Development and Validation of a Nomogram Prediction Model for In-hospital Mortality in Patients with Cardiac Arrest: A Retrospective Study

Abstract

Background:

Cardiac arrest (CA) is associated with high incidence and mortality rates. Hence, assessing the prognosis of CA patients is crucial for optimizing clinical treatment. This study aimed to develop and validate a clinically applicable nomogram for predicting the risk of in-hospital mortality in CA patients.

Methods:

We retrospectively collected the clinical data of CA patients admitted to two hospitals in Zhejiang Province between January 2018 and June 2024. These patients were randomly assigned to the training set (70%) and the internal validation set (30%). Variables of interest included demographics, comorbidities, CA-related characteristics, vital signs, and laboratory results, and the outcome was defined as in-hospital death. Variables were selected using least absolute shrinkage and selection operator (LASSO) regression, recursive feature elimination (RFE), and eXtremely Gradient Boosting (XGBoost). Meanwhile, multivariate regression analysis was used to identify independent risk factors. Subsequently, prediction models were developed in the training set and validated in the internal validation set. Receiver operating characteristic (ROC) curves were plotted and the area under these curves (AUC) was calculated to compare the discriminative ability of the models. The model with the highest performance was further validated in an independent external cohort and was subsequently represented as a nomogram for predicting the risk of in-hospital mortality in CA patients.

Results:

This study included 996 CA patients, with an in-hospital mortality rate of 49.9% (497/996). The LASSO regression model significantly outperformed the RFE and XGBoost models in predicting in-hospital mortality, with an AUC value of 0.81 (0.78, 0.84) in the training set and 0.85 (0.80, 0.89) in the internal validation set. The AUC values for these sets in the RFE model were 0.74 (0.70, 0.78) and 0.77 (0.72, 0.83), respectively, and those for the XGBoost model were 0.75 (0.71, 0.79) and 0.77 (0.72, 0.83), respectively. For the optimal prediction model, the AUC value of the LASSO regression model in the external validation set was 0.84 (0.78, 0.90). The LASSO regression model was represented as a nomogram incorporating several independent risk factors, namely age, hypertension, cause of arrest, initial heart rhythm, vasoactive drugs, continuous renal replacement therapy (CRRT), temperature, blood urea-nitrogen (BUN), lactate, and Sequential Organ Failure Assessment (SOFA) scores. Calibration and decision curves confirmed the predictive accuracy and clinical utility of the model.

Conclusions:

We developed a nomogram to predict the risk of in-hospital mortality in CA patients, using variables selected via LASSO regression. This nomogram demonstrated strong discriminative ability and clinical practicality.

Graphical abstract

Keywords

cardiac arrest / mortality / nomogram / prediction model / LASSO regression / machine learning

1. Introduction

Cardiac arrest (CA) is characterized by abrupt cessation of the heart’s pumping function and is associated with a high mortality rate [1, 2]. In the United States, more than 400,000 individuals die from CA annually, with a survival-to-discharge rate of 10% [1]. Despite the widespread implementation of basic life support and substantial progress in therapeutic interventions, the management of CA remains a significant challenge [3].

Increasing the survival rate of CA survivors is a critical issue that warrants immediate attention in the field of critical care medicine. The poor prognosis of CA patients is often attributed to hypoxic-ischemic brain injury and dysfunction of other organs [4]. Prognostic assessment is an essential component of CA management. At present, serum biomarkers, neurophysiological tests, and imaging are commonly used to assess neuroprognosis for CA patients [5]. However, these methods can be influenced by sedation or limited by the unavailability of equipment and life support conditions [6, 7]. Although severity scoring systems, such as Sequential Organ Failure Assessment (SOFA), Acute Physiology and Chronic Health Evaluation (APACHE) II, and Simplified Acute Physiology Score (SAPS) II, are commonly used for prognostic assessment, their accuracy is reported to be moderate [8, 9, 10]. The advent of machine learning (ML)-based prediction models marks an innovative shift in the prognosis assessment of CA. As a specialized branch of artificial intelligence (AI), ML empowers computers to autonomously discern and learn from historical data, identifying underlying rules and patterns. By constructing precise algorithms, ML is capable of predicting targeted events or trends, thus enhancing the efficiency and accuracy of prognosis assessment [11]. However, ML-based models often suffer from the “black box” issue, that is, their internal mechanisms lack transparency, posing certain challenges in practical application [12].

