Background

Acute respiratory distress syndrome (ARDS) is a life-threatening respiratory failure characterized by hypoxemia, and impaired clearance of carbon dioxide (CO2), with most patients requiring invasive mechanical ventilation for support [1, 2]. The primary goals of mechanical ventilation in ARDS management are to maintain adequate oxygenation and ventilation [3, 4]. Clinically, oxygenation is typically assessed by the ratio of arterial oxygen partial pressure to inspired fraction of oxygen (PaO2/FiO2) [1], while ventilation is primarily reflected by arterial carbon dioxide pressure (PaCO2), which depends on both CO2 production and alveolar ventilation. Despite its significance, the relationship between prolonged hypercarbia and prognosis in ARDS patients remains unresolved, with no consensus currently established [5, 6].

Ventilatory inefficiency, however, can manifest in clinical practice through increased PaCO2, elevated minute ventilation, or a combination of both. Therefore, a composite index, the ventilatory ratio (VR), which compares actual measurements of minute ventilation and PaCO2 to predicted values, has been proposed to better reflect ventilatory inefficiency [7]. Despite the potential of VR as a marker, previous studies investigating its association with ARDS prognosis have reported inconsistent results, likely due to limitations in sample sizes and the variability in controlling for confounding factors [8, 9]. Furthermore, findings from studies focusing on COVID-related ARDS may not be generalizable to the broader population of patients with classical ARDS due to differences in lung volume, respiratory mechanics, and ventilatory requirements [10,11,12]. Additionally, earlier researches on PaCO2 and VR often focused on single measurements upon admission or was restricted to the early phases of ARDS [5, 6, 12,13,14]. As a result, it remains unclear whether the relationship between ventilatory inefficiency and mortality in ARDS patients persists over time.

In this study, our primary objective was to evaluate the impact of time-varying exposure to ventilatory inefficiency—measured by PaCO2 and VR—on 28-day mortality in patients with ARDS. We also sought to determine whether the strength of these associations persisted over time and to quantify the cumulative impact of these exposures over the study period.

Methods

Study design and patients

We performed a secondary analysis of data from four published randomized controlled trials: FACTT (Fluid and Catheter Treatment Trial) [15, 16], ALTA (Albuterol for the Treatment of Acute Lung Injury) [17], EDEN (Early vs Delayed Enteral Nutrition in ARDS) [18], and SAILS (Statins for Acutely Injured Lungs) [19]. These trials focused on patients with classical ARDS and adhered to the low tidal volume ventilation protocol, reflecting current clinical practice standards. The details of these trials are summarized in Additional file 1: Table S1.

Included patients were adult subjects who were intubated and received mechanical ventilation. Exclusion criteria were: (1) Patients under the age of 18, (2) Patients lacking measurements of predicted body weight (PBW) or height needed to calculate VR, (3) Patients treated with extracorporeal life support, (4) Patients receiving invasive ventilation for less than one day, and (5) Patients lacking on-study ventilatory parameter measurements.

All studies obtained informed consent from patients and were approved by the respective institutional review boards. This study protocol, titled “The Association Between Time-Varying Intensity of Ventilatory Indices and Mortality in Patients with Acute Respiratory Distress Syndrome,” was approved by the Research Ethics Commission of Zhongda Hospital, Southeast University (Approval ID: 2023ZDSYLL158-P01, 20,230,511). The commission determined that the activities involved in this research did not constitute human subjects research, thus waiving the requirement for informed consent. Data were obtained from the Biologic Specimen and Data Repository Information Coordinating Center (BioLINCC, https://biolincc.nhlbi.nih.gov). This article complies with the STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) guidelines for observational studies.

Data collection

In the ARDS Network trials, Day 0 was defined as the day of randomization following patient enrollment. Per trial protocol, patients were required to begin low tidal volume ventilation within one hour of meeting the inclusion criteria. Demographic data collected included age, gender, primary risk factors for ARDS, chronic comorbidities, and severity of illness as measured by the Acute Physiology and Chronic Health Evaluation (APACHE) III score at admission.

