Cardiol Res

Cardiology Research, ISSN 1923-2829 print, 1923-2837 online, Open Access

Article copyright, the authors; Journal compilation copyright, Cardiol Res and Elmer Press Inc

Journal website https://cr.elmerpub.com

Original Article

Volume 17, Number 1, February 2026, pages 10-22

Development and Validation of a Prognostic Model to Predict Mortality in Patients With Heart Failure With Mildly Reduced Ejection Fraction After Acute Myocardial Infarction

Figure 1. Flow diagram for participant screening, eligibility, and analysis. HFmrEF: heart failure with mildly reduced ejection fraction; LVEF: left ventricular ejection fraction.

Figure 2. LASSO regression coefficient path and CV LASSO regression coefficient path. (a) LASSO regression coefficient path. (b) CV LASSO regression coefficient path. The LASSO regression coefficient path displays how the coefficients of each variable change with increasing values of the regularization parameter λ. The CV LASSO regression coefficient path illustrates the coefficients’ behavior with λ tuned through cross-validation. Both paths provide insights into the impact of regularization on variable selection and coefficient estimation in the LASSO regression model. LASSO: least absolute shrinkage and selection operator.

Figure 3. Area under the receiver operating characteristic (ROC) curve and bootstrap validation. (a) ROC curves for the training set at 6 months, 2 years, and 3 years. (b) ROC curves for the validation set at 6 months, 2 years, and 3 years. (c) Comparison of model stability between the original model and 500 rounds of bootstrap validation on the training set. (d) Comparison of model stability between the original model and 500 rounds of bootstrap validation on the validation set. AUC: area under the curve; CI: confidence interval.

Figure 4. Calibration curves at different time points. (a) Calibration curves for the training set at 6 months, 2 years, and 3 years. (b) Calibration curves for the validation set at 6 months, 2 years, and 3 years. The calibration curves depict the agreement between the predicted probabilities and the observed outcomes at different time points. The curves represent the performance of the predictive model in terms of calibration, indicating how well the model’s predicted probabilities align with the actual probabilities. OS: overall survival.

Figure 5. Decision curve analysis (DCA) with time and DCA nomogram. (a) DCA with time for the training set. (b) DCA with time for the validation set. (c) DCA nomogram for the training set. (d) DCA nomogram for the validation set. The DCA curves in Figure 5a and 5b illustrate the net benefit of the predictive model over a range of threshold probabilities at different time points for the training and validation sets. These curves provide insights into the clinical usefulness and added value of the model compared to alternative decision strategies. Additionally, the DCA nomograms in Figure 5c and 5d provide a graphical representation of the decision curves, allowing for a more intuitive interpretation and application of the model’s results. Hb: hemoglobin; NYHA: New York Heart Association; eGFR: estimated glomerular filtration rate; PCI: percutaneous coronary intervention.

Figure 6. Nomogram for all-cause mortality risk prediction. The nomogram presents a visual tool for predicting the risk of all-cause mortality. It combines various predictors or risk factors into a comprehensive model that provides an individualized risk assessment. The nomogram allows for a simple and intuitive estimation of the probability of mortality based on the values assigned to each predictor. Clinicians can use this nomogram as a practical aid in risk assessment and shared decision-making with patients regarding appropriate interventions and management strategies. NYHA: New York Heart Association; eGFR: estimated glomerular filtration rate; PPCI: primary percutaneous coronary intervention.

Figure 7. Rationality analysis: Kaplan-Meier survival curves of high-score and low-score groups. (a) Rationality analysis for the training set. (b) Rationality analysis for the validation set. The Kaplan-Meier survival curves depicted in Figure 7a and 7b demonstrate the differences in survival outcomes between the high-score and low-score groups. These curves serve as a rationality analysis to evaluate the predictive performance of the scoring system or model. The separation of the survival curves indicates the ability of the scoring system to stratify patients into distinct risk groups. This analysis provides insights into the reliability and validity of the scoring system in predicting survival outcomes and aids in assessing its clinical utility.