A nomogram is a graphical tool that represents predictive factors in scaled segments to demonstrate the relationship between variables and outcomes [13]. Its intuitive design and ease of use allow clinicians to rapidly comprehend and apply complex prediction models [14]. Nomograms have demonstrated efficacy in predicting the incidence [15], complications [16], and outcomes [17, 18] of cardiovascular diseases. Therefore, in this study, we developed and validated a nomogram for predicting the risk of in-hospital mortality in CA patients.

2. Materials and Methods

2.1 Data Sources and Patient Cohort

This retrospective study included CA patients admitted to Hangzhou First People’s Hospital affiliated to Westlake University School of Medicine and Second Affiliated Hospital of Zhejiang University School of Medicine (Zhejiang, China) between January 1, 2018, and June 30, 2024. The inclusion criteria for CA patients were as follows: (1) survival for >24 hours after resuscitation; (2) an age of \ge18 years; and (3) availability of the records of the first intensive care unit (ICU) admission. The external validation set came from Huzhou Central Hospital and Jinhua Central Hospital. Patients were enrolled following the same inclusion and exclusion criteria. This study was approved by the Ethics Committee of Hangzhou First People’s Hospital, Westlake University School of Medicine (IIT-20230420-0077-01).

2.2 Data Extraction and Preprocessing

We followed the criteria developed by Riley et al. [19] to calculate the minimum sample size required for a binary multivariate prediction model. It was performed through the “pmsampsize” package in R (version 4.3.2, R Foundation for Statistical Computing, Vienna, Austria). The shrinkage factor, absolute difference between the apparent and adjusted Nagelkerke R2, prevalence and C-statistics were defined as 0.9, 0.05, 0.5 and 0.8, respectively. Based on these parameters, the calculated sample size was 885.

Data were extracted from the electronic medical record systems of the two hospitals. The data of 54 variables were retrieved, including demographic characteristics, comorbidities, location of arrest, presumed etiology (cardiac or non-cardiac), initial rhythm (shockable or non-shockable), treatment methods, scoring systems, vital signs, and laboratory tests within 24 hours after ICU admission. The mean values were calculated for variables with multiple measurements such as vital signs and laboratory results. The primary outcome was in-hospital mortality.

Addressing missing values was a critical step in data preprocessing. Variables with \ge25% missing data were directly excluded. For variables with 25% missing data, multiple imputation was used, introducing randomness to reflect the uncertainty of missing data more accurately than that achieved via single imputation [20]. This approach was implemented using the “mice” package in R (version 4.3.2, R Foundation for Statistical Computing, Vienna, Austria).

2.3 Statistical Analysis

Statistical analyses were performed using the SPSS (version 25.0, IBM Corp., Chicago, IL, USA) and R software. Continuous variables were expressed as the means with standard deviations (SDs) or medians with interquartile ranges (IQRs). Student’s t-test or Mann-Whitney U test was used for intergroup comparisons. Categorical variables were expressed as numbers with percentages and compared using Chi-square test or Fisher’s exact test. A p-value of 0.05 was considered statistically significant.