Longitudinal data were collected for preselected variables, which were categorized under “on-study ventilator parameters.” These included arterial blood gases and ventilator parameters, which were recorded as close as possible to 08:00 AM on Days 0–4, 7, 12/14, 21, and 28 of mechanical ventilation. Ventilatory ratio is defined as [minute ventilation(mL/min) × PaCO2(mmHg)]/[PBW(kg) × 100(mL/min) × 37.5(mmHg)]. Data collection spanned from Day 0 until the earliest of the following events: death, discharge from the intensive care unit (ICU), liberation from mechanical ventilation for more than 48 h, or 28 days of ICU stay. The primary outcome of interest was 28-day mortality.

Statistical analysis

Categorical variables were summarized as proportions, while continuous variables were presented as means (standard deviations) or medians [interquartile ranges (IQRs)], depending on their distribution. Comparisons between groups were conducted using the Student’s t-test or Mann–Whitney U test for continuous variables, and the Chi-squared (Χ2) test or Fisher’s exact test for categorical variables, as appropriate.

We first employed cause-specific Cox proportional hazard models to evaluate the relationship between baseline ventilatory parameters (PaCO2 and VR) and 28-day mortality. Restricted cubic splines were used within these models to express hazard ratios (HRs) and corresponding two-sided 95% credible intervals (CIs). Based on the model outputs, we identified approximate thresholds for PaCO2 and VR.

Potential confounders were identified and assessed based on directed acyclic graphs (DAG) and change-in-estimate methods, while addressing collinearity and handling missing data to ensure robust and unbiased variable selection. (Additional file 1: Fig. S1-S2 & Table S2). The following covariates were selected for inclusion in the models:

  • Baseline confounders: Age, gender, body mass index (BMI), APACHE III score, comorbidities (Hypertension, Diabetes Mellitus, Chronic Pulmonary Disease), tidal volume per predicted body weight (PBW), positive end-expiratory pressure (PEEP), use of sedatives or neuromuscular blocking agents (NMBAs) (Yes/No), and use of vasopressors or inotropes(Yes/No).

  • Time-varying confounder: PaO2/FiO2.

To assess the association between longitudinal ventilatory parameters (PaCO2 and VR) and mortality, we utilized Bayesian joint models incorporating shared random effects. These models allow for the analysis of correlations between individual longitudinal profiles and 28-day mortality by accounting for non-random dropouts during follow-up. Shared parameter joint models combine mixed-effects models with Cox regression, linking patient-specific longitudinal trajectories to their prognosis. This approach assumes that latent random effects fully account for correlations between longitudinal exposures and outcomes after adjusting for covariates [20, 21].

Natural cubic splines were applied within both fixed-effects and random-effects models to accommodate any nonlinearity in the longitudinal exposure profiles. Estimations were performed using the JMbayes2 package, with additional details provided in Additional file 1 [22]. Standard Markov Chain Monte Carlo diagnostics were employed to assess model convergence [23], and the results were derived from the posterior distribution to predict the hazard of death within 28 days.

Given that the initial joint model assumed a constant strength of association over time, we incorporated an interaction term with a natural cubic spline of time to assess whether the association between ventilatory inefficiency and mortality persisted across time. We also explored the time-varying impact of daily high exposure to ventilatory inefficiency, defined as PaCO2 > 50 mmHg or VR > 2, on 28-day mortality. Additionally, we quantified the effect of cumulative exposure to elevated PaCO2 or VR by calculating the area beneath each subject’s longitudinal profile and above the specified thresholds, across the corresponding time period.

