Easy D_AO₂ index: a novel hemodynamic risk factor for predicting mortality in surgical and critically ill patients

Abstract

Background

Measurement of the arterial oxygen delivery index (D_AO₂I) requires substantial medical resources and invasive procedures. We proposed a novel hemodynamic parameter reflecting D_AO₂I, the Easy D_AO₂ index (EDI), and examined its association with mortality in non-cardiac surgical and critically ill patients.

Methods

We retrospectively analyzed the data of 95 115 surgical cases from an Asian hospital and 90 420 intensive care unit (ICU) admissions from multicenter hospitals in the United States. EDI was the product of pulse pressure, heart rate, hemoglobin, and peripheral oxygen saturation, divided by body surface area, measured every 5 minutes during anesthesia and hourly for 24 hours post-ICU admission. We assessed the association between 7-day in-hospital mortality and duration of exposure to EDI values below the fifth percentile levels.

Results

In non-cardiac surgical patients, mortality risk increased with duration of exposure below the low EDI threshold (adjusted odds ratio [aOR] 1.003 per minute; 95% CI [1.000–1.005]). In critically ill patients, mortality risk increased with duration of exposure below the low EDI threshold (aOR 1.014 per hour; 95% CI [1.004–1.023]).

Conclusions

Low EDI values were independently associated with mortality in non-cardiac surgical and critically ill patients, suggesting that EDI may be a useful hemodynamic parameter for risk assessment.

Introduction

Comprehensive hemodynamic monitoring requires flow and pressure parameters to ensure adequate tissue perfusion [1]. The arterial oxygen delivery index (D_AO₂I) provides crucial information about tissue oxygenation and flow status in surgical and critically ill patients, with inadequate delivery being associated with various adverse outcomes. However, routine monitoring faces significant challenges in clinical practice. The gold standard for measuring cardiac output (CO) involves the use of a pulmonary artery catheter, which risks complications such as arrhythmias, pulmonary artery rupture, and infections [2]. These challenges are particularly pronounced in low-income countries, where the burden of critical illness is high and access to advanced monitoring devices and specially trained healthcare providers is limited.

Mean arterial pressure (MAP) has been widely adopted as a hemodynamic parameter, regardless of resource availability in clinical settings. However, blood pressure alone is an unreliable parameter of tissue perfusion. Uncompensated hypotension can disrupt blood flow to end organs and lead to adverse outcomes [3–7]; however, normal blood pressure does not guarantee adequate tissue oxygenation. Hypotension may not indicate tissue hypoxemia if autoregulation is intact [8], and low CO can occur despite normal blood pressure [9].

To address this clinical need for a reliable yet accessible hemodynamic flow monitoring parameter that can be used alongside MAP, we propose the Easy D_AO₂ index (EDI) as a potential surrogate for D_AO₂I. Using EDI, D_AO₂I can be easily estimated even in resource-constrained environments. The EDI is based on the principle that CO is proportional to pulse pressure and heart rate, which can be routinely measured [10]. We hypothesized that lower EDI values would be associated with increased mortality, and that EDI might provide additional prognostic information complementary to conventional blood pressure monitoring. To test this hypothesis, we examined the association of EDI with 7-day in-hospital mortality in two large cohorts: a surgical cohort of 95 115 surgical cases from a single academic hospital in South Korea and a multicenter intensive care unit (ICU) cohort of 90 420 ICU admissions from the United States.

Materials and Methods

Patient population and data collection

This single-center retrospective study was approved by the Institutional Review Board (IRB No. H-2409-038-1569). The requirement for written informed consent was waived due to the retrospective nature of this study. Data were collected from patients who underwent surgery under general anesthesia at Seoul National University Hospital, Seoul, Republic of Korea, from January 2011 to December 2020. We excluded patients < 18 or > 90 years of age, those classified under the American Society of Anesthesiologists Physical Status Classification 6, and those with an anesthesia duration of < 2 hours. Vital signs measured at 1-minute intervals during surgery were extracted from the clinical data warehouse of Seoul National University Hospital. However, we used the 5-minute median of the measured values. In addition, we excluded patients without preoperative hemoglobin (Hb) measurements within 7 days before surgery, those without body surface area data, those with >30% missing intraoperative vital signs, and those who underwent cardiac surgery due to the different meanings of pulse pressure during cardiopulmonary bypass.