Eligible CA patients were randomly assigned to the training set (70%) and internal validation set (30%). Predictors of in-hospital mortality were identified in the training set, and three methods were compared. The Least Absolute Shrinkage and Selection Operator (LASSO) regression is a variation of the linear regression model. It incorporates a penalty function (L1 regularization term) into the general linear regression. By adjusting the lambda (\lambda) parameter through 10-fold cross-validation to compress some coefficients to zero, LASSO regression can achieve variable selection and model simplification [21]. Recursive Feature Elimination (RFE) is an iterative variable selection method. It repeatedly trains models and ultimately identifies the optimal subset of features with the best performance by assessing the importance of each feature and progressively removing the least important features [22]. EXtremely Gradient Boosting (XGBoost) is an ensemble learning algorithm based on tree models. It can automatically evaluate the importance of features through its internal structure. During the construction of tree models, the importance score of each feature is generated by accumulating the split contributions across all trees to provide reference for variable selection [23].

Variables selected using the three aforementioned methods were analyzed using univariate and multivariate logistic regression analyses to identify significant risk factors for in-hospital mortality in CA patients, and these factors were used to construct prediction models. Receiver operating characteristic (ROC) curves were plotted, and the area under the curves (AUC) was calculated to assess the discriminative ability of the models. Calibration curves were plotted to evaluate the consistency between predicted and actual outcomes, and decision curves were plotted to assess the practical utility of the models. The model with the highest performance was further validated in the external validation set and was subsequently represented as a nomogram for predicting the risk of in-hospital mortality in CA patients.

3. Results

3.1 Baseline Characteristics

A total of 996 CA patients were included in this study (Fig. 1). Of these patients, 497 (49.9%) died upon discharge. As detailed in Table 1, age, heart rate, aspartate aminotransferase (AST), bilirubin, creatinine, blood urea nitrogen (BUN), glucose, sodium, prothrombin time (PT), international normalized ratio (INR), lactate, base excess, and SOFA scores were higher in the non-survivor group than in the survivor group. The non-survivor group had a higher prevalence of diabetes, cerebral infarction, and chronic kidney disease (CKD); more frequent use of vasoactive drugs, sodium bicarbonate, continuous renal replacement therapy (CRRT), and mechanical ventilation; a lower body temperature, hemoglobin, platelet, albumin, pH, actual bicarbonate; and less frequent use of percutaneous coronary intervention (PCI). Additionally, the survivor group had a higher ratio of cardiac cause of CA and shockable rhythms.

3.2 Variable Selection

Fig. 2A shows the coefficient profile plot for LASSO regression, wherein each curve represents a variable’s coefficient trajectory. As the log \lambda parameter increased, the regression coefficients continually converged toward zero. Fig. 2B shows the cross-validation plot for LASSO regression, with dotted lines indicating specific \lambda values. In particular, \lambdamin on the left denotes the \lambda value with minimal likelihood deviation and an optimal model fit, retaining 33 variables, whereas \lambda-se on the right denotes one standard error from the minimum \lambda value, offering a good fit with a simpler model owing to the inclusion of fewer variables. Therefore, \lambda-se was chosen as the final criterion, which included 11 variables as follows: age, hypertension, non-cardiac cause of CA, shockable rhythm, vasoactive drugs, CRRT, temperature, chloride, BUN, lactate, and SOFA score. Fig. 2C shows the ranking of these variables by the magnitude of their regression coefficients. Similarly, RFE and XGBoost were used for variable selection, with Fig. 3A,B showing the top 13 variables.

Logistic regression analyses were used to identify risk factors for in-hospital mortality (Tables 2,3,4). The risk factors identified using LASSO regression included age, hypertension, non-cardiac cause of arrest, shockable rhythm, vasoactive drugs, CRRT, temperature, BUN, lactate, and SOFA. The risk factors identified using RFE included vasoactive drugs, CRRT, temperature, creatinine, BUN, sodium, lactate, and SOFA. In addition, the risk factors identified using XGBoost included age, temperature, respiratory rate, hemoglobin, bilirubin, creatinine, BUN, sodium, lactate, and SOFA.