**Table 1.** Baseline Characteristics of Patients With HFmrEF After Acute Myocardial Infarction in the Mortality Prognostic Model Development and Validation
	Training cohort (n = 611)	Validation cohort (n = 262)	P value
According to a 7:3 ratio, the population was randomly divided into a training cohort and a validation cohort. Categorical variables were presented as n (%). Values for continuous variables are given as means ± SD or medians with interquartile ranges. HFmrEF: heart failure with mildly reduced ejection fraction; NYHA: New York Heart Association; COPD: chronic obstructive pulmonary disease; ACEI: angiotensin-converting enzyme inhibitor; ARB: angiotensin receptor blocker; ARNI: angiotensin receptor-neprilysin inhibitor; SGLT2i: sodium–glucose cotransporter 2 inhibitors; NT-proBNP: N-terminal pro-brain natriuretic peptide; eGFR: estimated glomerular filtration rate; LVd: left ventricular end-diastolic diameter; RVd: right ventricular end-diastolic diameter; E/e’: early diastolic peak velocity/early diastolic peak velocity of the lateral or septal mitral annulus; PASP: pulmonary artery systolic pressure; SD: standard deviation.
Demographics
Age, years	69.0 (61.0; 77.0)	69.0 (61.0; 77.0)	0.734
Male, n (%)	434 (71.0%)	174 (66.4%)	0.201
Body mass index, kg/m²	24.4 (22.8; 30.0)	24.4 (22.9; 30.0)	0.988
NYHA III + IV, n (%)	324 (53.0%)	123 (46.9%)	0.116
Medical history, n (%)
Current smoker	221 (36.2%)	95 (36.3%)	1.000
Current drinker	53 (8.67%)	26 (9.92%)	0.645
Hypertension	432 (70.7%)	168 (64.1%)	0.065
Hyperlipidemia	126 (20.6%)	57 (21.8%)	0.775
Coronary heart disease	605 (99.0%)	261 (99.6%)	0.681
Atrial fibrillation	71 (11.6%)	28 (10.7%)	0.778
Stroke	77 (12.6%)	29 (11.1%)	0.601
COPD	66 (10.8%)	22 (8.40%)	0.338
Renal insufficiency	127 (20.8%)	42 (16.0%)	0.124
Diabetes	206 (33.7%)	96 (36.6%)	0.450
Serology
NT-proBNP/100, pg/mL	17.7 (4.50; 57.5)	21.1 (4.36; 63.3)	0.797
Hemoglobin, g/L	126 (112; 139)	130 (114; 142)	0.164
White blood cells, × 10⁹/L	8.33 (6.35; 10.8)	8.41 (6.42; 10.7)	0.959
Platelets, × 10⁹/L	187 (150; 227)	187 (148; 231)	0.908
Alanine aminotransferase, U/L	25.7 (14.9; 43.8)	26.9 (14.5; 46.9)	0.756
Aspartate aminotransferase, U/L	32.1 (20.1; 150)	36.2 (21.1; 134)	0.413
Creatine kinase-MB, U/L	24.5 (14.0; 88.2)	25.9 (14.8; 113)	0.550
Uric acid, µmol/L	340 (276; 416)	332 (264; 415)	0.378
eGFR, mL/min/1.73 m²	73.9 (51.0; 93.7)	73.7 (57.6; 93.2)	0.680
Sodium, mg/L	140 (137; 142)	140 (137; 141)	0.972
Potassium, mg/L	4.12 (3.80; 4.48)	4.08 (3.77; 4.40)	0.248
Low-density lipoprotein, mmol/L	2.42 (1.73; 3.13)	2.50 (1.78; 3.18)	0.280
Treatment, n (%)
PPCI	392 (64.2%)	173 (66.0%)	0.122
Beta-blocker	534 (87.4%)	235 (89.7%)	0.397
ACEI or ARB	498 (81.5%)	221 (84.4%)	0.361
ARNI	34 (5.56%)	12 (4.58%)	0.666
SGLT2i	2 (0.33%)	1 (0.38%)	1.000
Diuretics	319 (52.2%)	130 (49.6%)	0.530
Spironolactone	292 (47.8%)	124 (47.3%)	0.959
Echocardiography
Aortic size, mm	33.0 (31.0; 36.0)	33.5 (31.0; 36.0)	0.762
Left atrium size, mm	37.0 (34.0; 40.0)	37.0 (35.0; 40.0)	0.992
LVd, mm	51.0 (48.0; 55.0)	51.0 (47.0; 55.0)	0.160
Right atrium size, mm	35.0 (33.0; 38.0)	36.0 (34.0; 38.0)	0.023
RVd, mm	19.0 (17.0; 20.0)	19.0 (18.0; 20.0)	0.176
E/e’, cm/s	13.3 (9.80; 18.4)	13.7 (10.4; 18.0)	0.396
PASP, mm Hg	31.0 (18.0; 40.0)	31.0 (22.0; 39.8)	0.884
Clinical endpoints, n (%)
Death	128 (20.9%)	55 (21.0%)	1.000