For critically ill patients, we used data from the electronic ICU (eICU) Collaborative Research Database [11], a multicenter database containing information on 139 367 patients admitted to 208 ICUs across the United States from 2014 to 2015. We considered only the first ICU admission for each patient, excluding admissions of patients discharged within 24 hours. We excluded patients whose vital signs were not recorded within the first 4 hours of admission, those with > 30% missing vital sign data in the first 24 hours, and those without Hb measurements or insufficient data to calculate body surface area.

EDI measurements and data preprocessing

EDI was designed as a non-invasive surrogate for D_AO₂I. D_AO₂I is calculated as follows:

$$D_A{O}_{2}I=CI\times Ca{O}_2\times 10$$ (1)

where CI is a cardiac index (L/min/m²). Arterial oxygen content (CaO₂) is calculated using arterial oxygen saturation (SaO₂, %) and partial pressure of oxygen in arterial blood (PaO₂, mmHg). Total CaO₂, which represents the sum of oxygen bound to Hb and oxygen dissolved in plasma, is calculated as follows:

$$Ca{O}_2=(1.34\times Hb\times \frac{Sa{O}_2}{100})+(0.003\times Pa{O}_2)$$ (2)

EDI was calculated as the product of pulse pressure (mmHg), heart rate (beats/min), Hb (g/dL), and peripheral oxygen saturation (SpO₂, %), multiplied by a unit conversion constant (k) to yield a dimensionless index, divided by body surface area (m²) as follows:

$$\mathrm{EDI}=\frac{\mathrm{Pulse} \mathrm{Pressure} \left(mmHg\right)\times \mathrm{Heart} \mathrm{Rate} \left(mi{n}^{-1}\right)\times \mathrm{Hb} (\mathrm{g}/\mathrm{dL})\times {\mathrm{SpO}}_2}{\mathrm{Body} \mathrm{Surface} \mathrm{Area} \left(m^2\right)}\times \mathrm{\kappa }$$ (3)

EDI approximates oxygen delivery by substituting pulse pressure × heart rate for CO and SpO₂ for SaO₂, while omitting the dissolved oxygen term, which minimally contributes to total oxygen content.

We applied the following exclusion criteria, similar to those used in previous intraoperative studies, to remove physiological artifacts [4,12,13]: (1) MAP < 20 or > 200 mmHg, (2) systolic blood pressure < 10 or > 300 mmHg, (3) diastolic blood pressure < 10 or > 200 mmHg, (4) heart rate < 30 beats/min, or (5) pulse pressure < 10 mmHg.

For surgical patients, we considered only Hb values measured within 7 days before the start of anesthesia. If hematocrit (Hct) or Hb levels were measured during anesthesia, these values were carried forward. We analyzed the EDI for surgical patients during anesthesia, calculating it at 5-minute intervals.

For critically ill patients, the most recent Hb or Hct was carried forward for EDI calculation. We analyzed the EDI within the first 24 hours following ICU admission, calculating it at 1-hour intervals.

For surgical and critically ill patients, we used the formula Hb ≈ Hct/3 to approximate Hb and all available measurements, including those from point-of-care testing. Non-invasive and invasive blood pressure measurements were used in the analysis. The average rate of missing vital signs was 3.6% for 5-minute interval data in surgical patients and 4.8% for hourly data in critically ill patients. For these missing vital signs, we employed forward-fill imputation.

Primary outcome

We analyzed in-hospital all-cause mortality within 7 days for surgical and critically ill patients. For surgical patients, mortality was assessed from the end of anesthesia. For critically ill patients, mortality was defined as an all-cause death occurring within 7 days of ICU admission.

