Statistical correction for non-parallelism in a urinary enzyme immunoassay

J Immunoassay Immunochem. 2004;25(3):259-78. doi: 10.1081/ias-200028078.


Our aim was to develop a statistical method to correct for non-parallelism in an estrone-3-glucuronide (E1G) enzyme immunoassay (EIA). Non-parallelism of serially diluted urine specimens with a calibration curve was demonstrated in an EIA for E1G. A linear mixed-effects analysis of 40 urine specimens was used to model the relationship of E1G concentration with urine volume and derive a statistical correction. The model was validated on an independent sample and applied to 30 menstrual cycles from American women. Specificity, detection limit, parallelism, recovery, correlation with serum estradiol, and imprecision of the assay were determined. Intra-and inter-assay CVs were less than 14% for high- and low-urine controls. Urinary E1G across the menstrual cycle was highly correlated with serum estradiol (r= 0.94). Non-parallelism produced decreasing E1G concentration with increase in urine volume (slope = -0.210, p < 0.0001). At 50% inhibition, the assay had 100% cross-reactivity with E1G and 83% with 17beta-estradiol 3-glucuronide. The dose-response curve of the latter did not parallel that of E1G and is a possible cause of the non-parallelism. The statistical correction adjusting E1G concentration to a standardized urine volume produced parallelism in 24 independent specimens (slope = -0.043+/-0.010), and improved the average CV of E1G concentration across dilutions from 19.5%+/-5.6% before correction to 10.3%+/-5.3% after correction. A statistical method based on linear mixed effects modeling is an expedient approach for correction of non-parallelism, particularly for hormone data that will be analyzed in aggregate.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Adult
  • Data Interpretation, Statistical*
  • Enzyme-Linked Immunosorbent Assay / methods
  • Enzyme-Linked Immunosorbent Assay / statistics & numerical data
  • Estradiol / analogs & derivatives*
  • Estradiol / blood*
  • Estrone / analogs & derivatives*
  • Estrone / urine*
  • Female
  • Humans
  • Menstrual Cycle / blood*
  • Menstrual Cycle / urine*
  • Middle Aged
  • Sensitivity and Specificity


  • estradiol-3-glucuronide
  • estrone-3-glucuronide
  • Estrone
  • Estradiol