Non-linear imputation of PaO₂/FIO₂ from SpO₂/FIO₂ among mechanically ventilated patients in the intensive care unit: a prospective, observational study

Abstract

Objectives

In the contemporary intensive care unit (ICU), mechanically ventilated patients may not have arterial blood gas (ABG) measurements available at relevant timepoints. Severity criteria often depend on ABG results. Retrospective studies suggest that non-linear imputation of PaO₂/FIO₂ from SpO₂/FIO₂ is accurate, but this has not been established prospectively among mechanically ventilated ICU patients. The objective was to validate the superiority of non-linear imputation of PaO₂/FIO₂ among mechanically ventilated patients and understand what factors influence the accuracy of imputation.

Design

Simultaneous SpO₂, oximeter characteristics, receipt of vasopressors, and skin pigmentation were recorded at the time of a clinical ABG. ARDS criteria were recorded. For each imputation method, we calculated both imputation error and the area under the curve (AUC) for patients meeting criteria for ARDS (PaO₂/FIO₂≤300) and moderate-severe ARDS (PaO₂/FIO₂≤150).

Setting

Nine hospitals within the Prevention and Early Treatment of Acute Lung Injury network.

Patients

We prospectively enrolled 703 mechanically ventilated patients admitted to the emergency departments or ICUs of participating study hospitals.

Interventions

None.

Measurements and Main Results

We studied 1034 ABGs from 703 patients; 650 ABGs were associated with SpO₂≤96%. Non-linear imputation had consistently lower error than other techniques. Among all patients, non-linear had a lower error (p<0.001) and higher (p<0.001) AUC (0.87; 95% CI 0.85–0.90) for PaO₂/FIO₂ ≤300 than linear/log-linear (0.80; 95%CI 0.76–0.83) imputation. All imputation methods better identified moderate-severe ARDS (PaO₂/FIO₂ ≤150); non-linear imputation remained superior (p<0.001). For PaO₂/FiO₂≤150, the sensitivity and specificity for non-linear imputation were 0.87 (95% CI 0.83–0.90) and 0.91 (95% CI 0.88–0.93) respectively. Skin pigmentation and receipt of vasopressors were not associated with imputation accuracy.

Conclusions

In mechanically ventilated patients, non-linear imputation of PaO₂/FIO₂ from SpO₂/FIO₂ appears accurate, especially for moderate-severe hypoxemia. Linear and log-linear imputation cannot be recommended.

INTRODUCTION

The ratio of partial pressure of arterial oxygen (PaO₂) to the fraction of inspired oxygen (FIO₂), the PaO₂/FIO₂ ratio, is commonly used to measure the severity of hypoxemia in patients with respiratory failure. The PaO₂/FIO₂ ratio is fundamental to the consensus definition of ARDS(1) as well as general critical illness severity indices such as the Sequential Organ Failure Assessment (SOFA) score.(2) Among mechanically ventilated patients, the PaO₂/FIO₂ ratio may be necessary to diagnose ARDS. However, the PaO₂/FIO₂ ratio requires that an arterial blood gas (ABG) be obtained to measure PaO₂.

Because many clinicians rely on pulse oximetry to evaluate hypoxemia and make adjustments to the mechanical ventilator, patients with ARDS may not have an ABG available in a relevant timeframe for early diagnosis of ARDS or calculation of severity scores. Arterial catheters (which make ABG testing more convenient) are falling out of favor,(3, 4) pulse oximeters have become ubiquitous, and clinicians may use venous blood gases (or exhaled gas sampling) to monitor PCO₂ or pH.(5) A non-invasive surrogate for the PaO₂/FIO₂ ratio, based on measuring the oxyhemoglobin percent saturation with a pulse oximeter, would allow patients without ABGs to be assessed for disease severity and/or evaluated for the hypoxemia criterion for ARDS. To assure equivalence, a non-invasive surrogate for PaO₂/FIO₂ would require imputation of PaO₂ from SpO₂. The SpO₂/FIO₂ ratio has therefore been proposed as a non-invasive surrogate for the PaO₂/FIO₂ ratio.(6–11)