Univariable logistic regression was employed to assess the crude relationship between mortality and the duration of exposure time to below specific EDI or MAP thresholds, as well as potential confounding variables. For surgical patients, we analyzed exposure time during the entire period of general anesthesia. For critically ill patients, we examined this relationship using EDI and MAP exposure time during the first 24 hours following ICU admission. For the primary analysis, we defined the values corresponding to the fifth percentiles as “low EDI” and 65 mmHg as the “low MAP” threshold based on established clinical criteria [4,6].

We then performed multivariable logistic regression analyses to obtain adjusted odds ratios (aORs), controlling for confounding variables, including the Acute Physiology and Chronic Health Evaluation IV score, to adjust for disease severity [14]. Variables with P < 0.2 in the univariable analysis, those with clinical importance, and variance inflation factor < 10 were initially included in the model. Subsequently, a backward elimination procedure was applied to determine the final multivariable model.

For surgical patients, the odds ratio (OR) unit was per minute of exposure during general anesthesia, whereas for critically ill patients, it was per hour of exposure during the first 24 hours after ICU admission.

To evaluate the discriminative performance of hemodynamic exposure variables for mortality prediction, we performed receiver operating characteristic (ROC) curve analysis. We calculated the area under the receiver operating characteristic curve (AUROC) for univariable models using low EDI and MAP exposures and the multivariable model incorporating confounders.

A subgroup analysis was conducted for patients with non-invasive blood pressure (NIBP). A supplementary quadrant analysis classified hemodynamic exposure into four mutually exclusive states based on the defined low thresholds: preserved EDI with preserved MAP (reference), low EDI with preserved MAP, low MAP with preserved EDI, and concurrent low EDI and low MAP. Associations with mortality were assessed, adjusting for the same covariates included in the primary multivariable model. To further evaluate whether EDI provides prognostic value independent of MAP, a direct comparison of mortality risk was performed between patients with concurrent low EDI and MAP and those with preserved EDI and low MAP, using the latter as the reference group and adjusting for the same covariates.

Secondary outcome

The secondary outcome of this study was the correlation between EDI and the invasively measured D_AO₂I. The relationship between MAP and D_AO₂I was also evaluated for comparison. Since the invasively measured D_AO₂I requires CO measurement, we analyzed data from patients with pulmonary artery catheters using continuous thermodilution methods. Given the inherent measurement delay in continuous thermodilution, we only included measurements where the CO changed by < 10% within 20 minutes before and after each time point. Per-patient Spearman’s rank correlation coefficient was calculated between D_AO₂I and EDI and between D_AO₂I and MAP. We included patients with ≥ 10 measurement pairs in the analysis.

Statistical analysis

Statistical comparisons were performed using independent t-tests or Mann–Whitney U tests for continuous variables, while categorical variables were analyzed with chi-square tests.

For primary outcome analysis, the significance of individual coefficients was tested using the Wald test, and the overall model fit was assessed using the likelihood ratio test.

For secondary outcome analysis, Spearman’s rank correlation coefficients were calculated and compared using the Wilcoxon signed-rank test. To quantify the magnitude of the difference, we calculated the mean difference and effect size using Cohen’s d for paired samples. All statistical analyses were performed using Python version 3.10.9 with SciPy package version 1.14.1 and Statsmodels package version 0.14.3 [15]. P < 0.05 was considered statistically significant for all analyses.

Results

Overall, the data of 95 115 surgical cases under general anesthesia and 90 420 ICU admissions were analyzed in this study (Fig. 1). Tables 1 and 2 show the baseline characteristics of surgical and critically ill patients, respectively.

Fig. 1.

Flow diagram describing the retrospective design. (A) Patient selection flow chart for surgical patients. (B) Patient selection flow chart for critically ill patients. CO: cardiac output, D_AO₂I: arterial oxygen delivery index, ICU: intensive care unit.

