Average of delta – a new concept in quality control grd jones

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  • GRD Jones

  • Department of Chemical Pathology, St Vincents Hospital, Sydney, Australia


  • The Average of Normals (AON) is an accepted QC process for clinical laboratories.

  • AON is the average of a set number of patient results, usually within set limits (eg normal range).

  • The AON rule “fires” when the function exceeds a pre-set limit (eg 2.5 x analytical CV).

  • Delta checks are the comparison of a result with a previous result from the same patient.

  • Delta checks are used to detect blunders or other errors

  • I combine these concepts to produce the Average of Delta (AOD) a new QC tool for clinical laboratories.


  • A Delta Value is a recent patient result minus the preceding result for that patient.

  • An AOD function is the average of a series of delta values.

  • AODN is an AOD function averaging N delta values.

  • NAOD is the number of samples included in an AOD function.

  • N90 is the number of samples with valid previous result, required to detect a change in assay bias with 90% probability using an AOD function.

  • CVwi is the within-individual Biological Variation.

  • CVa is the analytical variation expressed as a CV.

  • SDAOD is the SD of the AOD function


  • AOD functions were modelled in a spreadsheet application using Microsoft Excel.

  • Variations in CVa and CVwi were modelled using the random number generator with a Normal distribution.

  • Models were based on 100 data sets, each of 110 delta values.

  • Factors adjusted in the model were:

    • the ratio of Cva/Cvwi
    • NAOD
    • Bias changes in assay performance.

Modelling Equations

  • Data sets were generated for various values of CVa and CVwi with the variation (CVdata set) in results described as follows

    • CVdata set = SQRT(CVa2 + CVwi2)
  • Second data sets were independently generated using the same values for CVa and CVwi

  • Delta Values were were obtained by subtracting the data points from the second data set from those in the first to produce a series of delta values.

  • Changes in bias were modelled by addition of fixed amounts to the delta values at a fixed point in the data set.

  • AOD functions were set to trigger if a data point fell outside limits defines by +/- 2.5 SDAOD.

AOD Functions

  • Figure 1

  • AOD functions for various values of NAOD. CVa = 0.1, CVwi = 0.2

  • As the value of N increases, the scatter of the AOD function decreases.

  • The decrease in SD with increasing N is equal to dividing by the square root of N. (data not shown)

Effects of Bias on AOD Functions

  • A fixed bias was added after delta value 10 in each data set.

  • The AOD function followed the change in bias with the following features:

    • With smaller values of NAOD, the response occurred more rapidly, but was smaller relative to the scatter of the AOD function
    • With higher values of NAOD, the response was slower, but was larger relative to the scatter of the AOD function.
  • Examples are shown in figure 2.

Error Detection with AOD

  • Error detection of bias can be measured as the number of delta values (samples with previous results) required to detect changes in bias with specified certainty.

  • N90 and average first detection for a range of values for Cva/Cvwi and NAOD are shown in figure 3.

  • The following conclusions can be drawn:

    • Earlier error detection occurs with lower values of Cva/Cvwi
    • Error detection generally varies with NAOD in a “U-shape” with an optimal range of values depending on CVa/CVwi .
  • Examples of actual values for CVa/CVwi are in the table.

Figure 3

  • Figure 3

  • Number of samples required for average 1st firing (A) and N90 (B) for detection of a shift of 2.5 x CVa for various values of CVwi/CVa and NAOD.

  • Earlier error detection with lower CVwi/CVa

  • Optimal error detection with NAOD 5-20


  • The limitation of AON is the ratio of group biological variation to analytical CV.

  • AOD may outperform AON if:

    • CVwi is small compared to between-person biological variation (a low Index of Individuality).
    • The frequency of samples with previous results is high.
    • Clinics or weekends affect AON results. Note than AOD should not be affected by change in patient mix as it uses patients as their own control.
  • AON may complement standard QC if it can:


  • Average of Delta may allow improved error detection without additional QC testing.

  • The process would most suit tests as follows:

    • A low within-individual biological variation compared to the analytical variation.
    • A high frequency of repeat testing.
  • Software programs must be written to further evaluate and this tool and allow for use in the routine environment.

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