The oxyhemoglobin percent saturation can be measured with a pulse oximeter (SpO₂), or directly in the arterial blood (SaO₂). The relationship between PaO₂ and SaO₂ (and therefore SpO₂) is sigmoidal. However, much prior work investigating the association between SpO₂/FIO₂ and PaO₂/FIO₂ ratios employed linear (or log-linear) regression modeling in adults(6, 7) and children.(8–11)

In a large, retrospective study of patients with ARDS enrolled in three clinical trials,(12) we demonstrated that a non-linear imputation based on the Ellis inversion(13) of the Severinghaus equation(14) outperformed linear and log-linear imputation methods, observations which complemented prior studies of non-intubated patients with pneumonia.(15–18) To externally validate these retrospective observations, we undertook a prospective study, with attention to patient characteristics that might affect the accuracy of imputation. We hypothesized that non-linear imputation was superior to other imputation methods and that the receipt of vasopressors and darker skin pigmentation would be associated with less accurate imputation.

MATERIALS AND METHODS

We studied mechanically ventilated patients admitted to the emergency departments (EDs) or intensive care units (ICUs) of participating study hospitals, which were part of the NIH Prevention and Early Treatment of Acute Lung Injury (PETAL) Network. We excluded children, pregnant women, and prisoners. At the time a clinical ABG was obtained for a ventilated patient, the nurse or respiratory therapist obtaining the ABG completed a brief case report form (CRF) that included current SpO₂, quality of the oximeter waveform, skin pigmentation (graded informally from very light to very dark, on a 5-point ordinal span, with reference skin pigments included on the CRF). Research coordinators then documented age, sex, body mass index (BMI), body temperature (as measured clinically, without preference for core vs. peripheral temperature measurements), ABG results, basic metabolic panel results, hemoglobin, Positive End Expiratory Pressure (PEEP), FIO₂, tidal volume, receipt of vasopressors (i.e., epinephrine, norepinephrine, phenylephrine, dopamine, or vasopressin) at the time the ABG was obtained, and whether the patient met consensus criteria for ARDS other than hypoxemia. Specifically, site investigators individually reviewed chest radiographs and the medical record to assess whether ARDS criteria (acute onset of bilateral lung opacities not fully explained by effusions, lobar/lung collapse, or nodules) other than hypoxemia were met. ARDS was then considered present if the PaO₂/FIO₂ met relevant thresholds. Given resource constraints, we did not require a specific ABG sampling strategy or collect denominator data on the total number of ABGs performed in participating hospitals.

Data were uploaded to the Clinical Coordinating Center (CCC) at Massachusetts General Hospital, where quality analysis and cleaning were undertaken according to standard procedures. Each participating Institutional Review Board (IRB), including the CCC IRB, approved this study with waiver of informed consent on the basis of compliance with 45 CFR 46.116d.

Statistical analysis

Because imputation is considered to be most accurate for SpO₂ ≤ 96%, based on the sigmoidal shape of the hemoglobin-oxygen dissociation curve(14) and our prior empirical observations,(12) we separately analyzed ABGs with an associated SpO₂ ≤ 96%. Because PIO₂ (partial pressure of inspired oxygen) varies by both FIO₂ and barometric pressure, we adjusted PaO₂/FIO₂ ratios at the Utah site (altitude ~1300m) by the ratio of local to sea level barometric pressure (0.845). We used the Ellis non-linear,(13) Rice linear,(6) and Pandharipande log-linear(7) equations for imputation, as we did in our prior, retrospective work.(12) (The equations are displayed in Table E1.) For purposes of description, we generated Bland-Altman plots of the difference between imputed and measured PaO₂/FIO₂ as a function of measured PaO₂/FIO₂ both for all patients and among patients in whom SpO₂ ≤ 96%. Secondarily, we calculated the error of the imputations, as well as the proportion of patients in whom the absolute error of the imputation was less than 25 (e.g., if the actual PaO₂/FIO₂ is 100, then the imputed PaO₂/FIO₂ is between 75 and 125) or 50 (e.g., if the actual PaO₂/FIO₂ is 100, then the imputed PaO₂/FIO₂ is between 50 and 150).

