Regression Analysis Guidelines

Deming Regression (Recommended)

Slope b = (Syy − λ·Sxx + √((Syy − λ·Sxx)² + 4λ·Sxy²)) / (2·Sxy)

The CLSI-preferred regression method for method comparisons. Unlike Ordinary Least Squares, Deming regression accounts for random measurement error in both the X and Y variables. The lambda (λ) parameter represents the ratio of error variances; λ = 1 is standard when both methods are assumed to have similar imprecision. Confidence intervals for the slope and intercept are calculated using the jackknife (leave-one-out) method, which is robust and does not require distributional assumptions about the residuals.

Passing-Bablok Regression (Non-Parametric)

Slope = median of all pairwise slopes Sᵢⱼ = (yⱼ − yᵢ) / (xⱼ − xᵢ), adjusted by rank K

A robust, non-parametric regression method that is resistant to outliers and makes no distributional assumptions about the data. The slope is estimated as the median of all pairwise slopes between data points, with a rank adjustment (K) for ties. The intercept is the median of (yᵢ − slope·xᵢ) across all points. Confidence intervals are computed using the bootstrap percentile method (1,000 resamples) per CLSI EP09C recommendations. Preferred when data contain influential outliers or when normality cannot be assumed.

Ordinary Least Squares (OLS)

Slope b = Σ(xᵢ − x̄)(yᵢ − ȳ) / Σ(xᵢ − x̄)²; Intercept a = ȳ − b·x̄

The classical least-squares regression that minimizes vertical residuals (error in Y only). OLS assumes the reference method (X) is measured without error — an assumption that is rarely satisfied in practice. As a result, OLS typically underestimates the true slope when X contains measurement error. It is provided for reference and compatibility but Deming or Passing-Bablok regression is generally preferred for method comparison studies.