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

Abstract

Background: The critical difference (CD), the smallest difference between sequential laboratory results which is associated with a true change in the patient, is commonly calculated by assuming the same standard deviation (SD) for the initial and subsequent measurements. The calculation of the CD is re-examined without making this assumption. Methods: A formula for CD is developed, which specifies that even with the assumption of constant coefficient of variations (CV) at the 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 increase the CD for rises in analyte concentration and to decrease the CD for falls in concentration. These effects are caused by increased SD for the second measurement compared with the first when the second measurement is higher, and the reverse when the second is lower. Conclusions: Replacing the usual assumption of similar total result SD for both measurements included in the CD calculation with a calculation of the SD at both analyte concentrations leads to an increase in the magnitude of the CD for rises in analyte concentration and a decrease for falls in analyte concentration. This change is proposed for all forms of CD calculations.