To mitigate bias resulting from missing data, we employed Multiple Imputation by Chained Equations (MICE), generating five imputed datasets to address the missing values. To verify the robustness of our findings, we repeated the joint model analyses using complete cases without imputation. We also performed subgroup analyses based on several factors, including age, gender, APACHE score, PaO2/FiO2 ratio, primary ARDS risk factors, and the use of sedatives or neuromuscular blocking agents (NMBAs), vasopressors or inotropes. For continuous variables, cut-off points were derived from existing knowledge or the interquartile ranges (IQRs). A P value < 0.05 (two-tailed) was considered statistically significant. All statistical analyses were conducted using R version 4.1.2 (R Core Team 2021, Vienna, Austria).

Results

Patients in the study

After reviewing data from 3027 patients, we included 2851 patients in the final analysis (Additional file 1: Fig. S3). The median age of the patients was 52 years (IQR 40–63), and 51.6% were male. The primary etiologies of ARDS were pneumonia (58.1%), sepsis (19.9%), and aspiration (11.4%). The median duration of invasive mechanical ventilation was 9 days (IQR 4–28 days), and the overall 28-day mortality rate was 21.3%.

Compared with survivors, non-survivors were older, had lower BMI, higher APACHE III scores, and were less likely to have received sedatives or NMBAs. In the cohort, tidal volumes were ≤ 8 mL/kg PBW in 1886 patients (79.0%), accounting for missing values (Additional file 1: Table S2). On Day 0 of mechanical ventilation, plateau pressures ≤ 30 cmH2O and driving pressures ≤ 15 cmH2O were observed in 1,542 patients (80.2%) and 952 patients (49.6%), respectively. Importantly, there were no significant differences in peak inspiratory pressure or driving pressure between survivors and non-survivors (Table 1).

Table 1 Baseline characteristics at Day 0 of mechanical ventilation
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Association of mortality with ventilatory parameters at baseline

A U-shaped relationship was identified between PaCO2 or VR and the risk of 28-day mortality. Inefficient ventilation, indicated by hypercapnia (PaCO2 > 50 mmHg) or high VR (VR > 2), was associated with an increased hazard of death within 28 days after adjustment (Fig. 1A and Fig. 1B). After adjusting for multiple covariates, including age, gender, BMI, APACHE III score, comorbidities (hypertension, diabetes, chronic pulmonary disease), tidal volume per PBW, PEEP, use of sedatives or NMBAs, use of vasopressors or inotropes, and PaO2/FiO2, only the ventilatory ratio (VR) at baseline remained significantly associated with mortality (HR 1.101, 95% CI 1.009–1.201). PaCO2, on the other hand, was not significantly associated with mortality after adjustment (HR 1.003, 95% CI 0.995–1.011) (Additional file 1: Table S3).

Fig. 1
figure 1

Outcomes in relation to ventilatory parameters at baseline. A Adjusted hazard ratio for 28-day mortality predicted by baseline PaCO2 using a cause-specific Cox proportional hazard model. B Adjusted hazard ratio for 28-day mortality predicted by baseline ventilatory ratio using a cause-specific Cox proportional hazard model. PaCO2 arterial carbon dioxide pressure

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Of the total cohort, 2769 patients (97.1%) had complete PaCO2 data on Day 0, with 12.4% of patients experiencing impaired carbon dioxide clearance (PaCO2 > 50 mmHg). Additionally, 2673 patients (93.8%) had complete VR data on Day 0, and 38.4% of patients had a VR > 2. Significant variations in patient characteristics and interventions were noted based on PaCO2 and VR levels at baseline (Additional file 1: Tables S4-S5).

Effect of time-varying intensities of ventilatory parameters

In the joint model analysis, time-varying ventilatory ratio (VR) (HR 1.548, 95% CI 1.309–1.835) was significantly associated with an increased risk of death after adjusting for covariates. In contrast, time-varying PaCO2 (HR 1.008, 95% CI 0.997–1.018) showed no significant association with mortality, consistent with the results from the baseline cause-specific Cox proportional hazard model (Table 2).

