This is the first external validation of three pCO2 conversion models in ED patients with respiratory distress or other indications for blood gas analysis.

Our results show comparable performance for all three models in terms of agreement and precision in estimating true arterial pCO2. The adaptive model derived by Farkas showed the overall best metrics with a mean difference of − 0.11 mmHg and 95% limits of agreement of − 6.86 ± 6.63 mmHg for estimated pCO2 versus true arterial pCO2. Zeserson's model, a commonly used linear model, performed worst with a mean difference between estimated and true arterial pCO2 of 2.55 mmHg with wide 95% limits of agreement between 7.43 and + 12.53 mmHg.

In comparison, the unadjusted mean difference between venous and arterial sample was 7.61 mmHg with a standard deviation of 4.7 mmHg. This is comparable to other datasets, the spread in mean difference between different studies is however big and depends on population, setting and studied disease [12,13,14,15]. The investigated conversion models performed differently in subgroup analysis, e.g., Lemoëls model showed best agreement for hypercapnic patients with a percentage error of 5.7%, compared to 6.1% (Farkas) and 8.9% (Zeserson). The remaining subgroup analyzes favored the model of Farkas. Variation around the mean is expected for subgroup analysis and since the regression analysis showed no significant association for these variables, and there is limited physiologic rationale around the derivation of coefficients for the models of Lemoel and Farkas, we believe that the results of the subgroups analysis should be interpreted with caution.

Diagnostic accuracy is critical for making informed decisions in critically ill patients, but there is no agreement on what is considered an acceptable precision for estimated pCO2 in blood gas analysis.

A prior study of 30 ICU patients showed an inter-sample variation with a 95% confidence interval of 2.4 mmHg for arterial pCO2 when blood gasses from both radial arteries were taken simultaneously in the same patient [24]. In another study from Thorson et al. a mean within-patient difference of 3 mmHg (SD 1.9) for pCO2 was found in 29 clinically stable ICU patients who underwent six arterial blood gas samplings over 50 min [25]. The mean difference of all models within our study is within this range, although the precision was lower with 95% LoA of − 6.86 to 6.63, − 5.65 to 10.8 and − 7.43 to 12.53 mmHg for Farkas, Lemoël and Zeserson, respectively. Specific clinical situations may still require arterial blood gas sampling but given the known variability in stable patients, a converted venous pCO2 is likely sufficient for a considerable share of ED patients.

Since there is currently no consensus on reasonable margins of error for estimated pCO2 in critical ill patients, we see a need for further dialogue among ED practitioners on this topic and its effects on clinical decision-making.

From an ICU perspective, the investigated conversion models open up for retrospective pCO2 evaluation with reasonable accuracy in critically ill patients initially investigated with venous blood gas sampling in the emergency department.

The administration of supplemental oxygen in the moment of blood gas sampling seemed to cause more outliers in our dataset compared to patients with no supplemental oxygen (Fig. 1). The addition of supplemental oxygen should, to some extent, be accounted for by the SvO2 variable for Farkas and Lemoël. The retained mean difference with larger LoA is more likely the result of the smaller sample of the supplemental oxygen group (n = 71 vs n = 243). Furthermore, when tested in a logistic regression analysis with other potential confounding variables, only age was significantly associated with the difference between arterial and estimated pCO2. This was only seen for the Farkas and Lemoël models and the effect was small (OR 0.97 and 0.96, respectively).

As previously shown by Pretto and O’Connor, time delay between sampling and analysis of more than 10 min can falsify analysis results through ingression of room air [19, 26]. In our dataset, the median time to analysis was 3 and 4 min for arterial and venous samples, respectively, and the time difference between venous and arterial sampling was in median 5 min with an IQR of 3 to 9 min. We strived for similar conditions if the clinical situation permitted.

Consequently, there was no influence of time on estimated pCO2 when looking at the time difference for Farkas (R = 0.013), Lemoël (R = − 0.028) or Zeserson (R = 0.054), respectively.

In summary, there was a low mean difference between estimated pCO2 from venous samples compared to arterial pCO2 with better agreement for the adaptive conversion models which is likely sufficient to guide management in most clinical situations in the ED.

Despite the goal of consecutive inclusion there were potentially eligible patients who were not enrolled. Some patients arriving during night hours were missed, primarily due to absence of the enrollment coordinator. However, we did include patients during most night shifts of the study period so it is unlikely that this affected the results in a systematic way.

Arterial blood gas sampling was only indicated in critically ill patients dictated by SOP or as assessed by the treating physician. In spite of that, many patients' vital signs were within normal ranges and the arterial pCO2 exceeded normal ranges in only 54% of cases. It is known that low blood pressure, blood loss and other factors compromising circulation in acutely ill patients make the evaluation of pCO2 more difficult [27]. A number of patients in a critical state who were directly admitted to intensive care could not be included within 12 h and neither later on. Thus, there may be limited generalizability for patients with more pronounced failure of vital functions. However, this group of patients may require extensive monitoring like an arterial line, removing most of the barriers for arterial blood gas sampling.

This was a single center study using only one type of blood gas analyzer from a single company. Despite the fact that this machine is commonly used in European EDs, we cannot exclude different results with other machines. Neither Lemoël nor Farkas report the blood gas analyzer machines used for analysis of their dataset.