For hypothesis testing, we compared the root mean squared error (RMSE; log transformed given its log normal distribution) of the imputation for each technique, using a paired t test and utilizing generalized estimating equations to account for the fact that some patients contributed multiple ABGs to the analysis.(19) We also calculated area under the receiver operating characteristic curve (AUC) at two diagnostic thresholds for PaO₂/FIO₂ (150 and 300) for the different imputation techniques. (We note that because linear and log-linear techniques impute PaO₂/FIO₂ from SpO₂/FIO₂ monotonically, their AUCs are identical to each other and to raw SpO₂/FIO₂; because the non-linear technique imputes from SpO₂ itself, its AUC can differ.) We used the threshold of ≤ 150 rather than the consensus threshold of ≤ 100 for severe ARDS because it is the threshold used in the PETAL Network’s Reevaluation of Systemic Early Neuromuscular Blockade (ROSE) trial (ClinicalTrials.gov NCT02509078) of neuromuscular blockade in moderate-severe ARDS,(20) following the ACURASYS trial threshold.(21) We compared AUCs using the method of DeLong.(22)

We considered whether other variables would improve the imputation of the PaO₂/FIO₂, from the point of view of the AUC for predicting that the PaO₂/FIO₂ was under 300 or under 150. Using linear regression models, we considered PEEP, serum bicarbonate, minute ventilation, FIO₂, age, ABG performed during the day (as opposed to at night), SpO₂, pulse oximeter location (at the time the ABG was obtained), serum chloride, serum creatinine, and serum sodium (the last three were included in case markers of renal dysfunction or electrolyte imbalance were related indirectly to shifts in the hemoglobin-oxygen dissociation curve), to see whether they improved the accuracy of the imputation.

In a secondary analysis, among the patients for whom more than one ABG was available, we evaluated whether knowledge of the error of measurement on the first ABG improved the imputation for the later ABGs. We attempted multiple complementary techniques to incorporate the first-ABG imputation error into later imputations, including adding the error term, adding a proportion of the error term (derived from linear regression), and the ratio of measured to imputed PaO₂/FIO₂ ratios.

Analyses were performed in the R Statistical Package version 3.2.3.(23)

RESULTS

We studied 1034 ABGs in 703 patients at 9 hospitals across the United States, among which 650 ABGs were associated with SpO₂ ≤ 96%. Patient characteristics are displayed in Table 1. Characteristics of the ABG and associated oximetry measurements are displayed in Table 2. The mean measured PaO₂/FIO₂ ratio was 226. Relevant laboratory results and ventilator settings are displayed in Tables E2–E3 of the Supplemental Digital Content. Mean PEEP was 7.8 cm H₂O; mean tidal volume, corrected for ideal body weight, was 6.9 ml/kg.

Table 1.

Patient Characteristics

Characteristic	Values
Female sex, k/n (%)	292/703 (41.5)
Age, years (± SD)	57.5 ± 16.3 (n = 703)
Height, cm (± SD)	170.1 ± 11.1 (n = 696)
Weight, kg (± SD)	88.6 ± 28.8 (n = 698)
Average PaO2/FIO2 for each patient (± SD)	225.7 ± 111.9 (n = 703)
PaO2/FIO2 ratio, values by threshold§
PaO2/FIO2 > 300, k/n (%)	166/703 (23.6)
PaO2/FIO2 ≤ 300, k/n (%)	537/703 (76.4)
PaO2/FIO2 ≤ 200, k/n (%)	322/703 (45.8)
PaO2/FIO2 ≤ 150, k/n (%)	188/703 (26.7)
PaO2/FIO2 ≤ 100, k/n (%)	58/703 (8.3)
# of SpO2 measurements
1 measurement, k/n (%)	460/703 (65.4)
2 measurements, k/n (%)	155/703 (22.1)
3 measurements, k/n (%)	88/703 (12.5)

^§Represents the average of PaO₂/FIO₂ ratios for each patient

Table 2.