Table 2 The effect of time-varying intensities of ventilatory parameters on mortality
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The lack of a significant correlation between PaCO2 intensity and mortality persisted throughout the entire ventilation period, as illustrated in Fig. 2A. By contrast, VR was consistently associated with 28-day mortality over the course of mechanical ventilation, as shown in Fig. 2B. Traceplots and density plots confirmed good convergence of the joint models (Additional file 1: Fig. S4-S5).

Fig. 2
figure 2

Time-varying effect of ventilatory parameters and mortality. A Adjusted time-varying effect of PaCO2 and 28-day mortality using Bayesian joint models. B Adjusted time-varying effect of ventilatory ratio and 28-day mortality using Bayesian joint models. PaCO2 arterial carbon dioxide pressure

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Cumulative effect of exposure to high intensities of ventilatory inefficiency

The risk of mortality increased consistently with daily exposure to PaCO2 > 50 mmHg and VR > 2. Each additional day of exposure to elevated VR (> 2) was associated with a heightened risk of death after adjustment (HR 1.088 per day, 95% CI 1.034–1.147). However, prolonged exposure to high PaCO2 levels (> 50 mmHg) did not show a significant effect on mortality (HR 1.040 per day, 95% CI 0.979–1.104) (Table 3).

Table 3 The effect of time-varying exposure to hypercapnia or high VR on mortality
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Additionally, a cumulative impact of higher intensities of ventilatory inefficiency was observed. An increased risk of mortality was linked to a larger cumulative area of VR > 2 (HR 1.085 per area, 95% CI 1.050–1.122) after adjustments. Conversely, cumulative exposure to PaCO2 > 50 mmHg did not significantly influence 28-day mortality (HR 1.002 per area, 95% CI 0.999–1.004) (Additional file 1: Table S6).

Subgroup analyses and sensitivity analyses

Subgroup analyses explored the relationship between time-varying hypercapnia and high VR with 28-day mortality (Fig. 3). The association between high VR and mortality appeared to be more pronounced in patients with lower severity of illness, as indicated by an APACHE III score ≤ 91 (HR 1.112 per day, 95% CI 1.012–1.218) or PaO2/FiO2 > 150 (HR 1.088 per day, 95% CI 1.011–1.169). Regarding hypercapnia, the hazard of death was elevated in patients receiving sedatives or neuromuscular blocking agents (NMBAs) (HR 1.073 per day, 95% CI 1.016–1.134) and in those receiving vasopressors or inotropes (HR 1.127 per day, 95% CI 1.030–1.232).

Fig. 3
figure 3

Subgroup analyses of the association between any exposure to hypercapnia or high VR. The hazard ratios were the adjusted hazard ratios comparing higher versus lower levels of the variable. PaCO2 arterial carbon dioxide pressure, HR hazard ratio, CI confidence interval, APACHE Acute Physiology and Chronic Health Evaluation, PaO2/FiO2 ratio of arterial oxygen partial pressure to inspired fraction of oxygen, NMBAs neuromuscular blocking agents

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To test the robustness of our initial findings, we repeated the joint model analyses after excluding patients with missing longitudinal data on PaCO2 and VR during follow-up. The results from the complete datasets were consistent with those derived from imputed datasets (PaCO2: HR 1.073, 95% CI 0.998–1.158 vs. VR: HR 1.088, 95% CI 1.021–1.164), confirming the reliability of our findings (Additional file 1: Table S7).

Discussion

In clinical practice, ventilation assessment has often been overshadowed by the emphasis on oxygenation during mechanical ventilation in patients with ARDS. Indices such as PaCO2 and the ventilatory ratio (VR), which are readily available and indicative of ventilatory inefficiency, have not been fully appreciated and require more attention in clinical studies [24]. Our study highlights the longitudinal relationship between PaCO2, VR, and 28-day mortality, suggesting that clinicians should attach importance to VR throughout the period of mechanical ventilation. We also found that time- and dose-dependent exposure to high levels of ventilatory inefficiency, as measured by VR > 2, rather than PaCO2 > 50 mmHg, was associated with increased mortality in ARDS.

