147 S/F94 as a proxy for COVID-19 severity 7 reference standard for both synthetic (Spearman r S/F: 0.40; S/F94: 0.85; Figure 1D) and real data (Spearman r S/F: 0.82; S/F94: 0.97, Supplementary Figure 1C). In parallel, we assessed the predictive validity of S/F and S/F94. As in our previous work18, we assert that if S/F 94 is measuring true oxygenation function well, then it should be able to more accurately predict a future event: the PaO2 value in a future arterial blood gas measurement taken from the same patient. We used a preexisting dataset of unselected ABG result pairs from hospitalised patients, described in detail previously18. We quantified the MAE above baseline in P aO2 to quantify predictive validity, with lower error values indicating better performance (Figure 1C, Supplementary Figure 2). Across a range of maximum cut-off values for SaO2, the lowest MAE value was obtained at 94% (Figure 1C; S/F MAE =4.41 kPa (IQR: 2.746.63 kPa); S/F94 MAE = 3.32 kPa (IQR: 1.87-5.26 kPa), p(MWU) = 3.7×10-18). SaO2 <1.00orFIO2 =0.21 SaO2 <0.98orFIO2 =0.21 SaO2 <0.96orFIO2 =0.21 SaO2 <0.94orFIO2 =0.21 SaO2 <0.92orFIO2 =0.21 SaO2 <0.90orFIO2 =0.21 0 20 40 60 80 PaO2/FIO2 ratio (kPa) 0 1 2 3 4 5 SaO2/FIO2 ratio 0.5 0.6 0.7 0.8 0.9 1.0 SaO2 0 1 2 3 4 5 SaO2/FIO2 ratio 0 20 40 60 80 100 PaO2/FI O2 ratio (kPa) 0.5 0.6 0.7 0.8 0.9 1.0 SaO2 n=4801 n=4390 n=3206 n=2105 n=1407 n=906 n=550 n=367 n=256 n=164 n=122 n=94 n=65 100 99 98 97 96 95 94 93 92 91 90 89 88 SaO2 threshold (%) 0 2 4 6 8 10 12 Error (difference from baseline, kPa) 100 98 96 94 92 90 88 SaO2 threshold(%) 0.4 0.5 0.6 0.7 0.8 Correlation with P/F - Spearmanr a c d b Figure 1. Comparison of P/F and S/F or S/F94 in synthetic data. (a,b) Scatterplots of P/F vs S/F individual measurements across a range of hypothetical physiological characteristics. Points are coloured according the SaO2 as shown in the colour scale. (a) including all values, showing linear regression of S/F against P/F in using different cut-off values for SaO2. Patients breathing air (FIO2=21%) were included in all bins. (b) including only values with SpO2 ≤ 0.94 or FIO2=21%) (c) Optimisation of cut-off value for SaO2 using predictive validity: the error in the prediction of a future PaO2, based on a previous one (using a pre-existing dataset of ABG results17). Centre line represents median values, box limits represent upper and lower quartiles, whiskers represent minimum and maximum values. (d) change in correlation coefficient (Pearson’s ρ) as the threshold for inclusion is lowered from SaO2<100% to SaO2<80%.
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