3.3 Development and Validation of Models

Multivariate logistic regression was used to develop models for predicting the risk of in-hospital mortality in CA patients. As shown in Fig. 4A, the LASSO model demonstrated superior discriminative ability in both the training and internal validation sets, with AUC values of 0.81 (0.78, 0.84) and 0.85 (0.80, 0.89), specificity of 0.89 (0.85, 0.92) and 0.89 (0.83, 0.94), and sensitivity of 0.64 (0.58, 0.69) and 0.67 (0.59, 0.75), respectively. The AUC values of the RFE model were 0.74 (0.70, 0.78) and 0.77 (0.72, 0.83) and those of the XGBoost model were 0.75 (0.71, 0.79) and 0.77 (0.72, 0.83) in the training and internal validation sets, respectively (Fig. 4B,C). The calibration curve of the LASSO model exhibited high consistency between predicted and observed outcomes, and the decision curve confirmed the clinical utility of the model (Fig. 5).

Totally 204 eligible CA patients were included in the external validation, of which the in-hospital mortality was 51.47% (105/204). Supplementary Table 1 showed that there were significant differences between the survivor and non-survivor groups for all 10 selected predictors (p 0.05). The ROC curve was shown in Supplementary Fig. 1, with AUC value of 0.84 (0.78, 0.90), specificity of 0.74 (0.65, 0.83) and sensitivity of 0.82 (0.74, 0.90).

3.4 Presentation of the Nomogram

As the LASSO model exhibited optimal predictive performance, it was used to create a nomogram for predicting in-hospital mortality (Fig. 6A). Each variable in the nomogram was presented as a scaled line, with the length of the line indicating the impact of the variable on prediction. Specifically, longer lines indicated a greater contribution. The score of each variable was located on the “Points” row, and the total score corresponding to the probability of mortality was shown at the bottom, with higher scores indicating a higher risk of mortality risk. Fig. 6B showed an actual case. The specific variable values of this patient were marked in the nomogram to find the corresponding points, and the total points were calculated to be 559, with the corresponding mortality risk going to 0.804.

4. Discussion

In this retrospective study, a total of 996 CA patients were included and the efficacy of three methods in selecting variables for prediction models was compared. The LASSO regression approach revealed 10 independent risk factors, demonstrating a superior discriminative ability to predict in-hospital mortality. The results of external validation supported the good performance of the model. Consequently, the LASSO model was represented as a nomogram to improve its clinical applicability.

Redundant variables may introduce multicollinearity and lead to model overfitting, as well as increasing model complexity and reducing the interpretability and operability. Consequently, the process of variable selection is imperative, as it contributes to the creation of a model with both accuracy and efficiency. LASSO regression converges variables based on L1 regularization, reduces model overfitting and enhances its interpretability [21]. RFE offers high flexibility and shows compatibility with various algorithms, identifying the most impactful variable set through continuous iteration [22]. But the results of RFE can be compromised if the algorithm is insensitive to relevant variables [22]. XGBoost effectively quantifies the importance of variables in the ensemble tree models and captures non-linear relationships and variable interactions, showing strong robustness in the computation of large datasets [23]. However, both RFE and XGBoost are susceptible to overfitting, particularly in case of small sample sizes, high noise, or overly complex models. In addition, we found that XGBoost did not consider categorical variables, such as cause of CA, initial rhythm, and vasoactive drugs (Fig. 2C), potentially owing to the reduced accuracy of feature importance after one-hot encoding [23]. Therefore, LASSO regression shows strong potential in screening key features [24, 25]. In this study, the LASSO model had superior discriminative ability and adaptability, which highlighted its advantages in variable selection.

