Scaling of Algorithmic Bias in Pulse Oximetry with Signal-to-Noise Ratio.

Recent work has noted a skin-color bias in existing pulse oximetry systems in their estimation of arterial oxygen saturation. Frequently, the algorithm used by these systems estimate a "ratio-of-ratios", called the "R-value", on their way to estimating the oxygen saturation. In this work, we focus on an "SNR-related" bias that is due to noise in measurements. We derive expressions for the SNR-related bias in R-value estimation, and observe how it scales with the signal-to-noise ratio (SNR). We show that the bias can arise at two steps of R-value estimation: in estimating the max and min of a pulsatile signal, and, additionally in taking ratios to estimate the R-value. We assess the bias resulting from the combination of the two steps, but also separate out contributions of each step. By doing so, we deduce that the bias induced in max and min estimation is likely to dominate. Because the SNR tends to get worse with higher melanin concentration, our result provides a sense of scaling of this bias with melanin concentration.