Table 1.

Baseline Characteristics of the Surgical Patient Cohort

Characteristic	Mortality (n = 200)	Survivors (n = 94 915)	P value
Female	76 (38.0)	48 038 (50.6)	< 0.001
	61.9 ± 15.3	55.6 ± 15.4	< 0.001
Surgical characteristics
Anesthesia duration (min)	248 ± 116	239 ± 113	0.264
Emergency	142 (71.0)	9639 (10.2)	< 0.001
ASA-PS
N/A	41 (21)	2736 (3)	< 0.001
1	13 (6.5)	28 967 (30.5)	< 0.001
2	52 (26.0)	53 501 (56.4)	< 0.001
3	62 (31.0)	9136 (9.6)	< 0.001
4	25 (12.5)	526 (0.6)	< 0.001
5	7 (3.5)	49 (0.1)	< 0.001
Department of surgery
General surgery	94 (47.0)	30 967 (32.6)	< 0.001
Neurosurgery	50 (25.0)	14 401 (15.2)	< 0.001
Thoracic surgery	23 (11.5)	9004 (9.5)	0.395
Urologic surgery	10 (5.0)	9375 (9.9)	0.028
Otolaryngologic surgery	9 (4.5)	5425 (5.7)	0.557
Orthopedic surgery	8 (4.0)	11 122 (11.7)	0.001
Obstetrics and gynecologic surgery	3 (1.5)	9030 (9.5)	< 0.001
Plastic surgery	2 (1.0)	4142 (4.4)	0.031
Other	1 (0.5)	1449 (1.5)	0.371
Comorbidities
Solid tumor	71 (35.5)	39 501 (41.6)	0.093
Ischemic heart disease	22 (11.0)	2709 (2.9)	< 0.001
Diabetes mellitus	19 (9.5)	5045 (5.3)	0.013
Chronic kidney disease	19 (9.5)	2501 (2.6)	< 0.001
Hypertension	18 (9.0)	5419 (5.7)	0.064
Cerebrovascular disease	15 (7.5)	2369 (2.5)	< 0.001
Peripheral vascular disease	9 (4.5)	920 (1.0)	< 0.001
Hematologic malignancy	6 (3.0)	538 (0.6)	< 0.001
Heart failure	6 (3.0)	287 (0.3)	< 0.001
Chronic obstructive lung disease	3 (1.5)	888 (0.9)	0.645
Asthma	0 (0.0)	752 (0.8)	0.387

Values are presented as number (%) or mean ± SD. ASA-PS: American Society of Anesthesiologists physical status.

Table 2.