Oximetry and arterial blood gas results

Oximetry.
Variables	Values
Patient Located in ICU, k/n (%)	1023/1034 (98.9)
ABG Done during the Day, k/n (%)	714/1034 (69.1)
Pulse Oximeter Location
Earlobe, k/n (%)	110/1013 (10.9)
Finger, k/n (%)	806/1013 (79.6)
Toe, k/n (%)	64/1013 (6.3)
Forehead, k/n (%)	18/1013 (1.8)
Other, k/n (%)	15/1013 (1.5)
Pulse Oximeter Type
Disposable Sensor, k/n (%)	523/1029 (50.8)
Reusable Sensor, k/n (%)	470/1029 (45.7)
Flex Sensor, k/n (%)	2/1029 (0.2)
Forehead (transreflectance) Sensor, k/n (%)	10/1029 (1.0)
Other, k/n (%)	24/1029 (2.3)
Pulse Oximeter Manufacturer
Masimo, k/n (%)	785/1034 (75.9)
Nellcor, k/n (%)	230/1034 (22.2)
Stryker, k/n (%)	19/1034 (1.8)
SpO2, %	95.0 ± 4.4 (n = 1034)
SpO2 (where SpO2 ≤ 96%), %	92.8 ± 4.0 (n = 650)
Adequate Pulse Oximeter Waveform, k/n (%)	973/1031 (94.4)
Skin Pigmentation
Light, k/n (%)	281/1033 (27.2)
Light/Medium, k/n (%)	429/1033 (41.5)
Medium, k/n (%)	169/1033 (16.4)
Medium/Dark, k/n (%)	70/1033 (6.8)
Dark, k/n (%)	84/1033 (8.13)
ABG Results.
Variables	Values
pH	7.36 ± 0.11 (n = 1034)
PCO2, mmHg	42.3 ± 12.6 (n = 1034)
PaO2, mmHg	98.1 ± 51.4 (n = 1034)
SaO2, %	93.8 ± 4.4 (n = 932)
Hgb, g/dL	9.8 ± 2.2 (n = 891)
Methemoglobin, %	0.8 ± 0.4 (n = 533)
Carboxyhemoglobin, %	1.4 ± 0.7 (n = 536)
Temperature at time of ABG, °C	37 ± 1 (n = 1030)
On a vasopressor at time of ABG, k/n (%)	388/1034 (37.5)

ICU: Intensive Care Unit; ABG: arterial blood gas; Hgb: hemoglobin

As displayed in Figure 1, Bland-Altman plots suggested that non-linear imputation was accurate, albeit with decreasing accuracy at higher PaO₂/FIO₂ ratios. This appeared true, especially for measured PaO₂/FIO₂ ratio ≤ 150 and for SpO₂ ≤ 96%. In Table 3, we quantitatively describe the performance of the different imputation techniques. Non-linear imputation had lower RMSE than log-linear or linear imputation methods for all ABGs and for ABGs where SpO₂ ≤ 96% (all p<0.001).

Figure 1. Bland-Altman plots of imputed vs. measured PaO₂:FIO₂ ratios.

Bland-Altman plot of the difference between measured and imputed PaO₂/FIO₂ ratios. Black represents non-linear, red linear, and blue log-linear imputation results.

Table 3.