Table 1. Baseline Characteristics of Patients With HFmrEF After Acute Myocardial Infarction in the Mortality Prognostic Model Development and Validation

Training cohort (n = 611)

Validation cohort (n = 262)

P value

According to a 7:3 ratio, the population was randomly divided into a training cohort and a validation cohort. Categorical variables were presented as n (%). Values for continuous variables are given as means ± SD or medians with interquartile ranges. HFmrEF: heart failure with mildly reduced ejection fraction; NYHA: New York Heart Association; COPD: chronic obstructive pulmonary disease; ACEI: angiotensin-converting enzyme inhibitor; ARB: angiotensin receptor blocker; ARNI: angiotensin receptor-neprilysin inhibitor; SGLT2i: sodium–glucose cotransporter 2 inhibitors; NT-proBNP: N-terminal pro-brain natriuretic peptide; eGFR: estimated glomerular filtration rate; LVd: left ventricular end-diastolic diameter; RVd: right ventricular end-diastolic diameter; E/e’: early diastolic peak velocity/early diastolic peak velocity of the lateral or septal mitral annulus; PASP: pulmonary artery systolic pressure; SD: standard deviation.

Demographics

Age, years

69.0 (61.0; 77.0)

0.734

Male, n (%)

434 (71.0%)

174 (66.4%)

0.201

Body mass index, kg/m²

24.4 (22.8; 30.0)

24.4 (22.9; 30.0)

0.988

NYHA III + IV, n (%)

324 (53.0%)

123 (46.9%)

0.116

Medical history, n (%)

Current smoker

221 (36.2%)

95 (36.3%)

1.000

Current drinker

53 (8.67%)

26 (9.92%)

0.645

Hypertension

432 (70.7%)

168 (64.1%)

0.065

Hyperlipidemia

126 (20.6%)

57 (21.8%)

0.775

Coronary heart disease

605 (99.0%)

261 (99.6%)

0.681

Atrial fibrillation

71 (11.6%)

28 (10.7%)

0.778

Stroke

77 (12.6%)

29 (11.1%)

0.601

COPD

66 (10.8%)

22 (8.40%)

0.338

Renal insufficiency

127 (20.8%)

42 (16.0%)

0.124

Diabetes

206 (33.7%)

96 (36.6%)

0.450

Serology

NT-proBNP/100, pg/mL

17.7 (4.50; 57.5)

21.1 (4.36; 63.3)

0.797

Hemoglobin, g/L

126 (112; 139)

130 (114; 142)

0.164

White blood cells, × 10⁹/L

8.33 (6.35; 10.8)

8.41 (6.42; 10.7)

0.959

Platelets, × 10⁹/L

187 (150; 227)

187 (148; 231)

0.908

Alanine aminotransferase, U/L

25.7 (14.9; 43.8)

26.9 (14.5; 46.9)

0.756

Aspartate aminotransferase, U/L

32.1 (20.1; 150)

36.2 (21.1; 134)

0.413

Creatine kinase-MB, U/L

24.5 (14.0; 88.2)

25.9 (14.8; 113)

0.550

Uric acid, µmol/L

340 (276; 416)

332 (264; 415)

0.378

eGFR, mL/min/1.73 m²

73.9 (51.0; 93.7)

73.7 (57.6; 93.2)

0.680

Sodium, mg/L

140 (137; 142)

140 (137; 141)

0.972

Potassium, mg/L

4.12 (3.80; 4.48)

4.08 (3.77; 4.40)

0.248

Low-density lipoprotein, mmol/L

2.42 (1.73; 3.13)

2.50 (1.78; 3.18)