Baseline Characteristics of the Critically Ill Patient Cohort

Characteristic	Mortality (n = 3552)	Survivors (n = 86 868)	P value
Female	1603 (45)	39 023 (44)	0.720
Age (yr)	66.7 ± 14.9	63.1 ± 15.8	< 0.001
APACHE IV Score	92.3 ± 33.3	56.4 ± 22.2	< 0.001
Ethnicity
Caucasian	2797 (79)	66 453 (77)	0.002
African American	333 (9)	9741 (11)	< 0.001
Hispanic	106 (3)	3352 (4)	0.009
Asian	65 (2)	1532 (2)	0.819
Native American	32 (1)	591 (0.7)	0.146
Unknown	177 (5)	4274 (5)	0.896
ICU type
Cardiac ICU	786 (22)	20 361 (23)	0.074
Surgical ICU	197 (6)	5907 (7)	0.004
Medical ICU	364 (10)	7652 (9)	0.003
Neurological ICU	215 (6)	7085 (8)	< 0.001
General ICU	1990 (56)	45 863 (53)	< 0.001
Comorbidities
Hypertension	1848 (52)	45 492 (52)	0.702
Diabetes	1066 (30)	26 746 (31)	0.334
Atrial fibrillation	493 (14)	10 137 (12)	< 0.001
Peptic ulcer disease	87 (2)	2282 (3)	0.551
Oncology	748 (21)	13 418 (15)	< 0.001
Peripheral vascular disease	207 (6)	4256 (5)	0.014
Asthma	209 (6)	6166 (7)	0.006
Hypothyroidism	324 (9)	7731 (9)	0.671
Congestive heart failure	693 (20)	13 537 (16)	< 0.001
Myocardial infarction	336 (10)	8452 (10)	0.614
COPD	666 (19)	13 680 (16)	< 0.001
DVT	151 (4)	3256 (4)	0.134
Angina	66 (2)	2648 (3)	< 0.001
Procedural coronary intervention	251 (7)	6088 (7)	0.921
Stroke	351 (10)	7576 (9)	0.018
Valve disease	188 (5)	4651 (5)	0.904
Renal insufficiency	310 (9)	6147 (7)	< 0.001
Cirrhosis	209 (6)	2704 (3)	< 0.001
Seizure	182 (5)	4787 (6)	0.340
Restrictive disease	65 (2)	674 (1)	< 0.001
AIDS	13 (0.4)	124 (0.1)	0.002
Home oxygen	148 (4)	3021 (3)	0.028
Renal failure	325 (9)	5641 (6)	< 0.001
Respiratory failure	80 (2)	1639 (2)	0.122
CABG	273 (8)	5190 (6)	< 0.001
Pulmonary embolism	77 (2)	1604 (2)	0.171
Pacemaker	151 (4)	2734 (3)	< 0.001
SLE	20 (0.6)	415 (0.5)	0.536
Immunosuppression	52 (2)	956 (1)	0.048
Rheumatoid arthritis	62 (2)	1523 (2)	1.000

Values are presented as number (%) or mean ± SD. APACHE IV Score: Acute Physiology and Chronic Health Evaluation IV score, ICU: intensive care unit, COPD: chronic obstructive pulmonary disorder, DVT: deep vein thrombosis, AIDS: acquired immune deficiency syndrome, CABG: coronary artery bypass graft surgery, SLE: systemic lupus erythematosus.

Among surgical patients, we observed 200 cases of 7-day in-hospital all-cause mortality. Among critically ill patients, we observed 3552 cases of 7-day in-hospital all-cause mortality.

Mortality prediction in surgical patients

Univariable analysis identified clinically significant predictors and hemodynamic exposures associated with mortality in surgical patients, as presented in Table 3. Among clinical variables, age, emergency operation status, ischemic heart disease, cerebrovascular accident, chronic kidney disease, hematologic malignancy, and neurosurgery were associated with increased mortality. Anesthesia duration was included in the analysis to control for differential exposure opportunities to low hemodynamic thresholds.

Table 3.

Univariable and Multivariable Analysis of Mortality in Surgical Patients

Variable	Univariable Analysis		Multivariable Analysis
	OR (95% CI)	P value	aOR (95% CI)	P value
Age (yr)	1.032 (1.022–1.042)	< 0.001	1.023 (1.013–1.034)	< 0.001
Emergency operation	21.207 (15.723–28.604)	< 0.001	15.367 (11.268–20.955)	< 0.001
Anesthesia duration (min)	1.001 (1.000–1.002)	0.253	0.997 (0.995–0.999)	< 0.001
Ischemic heart disease	4.217 (2.730–6.515)	< 0.001	2.385 (1.493–3.809)	< 0.001
Cerebrovascular disease	3.272 (1.962–5.457)	< 0.001	1.838 (1.071–3.155)	0.027
Chronic kidney disease	4.172 (2.653–6.561)	< 0.001	1.681 (1.036–2.730)	0.036
Hematologic malignancy	5.159 (2.281–11.667)	< 0.001	2.482 (1.046–5.887)	0.039
Neurosurgery	1.951 (1.428–2.667)	< 0.001	1.456 (1.047–2.025)	0.026
Orthopedic surgery	0.301 (0.148–0.610)	< 0.001	0.349 (0.170–0.715)	0.004
Hemodynamic Threshold Exposures
Time under low EDI (min)	1.007 (1.005–1.009)	< 0.001	1.003 (1.000–1.005)	0.042
Time under low MAP (min)	1.009 (1.008–1.010)	< 0.001	1.010 (1.008–1.012)	< 0.001

Values are presented as odds ratio (95% CI). OR: odds ratio, aOR: adjusted odds ratio, EDI: Easy D_AO₂ index, MAP: mean arterial pressure.

