A statistical basis for harmonization of thyroid stimulating hormone immunoassays using a robust factor analysis model

Clin Chem Lab Med. 2014 Jul;52(7):965-72. doi: 10.1515/cclm-2013-1038.


Background: Between-method equivalence ideally is achieved by calibration against an SI-traceable reference measurement procedure. For measurement of thyroid stimulating hormone (TSH), it is unlikely to accomplish this goal in mid-term. Therefore, we investigated a statistical alternative based on a factor analysis (FA) model.

Methods: The FA model was applied to TSH results for 94 samples generated by 14 immunoassays (concentration range: 0.0005-78 mIU/L). The dataset did not fulfill the assumption of a homogeneous sample from an elliptically symmetric distribution, and, therefore, required standardization prior to application of the FA model. As outliers and missing values also occurred, the key quantities of the FA model had to be estimated with a method that can handle these complications. We selected a robust alternating regressions (RAR) method, which replaces in the minimization criterion of the fitting process the squared differences between results xij and model fit x^ij ${\hat x_{ij}}$ by a weighted absolute difference. The weights are adaptively determined in successive regressions, which down weighs the outliers. The weights for missing values are set to zero.

Results: The quality of the estimated targets was reflected by their central position in the distributions, and description of the relationship between results and targets by a simple two-parameter regression equation with high correlation coefficients and low SDs of the percentage-residuals. Mathematical recalibration eliminated the method differences and improved the between-method CV from 11% to 6%.

Conclusions: RAR applied to a multimethod comparison dataset hampered by outliers and missing values, is fit to the purpose of harmonization.

MeSH terms

  • Factor Analysis, Statistical
  • Humans
  • Immunoassay*
  • Thyrotropin / analysis*


  • Thyrotropin