Requiem for the Passing-Bablok nonparametric regression in assessing the agreement between two measurement methods

Regulatory guidelines recommend non-parametric Passing-Bablok regression for evaluating the agreement between two measurement methods in laboratory settings. However, concluding for the agreement if the 95 % CI of the slope and of the intercept include 1 and 0, respectively is incorrect since the agreement assessment must focus on a null hypothesis of not equivalence and an alternative hypothesis of equivalence.

We exhaustively simulated appropriate structural models with several values of slope, intercept and measurement error by keeping equal variances and means of the two methods. We calculated the slope and intercept bias of four regressions: non-parametric Passing-Bablok, Theil, Ordinary Least Squares and Deming. In addition, we calculated the percentages of the agreement according to the not shareable Passing-Bablok suggestion. Furthermore, we calculated the percentages of the 95 % CI of the slope and of the intercept included within sensible equivalence thresholds for assessing the agreement.

Passing-Bablok procedure gives unbiased estimates, a little more and less biased than those from Deming's regression. The percentages of rejecting the hypothesis of no-agreement, according to the wrong Passing-Bablok's approach are correctly near to 0.05 Type I error under the agreement and also for 0.990≤slopes≤1.005. However, they are too low for slopes >1.05 and <0.950.

The Passing-Bablok 95 % CIs are too wide for being included in sensible agreement thresholds according to a population equivalence model and, finally, this approach cannot be considered under the best agreement model of the individual equivalence.