Comparison of error by imputation technique

Imputation technique	Mean absolute error	Standard deviation of error	P value (comparison with non-linear imputation)*	Proportion of ABGs with error§ < 25 mmHg (%)	Proportion of ABGs with error§ < 50 mmHg (%)
All ABGs (N=1034)
Non-linear	54.3	69.6	NA	48.7	68.8
Linear	63.5	73	<0.001	33.1	59.7
Log-linear	60.3	66.1	<0.001	28.6	61.7
ABGs with SpO2 ≤ 96% (N=650)
Non-linear	30.2	45.4	NA	65.1	84.9
Linear	41.2	44.6	<0.001	40.9	72.3
Log-linear	40.7	36.9	<0.001	31.5	73.5
ABGs where other ARDS criteria are met (N=417)
Non-linear	43.9	61.5	NA	55.9	75.8
Linear	47.3	58.2	<0.001	40.5	71
Log-linear	48.1	49.6	<0.001	28.1	69.1
ABGs with SpO2 ≤ 96% where other ARDS criteria are met (N=297)
Non-linear	26.4	44.9	NA	68.7	88.9
Linear	36.9	44.3	<0.001	45.5	77.4
Log-linear	40.6	37.1	<0.001	27.9	74.7

^*From a paired t-test of log-transformed root-mean-square error

^§Absolute value of error

ABG: arterial blood gas; ARDS: Acute Respiratory Distress Syndrome

All imputation methods displayed good to excellent discrimination, as outlined in Table 4, with AUCs ranging from 0.77 (95% CI 0.73–0.81) to 0.96 (95% CI 0.94–0.97) for different thresholds and sub-populations. Non-linear imputation had a significantly higher AUC than linear/log-linear imputation (p<0.001), with AUCs ranging from 0.86 (95% CI 0.82–0.89) to 0.96 (95% CI 0.94–0.97). The superiority of non-linear imputation was true for PaO₂/FIO₂ ≤ 150 and PaO₂/FIO₂ ≤ 300. AUCs were consistently higher for the lower threshold (≤150) than for the higher threshold (≤300). The observed AUCs were compatible with good sensitivity and specificity. At the PaO₂/FiO₂ ≤ 150 threshold, the sensitivity and specificity for non-linear imputation were 0.87 (95% CI 0.83–0.90) and 0.91 (95% CI 0.88–0.93), respectively. At the PaO₂/FIO₂ ≤ 300 threshold, sensitivity and specificity were 0.90 (95% CI 0.88–0.92) and 0.67 (95% CI 0.61–0.73), respectively.

Table 4.

AUC for severe ARDS and any ARDS

Severe ARDS (PF ratio ≤ 150)
Imputation method	All ABGs (N = 1034)		Other ARDS criteria are met (N = 421)		Other ARDS criteria are NOT met (N = 613)
	Area	95% CI	Area	95% CI	Area	95% CI
Nonlinear	0.95	(0.94, 0.97)	0.94	(0.92, 0.96)	0.96	(0.94, 0.97)
Linear/log-linear	0.92	(0.90, 0.93)	0.91	(0.88, 0.94)	0.92	(0.90, 0.94)
All ARDS (PF ratio ≤ 300)
Nonlinear	0.87	(0.85, 0.90)	0.87	(0.81, 0.93)	0.86	(0.82, 0.89)
Linear/log-linear	0.80	(0.76, 0.83)	0.84	(0.77, 0.91)	0.76	(0.72, 0.81)

AUC: Area under the receiver operating characteristic curve; ABG: Arterial blood gas; ARDS: Acute Respiratory Distress Syndrome

The results were generally similar for the 650 ABGs associated with SpO₂ ≤ 96% (see Tables 3, E4). In this group, AUC analysis yielded similar results, except for patients who otherwise met ARDS criteria at the PaO₂/FiO₂ ≤ 300 threshold, where discrimination was only good: AUCs were 0.77 to 0.81. The decrease in AUC appeared related to the relatively small number of individuals with SpO₂ ≤ 96% who also had PaO₂/FiO₂ > 300 and otherwise met criteria for ARDS. Among ABGs in patients that otherwise met ARDS criteria, restricting to ABGs with SpO₂≤96% again demonstrated the superiority of non-linear imputation (Table 3).