In the univariable analysis, mortality risk increased with each additional minute of exposure duration below the low EDI (13.4 × 10⁵) and low MAP thresholds.

After adjusting for clinical confounders including comorbidities and surgical departments in non-cardiac surgical patients, the aOR per minute of exposure below the low EDI threshold was 1.003 ((95% CI [1.000–1.005], P = 0.042). The aOR per minute of exposure below the low MAP threshold was 1.010 (95% CI [1.008–1.012], P < 0.001).

In the subgroup analysis for patients with NIBP only (n = 39 693), 7-day mortality was observed in 26 patients (0.07%) (Supplementary Table 1). In the quadrant analysis, the concurrent presence of low EDI and MAP was associated with the highest mortality risk, with an aOR of 1.012 (95% CI [1.008–1.015], P < 0.001) (Supplementary Table 2). Within the low MAP subgroup, patients with concurrent low EDI had significantly higher mortality compared to those with preserved EDI, with an aOR of 1.46 (95% CI [1.09–1.94], P = 0.011) (Supplementary Table 3).

In the ROC curve analysis, low EDI and MAP exposure durations showed AUROCs of 0.581 and 0.773, respectively. The multivariable model showed an AUROC of 0.882 for predicting mortality.

Mortality prediction in critically ill patients

In the univariable analysis, mortality risk increased with each additional hour of exposure duration below the low EDI (12.0 × 10⁵) and low MAP thresholds (Table 4).

Table 4.

Univariable and Multivariable Analysis of Mortality in Critically Ill Patients

Variable	Univariable Analysis		Multivariable Analysis
	OR (95% CI)	P value	aOR (95% CI)	P value
APACHE IV Score	1.044 (1.043–1.045)	< 0.001	1.043 (1.042–1.044)	< 0.001
Oncology	1.460 (1.344–1.586)	< 0.001	1.273 (1.164–1.392)	< 0.001
Restrictive disease	2.384 (1.844–3.082)	< 0.001	2.417 (1.824–3.203)	< 0.001
Angina	0.602 (0.471–0.771)	< 0.001	0.626 (0.483–0.810)	< 0.001
Congestive heart failure	1.313 (1.218–1.442)	< 0.001	1.082 (0.985–1.188)	0.108
Renal insufficiency	1.259 (1.118–1.419)	< 0.001	0.849 (0.745–0.967)	0.014
Pacemaker	1.369 (1.158–1.620)	< 0.001	1.224 (1.019–1.469)	0.030
Hemodynamic Threshold Exposures
Time under low EDI (h)	1.042 (1.034–1.051)	< 0.001	1.014 (1.004–1.023)	0.004
Time under low MAP (h)	1.074 (1.068–1.079)	< 0.001	1.038 (1.032–1.044)	< 0.001

Values are presented as odds ratio (95% confidence interval). OR: odds ratio, aOR: adjusted odds ratio, EDI: Easy D_AO₂ index, APACHE IV Score: Acute Physiology and Chronic Health Evaluation IV Score, MAP: mean arterial pressure.

After adjusting for clinical confounders in critically ill patients, the aOR per hour of exposure below the low EDI threshold was 1.014 (95% CI [1.004–1.023], P = 0.004). The aOR per hour of exposure below the low MAP threshold was 1.038 (95% CI [1.032–1.044], P < 0.001).

