Fairness across skin tones and the calibration problem

"They calibrated the light against the volunteers they could find. The volunteers they could find were the reason the numbers only worked for some of us."

A Chromatically Honest AI Agent

This section assumes the pulse-waveform optics of Section 30.1 and the SpO2 ratio-of-ratios of Section 30.3, and it treats the PPG as a physical measurement \(x = h(s;\theta) + \eta\) whose response \(h\) and noise \(\eta\) both depend on skin optics, the sensor-model view of Chapter 2. The subgroup-auditing discipline draws on the leakage-safe evaluation of Chapter 5, the calibration machinery of Chapter 18, and the regulatory framing of Chapter 34. Signal-quality gating (Section 30.6) is the first and cheapest fairness tool, so it recurs here.

The optics: why melanin dims the signal

Melanin lives in the epidermis, the outermost skin layer, above the dermal capillary bed whose pulsing blood volume the PPG is trying to see. Light must cross the epidermis twice, on the way in and on the way back, so its intensity is attenuated by the Beer-Lambert factor \(e^{-2\,\mu_a d}\), where \(\mu_a\) is the epidermal absorption coefficient and \(d\) its thickness. Melanin dominates \(\mu_a\) across the visible band, and its absorption falls steeply with wavelength: it is strong in the green (around 530 nm, the workhorse LED of wrist wearables), weaker in the red (660 nm), and weakest in the near-infrared (940 nm). The pulsatile part of the signal, the small AC component riding on a large DC offset, carries the heartbeat. Roughly doubling epidermal melanin can cut that AC amplitude by a large factor while leaving the electronic noise floor unchanged, so the pulse-to-noise ratio collapses. The device is not broken; it is simply photon-starved.

Two engineering consequences follow directly. First, wavelength choice is a fairness choice: green maximizes pulsatile contrast on light skin but penalizes dark skin most, whereas red and infrared penetrate deeper and are far less melanin-sensitive, which is one reason SpO2 sensors use them. Second, the same missing photons that raise heart-rate error on dark skin also perturb the SpO2 ratio, because any wavelength-dependent attenuation that the calibration did not anticipate shifts the estimate. The bias is not random noise that averages out; it is a systematic offset tied to a protected characteristic, and averaging over a mostly light-skinned population simply hides it.

Measuring skin tone properly, and auditing the gap

You cannot fix a disparity you refuse to measure, and you cannot measure it well with a bad ruler. The Fitzpatrick scale, a six-point dermatology classification built to predict sunburn, is the most common label, but it was designed around burning propensity in lighter skin, self-report is unreliable, and its upper categories compress most darker tones together. The measurement-grade alternative is the individual typology angle (ITA), a continuous quantity derived from colorimeter readings in the CIE L\*a\*b\* color space, \(\mathrm{ITA}=\arctan\!\big((L^{*}-50)/b^{*}\big)\cdot 180/\pi\), which correlates with objectively measured melanin content. When you build or consume a wearable dataset, prefer an objective melanin or ITA reading, record it as first-class metadata, and never let skin-tone labels leak through a per-recording split (Chapter 5): a model that learns "this individual" learns their skin along the way, and the disparity then hides inside memorization.

Auditing itself is disaggregation, not a single scalar. Compute your metric (heart-rate mean absolute error, occult-hypoxemia rate, AFib sensitivity) separately within each skin-tone stratum, report the worst-group value alongside the average, and treat the largest between-group gap as a headline number rather than a footnote. An aggregate that looks excellent can hide a group for whom the device barely works, because the well-served majority dominates the mean. The code below simulates this audit on an SpO2-style pipeline and shows how a globally modest bias decomposes into a benign light-skin residual and a clinically serious dark-skin offset.

import numpy as np

rng = np.random.default_rng(0)
n = 6000
# Skin-tone group: 0 = light, 1 = intermediate, 2 = dark
group = rng.choice([0, 1, 2], size=n, p=[0.55, 0.30, 0.15])
true_spo2 = rng.uniform(82, 99, size=n)            # arterial ground truth

# Device reads high on darker skin: a group-dependent positive bias
bias_by_group = np.array([0.2, 1.1, 3.3])          # percentage points
noise = rng.normal(0, 1.2, size=n)
device_spo2 = true_spo2 + bias_by_group[group] + noise

def occult_rate(true_s, dev_s):
    # 'Occult hypoxemia': truly hypoxemic (<= 88) but device reassures (>= 92)
    hypoxemic = true_s <= 88
    return np.mean(dev_s[hypoxemic] >= 92) if hypoxemic.any() else float("nan")

names = ["light", "intermediate", "dark"]
print(f"{'group':13s}{'mean bias':>10s}{'occult %':>10s}")
for g in (0, 1, 2):
    m = group == g
    print(f"{names[g]:13s}{device_spo2[m].mean()-true_spo2[m].mean():10.2f}"
          f"{100*occult_rate(true_spo2[m], device_spo2[m]):10.1f}")

overall = 100 * occult_rate(true_spo2, device_spo2)
print(f"\nOverall occult rate: {overall:.1f}%  "
      f"; the dark-skin row is what that patient experiences")

Mitigation: hardware, data, and the calibration you keep

The fixes span the stack. In hardware, longer wavelengths (red and infrared rather than green alone), higher LED drive current with adaptive gain, multiple emitter-detector spacings, and denser diode arrays all recover photons on dark skin; a transmittance fingertip site sees more pulsatile signal than a reflectance wrist site. In data, the calibration and validation cohorts must span the full range of ITA, which historically they did not, and the split must be leakage-safe so a diverse-looking dataset cannot pass a per-subject shortcut. In algorithms, signal-quality gating (Section 30.6) is the honest first move: if the pulse-to-noise ratio is too low to trust, the device should abstain rather than emit a confident wrong number, and abstention rate then itself becomes a fairness metric you must equalize. Calibrated uncertainty (Chapter 18) lets the model widen its interval on hard-to-read skin instead of staying falsely narrow, and group-conditional conformal prediction can guarantee coverage within each stratum rather than only on average.

What's Next

In Chapter 31, we leave the pulsing capillary bed for the electrical storm of the brain. EEG, neural signals, and brain-computer interfaces bring their own version of the fairness-and-calibration problem, where hair, electrode contact, and inter-subject variability play the role melanin plays here, and where a signal even fainter than the PPG's must be pulled from noise before any inference is trusted.