In our analysis to understand whether certain variables (e.g., skin pigmentation, oximeter sensor location, oximeter manufacturer, vasopressor use, PEEP, and others, as outlined in methods) were associated with changes in the accuracy of imputation, models incorporating those predictors yielded negligible improvement in the accuracy of the imputation. The AUC of the imputations increased at most by 1%. Notably, only 5.6% of ABGs were associated with an inadequate pulse oximeter waveform.

Similarly, when evaluating whether results from an initial ABG result could improve the accuracy of imputation for later ABGs, none of the techniques materially improved the accuracy of imputation.

DISCUSSION

In this large, prospective, multi-center study of clinical ABGs obtained in mechanically ventilated ICU patients, we externally validated prior retrospective observations that a non-linear imputation is best for estimating the degree of hypoxemia from pulse oximetry. While all tested imputations had reasonable accuracy among mechanically ventilated patients, a non-linear, physiologically based approach appeared best overall, especially when the PaO₂/FIO₂ ratio is low. Among patients who otherwise met ARDS criteria, accuracy was highest when restricted to ABGs where SpO₂≤96%.

The AUC analysis, which is most relevant to screening for the presence of hypoxemia consistent with ARDS, confirms that physiologically based, non-linear imputation of PaO₂/FIO₂ is superior to other imputation techniques. These estimates are less accurate for patients with higher SpO₂ and SpO₂/FIO₂ values. Contrary to our initial expectation, no variables were associated with greater or lesser accuracy to a substantial degree, suggesting that routine use of this technique would not require measurement of additional variables. In this respect, our findings differ from prior studies suggesting a relationship between PEEP and the accuracy of PaO₂/FIO₂ imputation.(6, 7) Because only one in twenty of study ABGs were associated with a low quality pulse oximeter waveform, we suspect that it is reasonable to restrict such imputations to situations where the waveform is of adequate quality. Based on physiological principles and our subgroup analysis, it also seems reasonable to restrict evaluation to ABGs where SpO₂≤96%, perhaps by downward titration of FIO₂ in patients with high SpO₂.

Our study has two key strengths differentiating it from prior studies of the imputation of PaO₂/FIO₂ from SpO₂/FIO₂ among patients with and at risk for ARDS, including our own retrospective work:(12) it is prospective—with real-time correlation of SpO₂ and PaO₂—and is multi-center. Our study design allowed us to evaluate, in a generalizable fashion, the accuracy of imputation and the relevance of the oximeter waveform, the oximeter type(24) and location, as well as skin pigmentation,(24, 25) body temperature, and other relevant parameters.

Our study has limitations. Because of resource limitations, we were unable to record all ABGs in study ICUs and were unable to obtain outcome data for study patients. We are thus unable to exclude ascertainment bias, which could affect generalizability, and we cannot determine whether inaccurate imputation is associated with mortality or other patient outcomes. For the patients in whom an ABG was associated with SpO₂ ≤ 96% the prevalence of PaO₂/FIO₂ > 300 was so uncommon, especially among patients who met other criteria for ARDS, that the AUC was a less reliable measure of accuracy. The error associated with non-linear imputation was still lower than for the other imputation techniques. Nevertheless, identification of mild ARDS may be somewhat more difficult on the basis of SpO₂/FiO₂. While the non-linear imputation equation is too complex to calculate easily by hand, we provide a lookup table (Table E5); a similar lookup table has been employed in the ROSE study protocol for screening.

CONCLUSIONS

Because the association between SpO₂ and PaO₂ is physiologically sigmoidal, the use of a non-linear imputation strategy appears preferable to other strategies for estimating PaO₂/FIO₂ from pulse oximetry. Such an imputation strategy displays good discrimination for ARDS at relevant diagnostic thresholds, albeit with lower specificity for mild ARDS, particularly when SpO₂ is allowed to remain >96% with high FIO₂. The use of linear or log-linear imputation methods can no longer be recommended.