The Passing-Bablok and Theil-Sen regression are closely related non-parametric methods to estimate the regression coefficients and build tests on the relationship between the dependent and independent variables. Both methods rely on the slopes of the connecting lines between pairwise measurements. While Theil and Sen assume no measurement errors in the independent variable, the method from Passing and Bablok accounts for errors in both variables. Here we consider the case where multiple, e.g. repeated, measurements with errors in both variables are available for m samples. We show that in this case the slopes between repeated measurements need to be excluded to obtain an unbiased estimate. We prove that the resulting Block-Passing-Bablok estimate for grouped data is asymptotically normally distributed. If measurements of the independent variable are without error the variance of the estimate equals the variance of the Theil-Sen method with tied ranks. If both variables are measured with imprecision the result depends on the fraction of measurements between groups that fall within the range of each other. Only if no overlap between measurements of different groups occurs the variance equals again the tied ranks version. Otherwise, the variance is smaller. We explicitly compute this variance and provide a method comparison test for data with repeated measurements based on the method from Passing and Bablok for independent measurements. If repeated measurements are considered this test has a higher power to detect the true relationship between two methods.

中文翻译：

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与重复测量的方法比较 - 两个变量都有误差的分组数据的 Passing-Bablok 回归

Passing-Bablok 和 Theil-Sen 回归是密切相关的非参数方法，用于估计回归系数并建立对因变量和自变量之间关系的检验。这两种方法都依赖于成对测量之间连接线的斜率。虽然 Theil 和 Sen 假设自变量中没有测量误差，但 Passing 和 Bablok 的方法考虑了两个变量中的误差。在这里，我们考虑对于 m 个样本可以使用多个（例如重复）在两个变量中都有误差的测量的情况。我们表明，在这种情况下，需要排除重复测量之间的斜率以获得无偏估计。我们证明了分组数据的 Block-Passing-Bablok 估计结果是渐近正态分布的。如果自变量的测量值没有错误，则估计的方差等于具有绑定等级的 Theil-Sen 方法的方差。如果两个变量的测量都不精确，则结果取决于落入彼此范围内的组之间的测量分数。只有当不同组的测量值之间没有重叠时，方差才再次等于并列等级版本。否则，方差较小。我们明确地计算了这个方差，并根据 Passing 和 Bablok 的独立测量方法为重复测量的数据提供了方法比较测试。如果考虑重复测量，则此测试具有更高的能力来检测两种方法之间的真实关系。