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AVERAGE OF DELTA – A NEW CONCEPT IN QUALITY CONTROL

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AVERAGE OF DELTA – A NEW CONCEPT IN QUALITY CONTROL

GRD Jones

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

APCCB 2004

- 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 theAverage of Delta(AOD) a new QC tool for clinical laboratories.

APCCB 2004

- A Delta Valueis 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

APCCB 2004

- 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.

APCCB 2004

- 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.

APCCB 2004

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)

AOD value

Sample Number

Purple: n=2 SD = 0.22

Red: n=10 SD = 0.10

Blue: n=50 SD = 0.045

APCCB 2004

- 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.

APCCB 2004

Figure 2.

- AOD functions for NAOD of 2, 10 and 50.
- CVa = 0.1, CVwi = 0.2
- A fixed bias of 0.3 was introduced at sample 10.
- The red lines show the 2.5 x SDAOD. For AOD2 the value is 0.56; for AOD10, 0.24; for AOD 50, 0.11.
- Five example AOD functions are shown in each graph ( ).
- Blue arrows show N90.
- Orange arrows show average first rule firing.

AOD2

14

36

AOD10

10

20

AOD50

18

30

Sample Number

APCCB 2004

- 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.

APCCB 2004

A

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

N90 Average 1st Firing

CVwi/CVa

B

CVwi/CVa

APCCB 2004

Table.

- Examples of Cvwi / CVa .
- CVwi from Westgard Website (www.westgard.com)
- CVa from SydPath Laboratory (Olympus AU2700)

APCCB 2004

- 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

APCCB 2004

- 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.

APCCB 2004