In the subgroup analysis for patients with NIBP only (n = 62 269), 1598 deaths were observed (Supplementary Table 1). In the quadrant analysis, the concurrent presence of low EDI and MAP was associated with the highest mortality risk, with an aOR of 1.072 (95% CI [1.052–1.092], P < 0.001) (Supplementary Table 2). Within the low MAP subgroup, patients with concurrent low EDI had significantly higher mortality compared to those with preserved EDI, with an aOR of 1.42 (95% CI [1.29–1.57], P < 0.001) (Supplementary Table 3).

In the ROC curve analysis, low EDI and MAP exposure durations showed AUROCs of 0.529 and 0.620, respectively. The multivariable model showed an AUROC of 0.825 for predicting mortality.

Correlation analysis

The correlation analysis between EDI and D_AO₂I included 86 surgical patients (Supplementary Table 4). EDI was moderately positively correlated with D_AO₂I, with a median (Q1, Q3) per-patient Spearman’s rank correlation coefficient of 0.62 (0.40, 0.77). Conversely, the association between MAP and D_AO₂I was weaker, yielding a median correlation of 0.19 (−0.11, 0.44) (Fig. 2). Compared to MAP, EDI was significantly more strongly correlated with D_AO₂I, with a mean difference in Spearman’s rank correlation coefficients of 0.38 and a large effect size (Cohen’s d = 0.93, P < 0.001).

Fig. 2.

Comparative analysis of EDI–D_AO₂I and MAP–D_AO₂I correlations. Boxplots illustrate the per-patient Spearman's rank correlation coefficient distributions across surgical patients (n = 86). (A) Distribution of per-patient correlation coefficients between EDI and D_AO₂I. (B) Distribution of per-patient correlation coefficients between MAP and D_AO₂I. In both panels, the central line within each box indicates the median correlation coefficient, while the box spans the interquartile range (IQR), from the first quartile (Q1) to the third quartile (Q3). The whiskers reach the maximum and minimum values that are within 1.5 times the IQR beyond the box boundaries. Data points outside this range are treated as outliers and represented as individual dots. D_AO₂I: arterial oxygen delivery index; EDI: Easy D_AO₂ index; MAP: mean arterial pressure.

Supplementary Figs. 1 and 2 show the overall scatter plot of D_AO₂I vs. EDI across all measurements and representative individual patient scatter plots, including examples from patients with the highest and lowest correlation coefficients, respectively. 

Discussion

In this study, we introduced EDI as a novel hemodynamic monitoring parameter and observed that EDI and MAP were independently associated with mortality in non-cardiac surgical and critically ill patients. In our primary analysis, prolonged exposure below the low EDI threshold was associated with increased mortality risk. In our secondary analysis, compared to MAP, EDI was moderately but significantly strongly correlated with invasively measured D_AO₂I (median r = 0.62 vs. 0.19), supporting its potential as a monitoring tool for oxygen delivery assessment. In resource-limited settings, EDI can serve as an effective indicator in several ways: it can be calculated using readily available clinical parameters without any patented algorithms, requires no additional equipment beyond standard hospital monitoring, and does not necessitate specialized training or skills for implementation.

The importance of oxygen delivery in surgical and critically ill patients has been recognized for a long time [16–18]. However, measuring D_AO₂I requires pulmonary artery catheter insertion, which is only feasible in a limited patient population [19], preventing large-scale cohort studies on the relationships between oxygen delivery and mortality. In this context, our findings showed that prolonged exposure to low EDI values was associated with increased mortality in surgical and critically ill patients. These findings align with previous studies showing adverse outcomes with inadequate oxygen delivery [20–22]. In our multivariable analysis, low EDI and MAP exposures were independently associated with mortality when analyzed together. This finding suggests that flow-related (EDI) and pressure-related (MAP) parameters may provide complementary prognostic information in hemodynamic monitoring. These independent associations remained significant after adjustment for surgical department, comorbidities, and disease severity, with these clinical factors explaining the sex differences observed in the univariable analysis. Furthermore, within the low MAP subgroup, concurrent low EDI was independently associated with significantly higher mortality than preserved EDI in the cohorts, suggesting that EDI may offer incremental prognostic information even in the setting of established hemodynamic compromise. Given that normal blood pressure alone does not guarantee adequate organ perfusion [8,23] and prior studies have demonstrated the particularly high risk associated with concurrent hypotension and hypoperfusion, concurrent monitoring of EDI and MAP may contribute to tissue perfusion risk assessment [24], with EDI potentially providing additional information that blood pressure monitoring alone may not capture.