0.280

Treatment, n (%)

PPCI

392 (64.2%)

173 (66.0%)

0.122

Beta-blocker

534 (87.4%)

235 (89.7%)

0.397

ACEI or ARB

498 (81.5%)

221 (84.4%)

0.361

ARNI

34 (5.56%)

12 (4.58%)

0.666

SGLT2i

2 (0.33%)

1 (0.38%)

1.000

Diuretics

319 (52.2%)

130 (49.6%)

0.530

Spironolactone

292 (47.8%)

124 (47.3%)

0.959

Echocardiography

Aortic size, mm

33.0 (31.0; 36.0)

33.5 (31.0; 36.0)

0.762

Left atrium size, mm

37.0 (34.0; 40.0)

37.0 (35.0; 40.0)

0.992

LVd, mm

51.0 (48.0; 55.0)

51.0 (47.0; 55.0)

0.160

Right atrium size, mm

35.0 (33.0; 38.0)

36.0 (34.0; 38.0)

0.023

RVd, mm

19.0 (17.0; 20.0)

19.0 (18.0; 20.0)

0.176

E/e’, cm/s

13.3 (9.80; 18.4)

13.7 (10.4; 18.0)

0.396

PASP, mm Hg

31.0 (18.0; 40.0)

31.0 (22.0; 39.8)

0.884

Clinical endpoints, n (%)

Death

128 (20.9%)

55 (21.0%)

1.000

**Table 2.** Univariate Cox Regression Analysis of Factors Associated With Mortality in Patients With HFmrEF After Acute Myocardial Infarction
characteristics	β	SE	HR	95% CI	Z score	P value
^aP < 0.05. HFmrEF: heart failure with mildly reduced ejection fraction; NYHA: New York Heart Association; COPD: chronic obstructive pulmonary disease; ACEI: angiotensin-converting enzyme inhibitors; ARB: angiotensin receptor blocker; ARNI: angiotensin receptor-neprilysin inhibitor; SGLT2i: sodium–glucose cotransporter 2 inhibitors; PPCI: primary percutaneous coronary intervention; NT-proBNP: N-terminal pro-brain natriuretic peptide; eGFR: estimated glomerular filtration rate; LVd: left ventricular end-diastolic diameter; RVd: right ventricular end-diastolic diameter; E/e’: early diastolic peak velocity/early diastolic peak velocity of the lateral or septal mitral annulus; PASP: pulmonary artery systolic pressure; SE: standard error; HR: hazard ratio; CI: confidence interval.
Age	0.077	0.009	1.08	1.061–1.1	8.297	< 0.001^a
Male vs. female	0.074	0.198	1.076	0.73–1.588	0.371	0.711
Body mass index	–0.004	0.022	0.996	0.954–1.041	–0.159	0.874
Current smoker	–0.263	0.191	0.769	0.529–1.117	–1.378	0.168
Current drinker	–0.234	0.329	0.791	0.415–1.51	–0.71	0.478
Diabetes	0.389	0.18	1.476	1.037–2.1	2.16	0.031^a
Renal insufficiency	1.05	0.183	2.857	1.995–4.09	5.731	< 0.001^a
COPD	0.804	0.223	2.236	1.443–3.463	3.603	< 0.001^a
Stroke	1.032	0.202	2.808	1.888–4.175	5.1	< 0.001^a
Atrial fibrillation	0.684	0.227	1.982	1.27–3.092	3.015	0.003^a
Hyperlipidemia	–0.617	0.261	0.539	0.324–0.899	–2.369	0.018^a
Hypertension	0.782	0.234	2.187	1.381–3.462	3.338	0.001^a
NYHA III + IV vs. NYHA II	1.006	0.202	2.735	1.84–4.065	4.974	< 0.001^a
Low-density lipoprotein	–0.153	0.095	0.858	0.713–1.034	–1.608	0.108
Sodium	0.05	0.152	1.052	0.781–1.416	0.332	0.74
Potassium	0.013	0.025	1.013	0.966–1.063	0.533	0.594
eGFR	–0.026	0.003	0.974	0.968–0.98	–8.33	< 0.001^a
Uric acid	0.002	0.001	1.002	1.001–1.004	3.277	0.001^a
Creatine kinase-MB	–0.003	0.001	0.997	0.995–0.999	–3.038	0.002^a
Alanine aminotransferase	–0.002	0.001	0.998	0.996–0.999	–2.716	0.007^a
Aspartate aminotransferase	–0.011	0.004	0.99	0.982–0.997	–2.642	0.008^a
White blood cells	–0.056	0.027	0.946	0.897–0.997	–2.063	0.039^a
Hemoglobin	–0.032	0.004	0.969	0.962–0.976	–8.512	< 0.001^a
NT-proBNP/100	0.005	0.001	1.005	1.003–1.006	5.919	< 0.001^a
PASP	0.01	0.002	1.01	1.007–1.013	5.826	< 0.001^a
E/e’	0.052	0.011	1.053	1.03–1.077	4.562	< 0.001^a
RVd	0.028	0.022	1.028	0.985–1.073	1.282	0.2
Right atrium size	0.029	0.017	1.029	0.996–1.063	1.739	0.082
LVd	0.041	0.014	1.042	1.013–1.072	2.887	0.004^a
Left atrium size	0.076	0.015	1.079	1.048–1.111	5.121	< 0.001^a
Aortic size	0.047	0.024	1.048	1–1.098	1.973	0.049^a
PPCI	–1.039	0.18	0.354	0.249–0.504	–5.772	< 0.001^a
Diuretics	0.262	0.179	1.3	0.915–1.847	1.464	0.143
ARNI	0.343	0.423	1.409	0.616–3.226	0.812	0.417
ACEI or ARB	–1.032	0.191	0.356	0.245–0.518	–5.402	< 0.001^a
Spironolactone	–0.141	0.178	0.868	0.613–1.229	–0.797	0.426
Beta-blocker	–0.913	0.209	0.401	0.266–0.604 –	–4.37	< 0.001^a

