation.