Critical difference calculations revised: inclusion of variation in standard deviation with analyte concentration

This version was published on 1 November 2009

Ann Clin Biochem 2009;46:517-519
© 2009 Association for Clinical Biochemistry


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Graham Ross Dallas Jones1,2

1 Department of Chemical Pathology, SydPath, St Vincent’s Hospital, Sydney, Victoria St, Darlinghurst, NSW, 2010, Australia;
2 Faculty of Medicine, University of New South Wales, Randwick, NSW, 2031, Australia

Corresponding author: Graham Ross Dallas Jones, Department of Chemical Pathology, SydPath, St Vincent’s Hospital, Sydney, Victoria St, Darlinghurst, NSW, 2010, Australia. Email: gjones{at}

Background: The critical difference (CD), the smallest difference betweensequential laboratory results which is associated with a truechange in the patient, is commonly calculated by assuming thesame standard deviation (SD) for the initial and subsequentmeasurements. The calculation of the CD is re-examined withoutmaking this assumption.

Methods: A formula for CD is developed, which specifies that even withthe assumption of constant coefficient of variations (CV) atthe two measurement concentrations used in the calculation,there will be different SDs due to different concentrations.

Results: The effect of removing the assumption of constant SD is to increasethe CD for rises in analyte concentration and to decrease theCD for falls in concentration. These effects are caused by increasedSD for the second measurement compared with the first when thesecond measurement is higher, and the reverse when the secondis lower.

Conclusions: Replacing the usual assumption of similar total result SD forboth measurements included in the CD calculation with a calculationof the SD at both analyte concentrations leads to an increasein the magnitude of the CD for rises in analyte concentrationand a decrease for falls in analyte concentration. This changeis proposed for all forms of CD calculations.

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