Patient characteristics

As illustrated in Tables 1 and 3, the mean age of the patients enrolled in the three groups exceeded 65 years. No statistically significant differences (P > 0.05) were observed between the POAF and control groups regarding gender, age, BMI, comorbidities ( including hypertension, diabetes mellitus, stroke, CHD, and OSAS), daily fluid intake, presentation for emergency surgery, surgical type (stratified into 16 categories based on the affected organ and surgical procedure; detailed results of this analysis are presented in the supplementary file), type of pathology, laboratory test variables (such as platelet count and phosphorus levels), and ECG variables (including P-wave amplitude, QRS wave duration, and LVH).

Table 1 Basic clinical characteristics of the POAF group and the control groupScreening for independent risk factors of POAF by logistic regression analysis

Univariate logistic regression analysis demonstrated that fever, sepsis, intestinal obstruction, ASA Class (II/III), blood cell count (WBC, neutrophil, lymphocyte, monocyte, and hemoglobin), hematocrit value, electrolytes (Na, K, Ca, and Mg), serum creatinine, BUN, albumin, prealbumin, CRP, NT-pro BNP, D-dimer, NLR, LMR, PLR, SIRI, SII, SIS, P-wave duration, PR interval, and Macruz index were variables that showed statistically significant differences between the two groups (P < 0.05, Table 2). The results of the multicollinearity analysis indicated that there was multicollinearity among the following variables: neutrophil count, lymphocyte count, monocyte count, hemoglobin, hematocrit value, NLR, PLR, SIRI, and SII, as their VIF > 10. In addition, multicollinearity of variables was visualized by the corrplot package of R software (Fig. 2). Subsequently, variables with statistical significance in the univariate regression analysis and VIF < 10 were subjected to multivariate regression analysis, which revealed that BUN, CRP, P-wave duration, and PR interval were independent risk factors for POAF in patients who underwent laparotomy (P < 0.05, Table 2).

Table 2 The risk factors of POAF explored by univariate and multivariate logistic regression analysisFig. 2

Correlation heatmap of variables between the POAF group and control group. *P < 0.05; **P < 0.01; ***P < 0.001; ****P < 0.0001

Candidate variables for model selected by LASSO regression analysis

Forty-eight candidate variables obtained preoperatively were screened for candidate predictors by LASSO regression analysis, excluding variable covariates. With the gradual contraction of the penalty parameter λ, the number of candidate variables for the model was 18 when the value of λ with the minimum error in the tenfold cross-validation was selected as the optimal value of the model. When the value of λ within 1 × the standard error of the minimum value was chosen as the optimal value of the model, the number of candidate variables for the model was seven (Fig. 3A, B). The aim of clinical predictive modeling is to keep the model variables as simple as possible while ensuring the predictive validity of the model. Therefore, we chose seven candidate variables (CRP, NT-pro BNP, LMR, Ca, albumin, BUN, and the Macruz index) as candidate variables for the prediction model.

Fig. 3

LASSO regression model. A LASSO coefficient profiles of the 51 features. Each curve represents a coefficient, and the X-axis represents the regularization penalty parameter. As λ changes, a coefficient that becomes non-zero enters the LASSO regression model. B Cross-validation to select the optimal tuning parameter (λ). The left dotted vertical line represents the value of λ that gives a minimum mean absolute error, and the right dotted vertical line represents the largest value of λ that error was within 1 × standard error of the minimum. C The nomogram model for predicting the risk of POAF in patients who underwent laparotomy

Construction and validation of the nomogram prediction model

The general information of the validation group and the training set is presented in Table 3. Based on the training set data, a logistic regression model with seven candidate variables was initially constructed. However, three variables (NT-pro BNP, Ca, and albumin) were excluded according to the Wald test (P > 0.05) (Table 4). The remaining four variables were CRP, LMR, BUN, and the Macruz index. Based on the outcomes of both univariate and multivariate logistic regression analyses, these four variables were chosen as the basis for constructing the logistic regression model, and all variables were tested by the Wald test (P < 0.05) (Table 5). The standardized regression coefficient of the Macruz index was the largest, indicating that it had the greatest influence on the dependent variable, i.e., the risk of POAF.

Table 3 Basic clinical characteristics of the training set and the validation groupTable 4 Logistic regression analysis of candidate variables for the modelTable 5 Logistic regression analysis of selected variables for the model

Based on the results of the regression model, a nomogram was generated using the rms package in the R software (Fig. 3C). The total score was calculated as the sum of the four index scores, with each index corresponding to a score on the upper-point line. To estimate the probability of POAF in patients who underwent laparotomy, the whole score was projected on the bottom scales.

The nomogram model’s capacity for discrimination was evaluated by ROC curve analysis after computing each patient’s total score with the nomogram prediction model. The area under the ROC curve (AUC) was 0.90 (95% CI 0.8509–0.9488) for the training set and 0.86 (95% CI 0.7142–1) for the test set, which indicates that the nomogram model has good discriminative ability (Fig. 4A, B). The nomogram model was externally validated using the data of the validation group with an AUC of 0.9792 (95% CI 0.9293–1), which was higher than the AUC values of the training and test sets, suggesting that the model had sufficient generalizability (Fig. 4C, D).

Fig. 4

The evaluation of the nomogram model. Receiver operating characteristic (ROC) curve of the prediction model in the training (A), test (B), and validation (C) datasets. D Comparison of ROC curves for the above three datasets. E Calibration curve of the nomogram model for predicting the risk of POAF. The calibration plot shows the agreement between the predicted (X-axis) and observed (Y-axis) risks of POAF. F The decision curve analysis (DCA) of the nomogram model. The gray line represents the assumption that all patients who underwent laparotomy had POAF, while the black horizontal line represents the assumption that all patients who underwent laparotomy did not have POAF. The red line represents the assumption that patients who underwent laparotomy will be judged positive if the positive probability obtained from the nomogram is higher than the threshold probability

The Hosmer–Lemeshow test indicated that there was no statistically significant deviation between the predicted values of the nomogram model and the actual observed values (χ2 = 1.1496, df = 8, P = 0.9971). This suggests that the predictive probabilities of the nomogram model were well-aligned with the actual probabilities. To validate the nomogram model, an internal bootstrap validation was conducted using 1000 sampling repetitions. The C-index of the bootstrap nomogram model was 0.8998, indicating a discrimination ability that was comparable to that of the initial nomogram model. Furthermore, the calibration curve from the internal bootstrap validation illustrated a mean absolute error of 0.022, signifying a high level of agreement between the calibration and ideal curves (Fig. 4E).

The decision curve analysis (DCA) of the nomogram model is depicted in Fig. 4F. It was observed that within the predicted risk range of 0.01–0.9 for POAF in laparotomy patients, implementing preventive measures based on this model yielded significantly higher net benefits compared to the scenario where no treatment was administered (Fig. 4F). Notably, the nomogram model exhibited the most substantial benefit when the predicted risk of POAF in laparotomy patients fell within the range of 0.01 to 0.9.