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The Passing-Bablok and Theil-Sen regression are closely relatednon-parametric methods to estimate the regression coefficients and build testson the relationship between the dependent and independent variables. Bothmethods rely on the slopes of the connecting lines between pairwisemeasurements. While Theil and Sen assume no measurement errors in theindependent variable, the method from Passing and Bablok accounts for errors inboth variables. Here we consider the case where multiple, e.g. repeated,measurements with errors in both variables are available for m samples. We showthat in this case the slopes between repeated measurements need to be excludedto obtain an unbiased estimate. We prove that the resultingBlock-Passing-Bablok estimate for grouped data is asymptotically normallydistributed. If measurements of the independent variable are without error thevariance of the estimate equals the variance of the Theil-Sen method with tiedranks. If both variables are measured with imprecision the result depends onthe fraction of measurements between groups that fall within the range of eachother. Only if no overlap between measurements of different groups occurs thevariance equals again the tied ranks version. Otherwise, the variance issmaller. We explicitly compute this variance and provide a method comparisontest for data with repeated measurements based on the method from Passing andBablok for independent measurements. If repeated measurements are consideredthis test has a higher power to detect the true relationship between twomethods.

Method comparison with repeated measurements -- Passing-Bablok regression for grouped data with errors in both variables