143 S/F94 as a proxy for COVID-19 severity 7 Relationship to the reference standard (P/F ratio) The P/F ratio is the oxygenation measure used in diagnostic criteria for acute respiratory failure, and is used in our analysis as the reference standard17. We evaluated the relationship between S/F and P/F in two datasets: a synthetic dataset of 1,529,176 predictions covering a wide range of possible physiological variation, generated by a mathematical model of oxygen delivery written in Python (available at https://github.com/baillielab/oxygen_delivery) and reported previously18, and 72,457 unselected arterial blood gas results from a critically ill population18. Taking P/F to be our reference standard, we evaluated S/F at different thresholds in both synthetic and real data. Predictive validity We considered the predictive validity of S/F and S/F94 compared to P/F and two other measures of oxygenation function: the A-a, and effective shunt fraction (ES)18. Predictive validity quantifies the extent to which a clinical measurement predicts an unseen event. The aim is not to optimise prediction, but to test the extent to which a measurement is describing a real feature of the patient’s illness19. In this case, we contend that a measure that accurately describes pulmonary oxygenation function will accurately predict PaO2 after a change is made to FIO2. Using the same pre-existing dataset of ABG results from critically ill patients as in our previous study18, we used this approach to assess the validity of S/F and S/F94. Briefly, in pairs of arterial blood gas results taken from the same patient <3h apart, in which FIO2 was decreased in the later sample, we used various measures of oxygenation (A-a, P/F, ES, S/F) in the first ABG to predict the PaO2 in the second sample and compared these predicted values with the PaO2 that was measured in the second sample. Predictive validity was quantified by the median absolute error (MAE). A baseline value, showing the difference between ABG results for matched pairs in which FIO2 did not change, is provided to contextualise the MAE results as a reasonable minimum error value. Results are presented as difference in MAE from this baseline. The Mann-Whitney U-test (MWU) was used for comparison of MAE difference from baseline. Evaluation in ISARIC4C data Inclusion criteria All subjects were part of the ISARIC Coronavirus Clinical Characterisation Consortium (ISARIC4C) WHO Clinical Characterisation Protocol UK (CCP- UK), a study in England, Wales, and Scotland prospectively collecting data from patients hospitalised with SARS-CoV-2 infection since the start of the pandemic.
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