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

AVERAGE OF DELTA – A NEW CONCEPT IN QUALITY CONTROL

• GRD Jones

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

Background

• 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.

Terminology

• 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

Methods

• 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

Discussion

• 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:

• Detect smaller errors than standard QC
• Detect errors before standard QC
• Allow less frequent use of standard QC

Conclusions

• 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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