Table 2. Univariate Cox Regression Analysis of Factors Associated With Mortality in Patients With HFmrEF After Acute Myocardial Infarction

characteristics

95% CI

Z score

P value

^aP < 0.05. HFmrEF: heart failure with mildly reduced ejection fraction; NYHA: New York Heart Association; COPD: chronic obstructive pulmonary disease; ACEI: angiotensin-converting enzyme inhibitors; ARB: angiotensin receptor blocker; ARNI: angiotensin receptor-neprilysin inhibitor; SGLT2i: sodium–glucose cotransporter 2 inhibitors; PPCI: primary percutaneous coronary intervention; NT-proBNP: N-terminal pro-brain natriuretic peptide; eGFR: estimated glomerular filtration rate; LVd: left ventricular end-diastolic diameter; RVd: right ventricular end-diastolic diameter; E/e’: early diastolic peak velocity/early diastolic peak velocity of the lateral or septal mitral annulus; PASP: pulmonary artery systolic pressure; SE: standard error; HR: hazard ratio; CI: confidence interval.

Age

0.077

0.009

1.08

1.061–1.1

8.297

< 0.001^a

Male vs. female

0.074

0.198

1.076

0.73–1.588

0.371

0.711

Body mass index

–0.004

0.022

0.996

0.954–1.041

–0.159

0.874

Current smoker

–0.263

0.191

0.769

0.529–1.117

–1.378

0.168

Current drinker

–0.234

0.329

0.791

0.415–1.51

–0.71

0.478

Diabetes

0.389

0.18

1.476

1.037–2.1

2.16

0.031^a

Renal insufficiency

1.05

0.183

2.857

1.995–4.09

5.731

< 0.001^a

COPD

0.804

0.223

2.236

1.443–3.463

3.603

< 0.001^a

Stroke

1.032

0.202

2.808

1.888–4.175

5.1

< 0.001^a

Atrial fibrillation

0.684

0.227

1.982

1.27–3.092

3.015

0.003^a

Hyperlipidemia

–0.617

0.261

0.539

0.324–0.899

–2.369

0.018^a

Hypertension

0.782

0.234

2.187

1.381–3.462

3.338

0.001^a

NYHA III + IV vs. NYHA II

1.006

0.202

2.735

1.84–4.065

4.974

< 0.001^a

Low-density lipoprotein

–0.153

0.095

0.858

0.713–1.034

–1.608

0.108

Sodium

0.05

0.152

1.052

0.781–1.416

0.332

0.74

Potassium

0.013

0.025

1.013

0.966–1.063

0.533

0.594

eGFR

–0.026

0.003

0.974

0.968–0.98

–8.33

< 0.001^a

Uric acid

0.002

0.001

1.002

1.001–1.004

3.277

0.001^a

Creatine kinase-MB

–0.003

0.001

0.997

0.995–0.999

–3.038

0.002^a

Alanine aminotransferase

–0.002

0.001

0.998

0.996–0.999

–2.716

0.007^a

Aspartate aminotransferase

–0.011

0.004

0.99

0.982–0.997

–2.642

0.008^a

White blood cells

–0.056

0.027

0.946

0.897–0.997

–2.063

0.039^a

Hemoglobin