Assessing the prognosis of CA patients has consistently been a subject that requires the attention and resolution for clinicians. Current research has raised a spectrum of evaluation methods, mainly encompassing risk scores derived from multiple regression analysis [26, 27, 28] and prediction models based on ML algorithms [29, 30, 31]. ML-based models have demonstrated promising predictive capabilities; however, nomogram has certain valuable advantages when used for survival analyses, especially for interpreting the outputs. Nomogram facilitates interaction with clinicians through a user-friendly, operable interface. It integrates multidimensional variables into a single chart, simplifying complex calculations and rendering the results intuitive and easy to comprehend. Fig. 6B displayed the actual prediction process for a patient. By merely collecting the values of the required variables, the risk of in-hospital mortality can be intuitively obtained through the nomogram, thereby enabling a personalized assessment of patient prognosis. Consequently, nomograms have been extensively employed in research as an advantageous clinical prediction model.

Chen et al. [32] and Sun et al. [33] both extracted data from the Medical Information Mart for Intensive Care IV (MIMIC-IV) database to construct nomogram models for predicting the risk of in-hospital mortality in CA patients, with AUC values of 0.801 (0.775, 0.835) and 0.799 (0.762, 0.837) in internal validation, respectively. Both studies used LASSO regression and logistic regression to identify independent risk factors. Chen et al. [32] selected age, malignant cancer, norepinephrine, heart rate, respiratory rate, temperature, peripheral oxygen saturation (SpO2), sodium, BUN, bicarbonate, and lactate, while Sun et al. [33] chose age, gender, heart rate, mean arterial pressure (MAP), respiratory rate, temperature, SpO2, PT, bicarbonate, Glasgow Coma Scale (GCS) score, and SAPS III score. However, considering the differences in the characteristics of the cohorts, the models based on the MIMIC-IV database often exhibit significant limitations in generalizability, with these two studies lacking the support from external validation. Nagy et al. [34] developed a nomogram for predicting 30-day mortality in 103 Out-of-hospital Cardiac Arrest (OHCA) patients, with the AUC value of 0.835 (0.755, 0.907) in internal validation. Variable selection was achieved through restricted cubic splines and the Akaike information criterion, including age, initial rhythm, heart rate, pH, and right ventricular end-diastolic diameter. Zhang et al. [18] developed a nomogram for predicting in-hospital mortality in 561 in-hospital cardiac arrest (IHCA) patients, identifying only rearrest, duration of cardiopulmonary resuscitation (CPR), and length of hospital stay as three independent risk factors through multivariate logistic regression, yet demonstrating good discriminative ability with an AUC value of 0.88 (0.83, 0.93). Both studies constructed robust nomogram models with fewer predictive factors, but faced issues with small sample sizes and a lack of external validation.

In this retrospective study, we initially constructed a nomogram model for predicting in-hospital mortality risk in a relatively large cohort of CA patients with an AUC value of 0.85 (0.80, 0.89). The calibration and decision curve confirmed its clinical applicability. Furthermore, we substantiated the generalizability of the model in the external validation set, with an AUC value of 0.84 (0.78, 0.90). Variable selection was achieved through LASSO regression and multivariate logistic regression, identifying age, hypertension, initial rhythm, cause of CA, CRRT, vasoactive drugs, temperature, BUN, lactate, and SOFA score as independently associated with mortality. These variables are readily accessible in clinical settings, enhancing the practicability and operation convenience of the nomogram.

However, this study has a few limitations that should be acknowledged. First, its retrospective nature might have introduced unavoidable biases. Second, although the final model was validated in an external cohort, the sample size is small and further validation in large-scale cohort is required. Third, OHCA and IHCA were simultaneously included in the analysis; consequently, some significant independent risk factors specifically associated with either of these conditions might have been overlooked.

5. Conclusions

In this study, we used variables identified via LASSO regression to developed a nomogram for predicting the in-hospital mortality in CA patients. The nomogram demonstrated robust discriminative ability and clinical utility.

Availability of Data and Materials

The datasets supporting the conclusions of this article are available from the corresponding author on reasonable request.

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Funding

Zhejiang Provincial Medical and Health Technology Project(WKJ-ZJ-2315)

Science and Technology Development Project of Hangzhou(202204A10)

Science and Technology Project of Hangzhou(20220919Y006)