Strengths of this study include its large sample size, diverse populations, and novel parameter integration; however, this study has some limitations. First, as a retrospective observational study involving surgical and critically ill patient cohorts, our findings showed associations between EDI exposure and mortality outcomes; however, causality could not be established. The retrospective design inherently limits our ability to control for all possible confounding variables, including unmeasured patient characteristics, treatment decisions, and temporal changes in care practices. Second, the 24-hour observation period for ICU patients may not have captured full clinical complexity, and discontinuous Hb measurements could affect EDI accuracy. Third, our analysis focused on patients with adequate vital sign monitoring and surgical patients with anesthesia duration of ≥ 2 hours, which may have introduced selection bias toward more complex cases requiring sustained monitoring; thereby potentially limiting generalizability to shorter or less intensive procedures. Fourth, the non-significant association between low EDI and mortality in the NIBP only subgroup may partly reflect the characteristics of this population, which is more likely to undergo lower-acuity procedures with inherently lower baseline mortality risk. Fifth, the use of point-of-care devices with varying accuracy, combined with forward-fill imputation for missing Hb values, may have introduced bias in EDI, especially during active bleeding, massive transfusion, or significant fluid shifts. EDI assumes that pulse pressure correlates with stroke volume; however, this relationship may be compromised in patients with altered arterial compliance, such as those receiving vasoactive medications. Finally, the single-center nature of the surgical cohort may limit generalizability. Our correlation analysis included only 86 high-risk surgical patients with pulmonary artery catheters, representing a small number of critically ill surgical cases. This limited sample size and selective patient population, those requiring invasive CO monitoring, may not be representative of the broader surgical population, potentially affecting the generalizability of the observed moderate correlation between EDI and D_AO₂I. Future studies should examine oxygen demand, longer observation periods, and continuous Hb monitoring, and employ multicenter designs. Future prospective interventional studies should determine optimal EDI targets across different populations and evaluate EDI-guided hemodynamic management.

In conclusion, EDI was independently associated with mortality in both surgical and critically ill patients, which may support its potential role as a hemodynamic parameter for risk assessment. Our findings suggest that EDI could offer additional prognostic information alongside conventional blood pressure monitoring. Although further validation is warranted, EDI, derived from readily available clinical parameters, may help address an important gap in hemodynamic monitoring across healthcare settings with varying resource levels.

Supplementary Materials

Supplementary Table 1.

Subgroup analysis on the association between hemodynamic exposures and mortality in surgical and critically ill patients with non-invasive blood pressure monitoring only.

Supplementary Table 2.

Quadrant analysis of the association between hemodynamic exposures and mortality in surgical and critically ill patients.

Supplementary Table 3.

Direct comparison of mortality risk by EDI status within the low MAP exposure group in surgical and critically ill patients.

Supplementary Table 4.

Baseline characteristics of the surgical patient cohort for the D_AO₂I (arterial oxygen delivery index) correlation analysis.

Supplementary Fig. 1.

Scatter plot of EDI versus D_AO₂I from 86 surgical patients. D_AO₂I: arterial oxygen delivery index, EDI: Easy D_AO₂ index.

Supplementary Fig. 2.

Examples of individual patient correlations between D_AO₂I and EDI. The two patients had the lowest (a,b) and highest (c,d) Spearman correlation coefficients among all participants in the study. The r represents the Spearman correlation coefficient of each patient.