Comparing two measurement methods (Passing-Bablok, Deming)

In brief

Two measurement methods measured the same samples. The method comparison under “Do ratings agree?” (with exactly two number columns, next to Bland-Altman) shows whether they differ by a fixed amount (constant not 0) or by a factor (slope not 1). Both procedures, Passing-Bablok and Deming, treat both measurements as having error; an ordinary regression would not and would give a slope that is too flat.

Passing-Bablok

• Calculates as the R package mcr (version 1.3.3.1): median of the slopes of all pairs of points, shifted by the rule of Passing and Bablok, angle measure, analytical interval. It is robust against outliers and needs no normal distribution.
• It is blocked for negative values (as in mcr; shifting the data would change the constant and is not done) and for a non-positive association. It needs continuous values: with fewer than 20 different values a note appears, the interval becomes coarse. It compares every pair with every other, so at most 4,000 samples are allowed.
• The cusum test for linearity shows only the test statistic h and the residual plot, no p value: the formula of the p value is not documented in the original. An unremarkable value is no proof of linearity.

Deming and the ratio λ

• λ is the error variance of the measurement on the horizontal axis divided by that on the vertical axis. The default is λ = 1: both methods measure with equally large error. The direction differs in every program; Statable follows the R package mcr.
• λ can be determined from repeated measurements (two measurements per sample and method), not from the data of the comparison alone. A wrong λ distorts the line; a table shows the slope for λ = 0.5, 1 and 2 so it becomes visible how much λ matters. The interval comes from the jackknife after Linnet (1990).

Reading the result

• If the interval of the constant does not contain 0, there is an indication of a constant deviation; if that of the slope does not contain 1, an indication of a proportional one. This is only an indication, not proof that the methods are equivalent or differ.
• The picture shows the samples, the identity line y = x (dashed) and both lines. The line applies only within the range of the measured values. Bland-Altman shows the differences against the mean, Passing-Bablok and Deming the line; the two belong together.
• With a case weight the method comparison is blocked: every sample counts once.

For specialists

Passing-Bablok follows calc_PaBa of mcr step by step (tolerance difference 1e-12, offset from angles up to −π/4, rank rule, C rounded to a whole number) and agrees with mcr and the reference sets of the program “Calanas” from the package test to 1e-9. Deming: Linnet (1990), jackknife with t(n − 2), as mcr. Sources: Passing and Bablok (1983), J Clin Chem Clin Biochem 21, 709-720; Linnet (1990), Statistics in Medicine 9, 1463-1473.