PaCO2, a frequently monitored parameter linked to alveolar ventilation, can rise due to ventilatory inefficiency or hypoventilation. Ventilatory inefficiency indicated by hypercapnia showed no significant association with ARDS prognosis when compared to VR. A possible explanation for this discrepancy is the beneficial effects of permissive hypercapnia in patients undergoing lung-protective ventilation [25]. By tolerating elevated PaCO2 levels, permissive hypercapnia mitigates acute lung injury through reduced mechanical stretch and anti-inflammatory effects [26, 27]. Moreover, hypercapnia improves ventilation-perfusion matching by enhancing bronchodilation and hypoxic vasoconstriction, contributing to better pulmonary and systemic oxygenation [28].

The dimensionless VR is widely recognized as a marker for assessing pulmonary dead space [29]. Increased pulmonary dead space reflects the lungs' inefficiency in eliminating CO2, which can lead to hypercapnia. Given that the anatomical portion of dead space is generally constant, increasing tidal volumes (VT) with a stable respiratory rate would increase alveolar ventilation, effectively lowering PaCO2. This tradeoff is captured by VR [30]. Ventilatory inefficiency, reflected by high VR(VR > 2) is independently associated with increased case fatality in patients with ARDS [31]. The utility of VR for quantifying physiological dead space, however, may be limited by factors such as venous admixture and the CO2 production [9]. As such, VR serves as a measure of global gas exchange efficiency and allows the quantification of ventilation-perfusion mismatch [29]. VR shows promise as a simple method to stratify ARDS patients that is not captured by conventional oxygenation indices.

We further attempted to address ARDS heterogeneity through subgroup analyses. The stronger association between higher VR and mortality in less severe cases, as indicated by APACHE III and PaO2/FiO2 scores, appears exploratory in nature, consistent with previous study [32]. A higher VR in these cases may reflect an early maladaptive response to underlying pathophysiological processes, such as subtle respiratory muscle fatigue or early ventilation-perfusion mismatch. In contrast, in patients with more severe disease, elevated VR may simply be a marker of overall critical illness, where multiple organ systems are already compromised [33]. This could dilute the specific impact of VR on mortality. Future prospective and interventional studies, guided by focused hypotheses and mechanistic insights, are needed to better understand the clinical significance of VR across varying severities of ARDS.

Our study has important implications for interpreting previous research. First, we extended the assessment period between VR and its association with mortality, capturing its dynamic evolution over the course of the ventilation. Second, Bayesian joint models were employed in our study to account for both baseline and time-varying confounders, offering a more precise estimation of temporal associations. Third, we identified clinically meaningful thresholds for VR > 2—aligning with evidence from previous studies [8, 31]. Finally, the larger sample size in our study enhances the statistical power, improving the robustness and external validity of the observed relationships. Overall, our results emphasize the role of VR in prognostication and highlight the importance of adequately powered studies in this area.

Several limitations of our study should be acknowledged. First, the study is a retrospective observational analysis based on datasets from four randomized controlled trials. This design introduces inevitable challenges, such as missing values and the inability to infer causality. Second, our dataset consists of arterial blood gas and ventilator data collected at a standardized time each morning. It is possible that these measurements were not taken simultaneously or did not fully capture the ventilatory parameters throughout the day. To address these limitations, a prospective study is warranted to confirm these findings and explore their potential implications for clinical interventions.

Conclusion

In conclusion, ventilatory inefficiency, as reflected by VR, is associated with increased mortality in patients with ARDS undergoing invasive mechanical ventilation. Long-term exposure to high VR levels correlates with higher mortality, underscoring the importance of vigilant monitoring. However, given the retrospective design, these findings suggest an association rather than causation and warrant further validation through well-designed prospective studies.