Diagnostics › Method comparison

Deming regression

Deming regression compares two measurement methods when both carry measurement error — the parametric counterpart to Passing-Bablok.

What is Deming regression?

Standard OLS regression assumes the X variable is known exactly. In method comparison both axes are measurements with noise — OLS biases the slope toward 0. Deming regression generalises by allowing error in both axes, with the variance ratio λ = σ_x² / σ_y² as an input.

When λ = 1 (equal precision both ways), Deming reduces to orthogonal regression. When you don't know λ, set it from prior repeatability studies; setting it wrong biases the slope in a predictable way (large λ ⇒ slope closer to OLS, small λ ⇒ slope closer to the y-on-x inverse).

Compared to Passing-Bablok: Deming is parametric (sensitive to outliers) but gives parametric CIs; PB is robust but needs bootstrap.

When should I use Deming regression?

  • Two-method comparison when both methods have non-trivial measurement error.
  • When you have prior knowledge of the measurement-error variance ratio.

What data does it need?

Two numeric columns (Method 1, Method 2) + variance ratio λ.

What does it report?

Intercept + slope with CIs + fitted line on scatter.

What does it assume?

  • Independent paired measurements.
  • Approximately normal measurement errors.
  • Variance ratio λ correctly specified.

How do I interpret the result?

Slope CI containing 1 + intercept CI containing 0 ⇒ the two methods are in agreement; otherwise proportional / systematic bias is present.

See also

References

  • Deming (1943). Statistical Adjustment of Data.