–0.032

0.004

0.969

0.962–0.976

–8.512

< 0.001^a

NT-proBNP/100

0.005

0.001

1.005

1.003–1.006

5.919

< 0.001^a

PASP

0.01

0.002

1.01

1.007–1.013

5.826

< 0.001^a

E/e’

0.052

0.011

1.053

1.03–1.077

4.562

< 0.001^a

RVd

0.028

0.022

1.028

0.985–1.073

1.282

0.2

Right atrium size

0.029

0.017

1.029

0.996–1.063

1.739

0.082

LVd

0.041

0.014

1.042

1.013–1.072

2.887

0.004^a

Left atrium size

0.076

0.015

1.079

1.048–1.111

5.121

< 0.001^a

Aortic size

0.047

0.024

1.048

1–1.098

1.973

0.049^a

PPCI

–1.039

0.18

0.354

0.249–0.504

–5.772

< 0.001^a

Diuretics

0.262

0.179

1.3

0.915–1.847

1.464

0.143

ARNI

0.343

0.423

1.409

0.616–3.226

0.812

0.417

ACEI or ARB

–1.032

0.191

0.356

0.245–0.518

–5.402

< 0.001^a

Spironolactone

–0.141

0.178

0.868

0.613–1.229

–0.797

0.426

Beta-blocker

–0.913

0.209

0.401

0.266–0.604 –

–4.37

< 0.001^a

**Table 3.** Multivariable Cox Regression Analysis of Factors Associated With Mortality in HFmrEF Patients
Characteristics	β	SE	HR	95% CI	Z score	P value
^aP < 0.05. HFmrEF: heart failure with mildly reduced ejection fraction; eGFR: estimated glomerular filtration rate; PPCI: primary percutaneous coronary intervention; NYHA: New York Heart Association; SE: standard error; HR: hazard ratio; CI: confidence interval.
Age	0.052	0.009	1.053	1.034–1.073	5.555	< 0.001^a
Hemoglobin	–0.016	0.005	0.984	0.975–0.993	–3.42	0.001^a
eGFR	–0.012	0.004	0.988	0.981–0.996	–2.98	0.003^a
PPCI	–0.594	0.187	0.552	0.383–0.797	–3.176	0.001^a
Stroke	0.525	0.205	1.69	1.13–2.528	2.556	0.011^a
NYHA III + IV vs. NYHA II	0.514	0.209	1.673	1.111–2.519	2.462	0.014^a

Table 3. Multivariable Cox Regression Analysis of Factors Associated With Mortality in HFmrEF Patients

Characteristics

95% CI

Z score

P value

^aP < 0.05. HFmrEF: heart failure with mildly reduced ejection fraction; eGFR: estimated glomerular filtration rate; PPCI: primary percutaneous coronary intervention; NYHA: New York Heart Association; SE: standard error; HR: hazard ratio; CI: confidence interval.

Age

0.052

0.009

1.053

1.034–1.073

5.555

< 0.001^a

Hemoglobin

–0.016

0.005

0.984

0.975–0.993

–3.42

0.001^a

eGFR

–0.012

0.004

0.988

0.981–0.996

–2.98

0.003^a

PPCI

–0.594

0.187

0.552

0.383–0.797

–3.176

0.001^a

Stroke

0.525

0.205

1.69

1.13–2.528

2.556

0.011^a

NYHA III + IV vs. NYHA II

0.514

0.209

1.673

1.111–2.519

2.462

0.014^a