A transformation of oxygen saturation (the saturation virtual shunt) to improve clinical prediction model calibration and interpretation

The relationship between peripheral oxygen saturation (SpO2) and the inspired oxygen concentration is non-linear. SpO2 is frequently used as a dichotomized predictor, to manage this non-linearity. We propose the saturation virtual shunt (VS) as a transformation of SpO2 to a continuous linear variable to improve interpretation of disease severity within clinical prediction models. We calculate the saturation VS based on an empirically derived approximation formula between physiological VS and SpO2. We evaluated the utility of the saturation VS in a clinical study predicting the need for facility admission in children in a low resource health-care setting. The transformation was saturation VS = 68.864 × log10(103.711 − SpO2) − 52.110. The ability to predict hospital admission based on a dichotomized SpO2 produced an area under the receiver operating characteristic curve of 0.57, compared to 0.71 based on the untransformed SpO2 and saturation VS. However, the untransformed SpO2 demonstrated a lack of fit compared to the saturation VS (goodness-of-fit test p value <0.0001 vs 0.098). The observed admission rates varied non-linearly with the untransformed SpO2 but varied linearly with the saturation VS. The saturation VS estimates a continuous linearly interpretable disease severity based on SpO2 and improves clinical prediction.