Guest Essay
Quality Goal Index
Dr. David Parry of St. Boniface General Hospital in Winnipeg, provides us with data on Sigma metrics in two laboratories. Dr. Parry's innovation is a Quality Goal Index, a metric that can distinguish between precision and accuracy problems, as well as techniques to deal with calibrator lot changes.
Its Use in Benchmarking and Improving Sigma Quality Performance of Automated Analytic Tests
- Sigma Quality Performance
- Quality Goal Index
- Complete listing of applications, Sigma metrics, and QGI: Laboratory A
- Complete listing of applications, Sigma metrics and QGI: Laboratory B
- Summary of Laboratory Performance Problems
- Sigma Quality Improvement
- References
The long-term goal of six sigma quality management is to achieve an error rate of 3.4 or less per million opportunities for all laboratory processes. In percent terms, that’s an error rate of less than 0.001%. This very demanding goal is achievable or within reach for many automated analytic processes, but implicitly requires knowledge of which processes fall short of this goal and why. Hence, a systematic approach to benchmarking sigma quality performance of analytic processes is fundamental to practicing six sigma quality management. In order to achieve six sigma quality, it is necessary to assess and document which analytical processes do and do not achieve six sigma quality performance and to understand why.
Sigma Quality Performance
As discussed elsewhere (1), quality performance of any analytical process in a laboratory can be described in terms of its sigma metric. Calculation of sigma performance is quite simple:
Sigma = (TEa – Bias) / CV
The harder part is making sure that data used in this calculation really reflects current analytical performance. In my region, we turned to our on-analyzer quality control databases for estimates of imprecision (CV). This data reflects actual analytical imprecision, if and only if, data integrity has been maintained. Data integrity can be assured only when procedures are in place and rigorously practiced to exclude erroneous quality control results due to procedural blunders and statistical outliers. This does not mean excluding out-of-control results; no statistically-valid data should be edited out.
For estimates of test bias, our region makes use of Randox Interlaboratory Quality Assessment Scheme (RIAQS). This external quality assessment program, run out of Ireland, provides biweekly (every 2 weeks) challenges for a broad range of automated chemistry tests. There are two main attributes that make this program of particular value for assessing test bias. First, challenges are blind and second, they are at varying analyte concentrations. These two attributes, combined with its biweekly frequency and relatively large user base, make this database reflective, as close as possible, of “real-world” testing bias. Bias is calculated for each test application based on the average (running mean) bias of the last 10 values obtained over the preceding five month period, updated every two weeks.
Sigma quality management forces one to think in terms of quality needs, not just performance capabilities and this is good since it focuses attention on what really matters. The next step is setting quality goals. This in itself can be a real eye-opener and a little daunting. There are multiple sources for quality goals but the proviso, of course, is objectivity in selecting these goals in deference to analytic capabilities. We selected quality goals for total error (TEa) based on either biological variation or proficiency testing target data accessible through this website (2, 3), fully recognizing that at least some of these goals may need customizing to specific clinical requirements as our experience with this approach develops. Selecting test specific goals, as uncomfortable or imperfect a process as this may be, it reinforces the fact that good clinical practice is implicitly linked to quality of laboratory testing.
Once current and reliable data for imprecision and bias has been obtained and quality goals set, sigma quality performance is then calculated for each test application. These sigma metrics are date documented and used to benchmark existing sigma performance for inter-instrument and inter-laboratory comparisons within our region and for future historical reviews to assess performance changes.
To illustrate this approach, the sigma metrics for 60 automated test applications over three analytic platforms at one laboratory (site A) in our region indicates that twenty eight (46%) of these applications fall short of meeting six sigma quality performance. Of these, twelve fail to meet minimum sigma quality performance with metrics less than three and another four just meet minimal acceptable performance with sigma metrics between three and four. At another laboratory (site B) in our regional group (seven sites in total), the original data collected indicates more than half (57%) of the automated test applications do not achieve six sigma quality performance.
Quality Goal Index
It must be kept in mind that six sigma quality management is not only a tool for defining process performance but also a method for moving a process from its present error rate to a very low error rate. In order to achieve quality improvement of automated analytic tests where needed, it is important to understand the test-specific reasons for their quality shortcomings, be it either excessive imprecision, excessive bias or both. To facilitate this, performance data is assessed by calculating the quality goal index (QGI) by the following expression:
QGI = Bias / 1.5 CV
Derivation of this expression is based on mathematical reduction of the ratio (Bias/Accuracy Goal) / (CV/Precision Goal). The QGI ratio represents the relative extent to which both bias and precision meet their respective quality goals. The quality goals chosen for use in this expression are 1.5*TEa/6 for bias and TEa/6 for precision based on their widespread use in six sigma methodology literature. For those who feel that inclusion of a1.5 sigma shift in calculating the bias goal is not justified, then both quality goals can be calculated as TEa/6. The corresponding expression would then reduce to QGI = Bias/CV.
Examination of the unreduced equation gives better insight into how this data-evaluating tool works. For example, QGI is higher for a test application when bias exceeds its accuracy goal and imprecision meets its precision goal and QGI is lower when bias meets its accuracy goal and imprecision exceeds its precision goal. The criteria we use for interpreting QGI when test applications fall short of six sigma quality is as follows:
QGI Problem <0.8 Imprecision 0.8 - 1.2 Imprecision & Inaccuracy >1.2 Inaccuracy This quantifiable approach to problem assessment is computer programmable in Microsoft Excel using Visual Basic for Applications (VBA). Macro programming simplifies its application which is particularly helpful when dealing with larger numbers of tests at multiple lab sites. As an example of this approach, QGI indicates that of the 29 test applications that failed to meet six sigma quality performance at lab site A in our region, the main problem is excessive imprecision in 52%, with excessive inaccuracy occurring in 17%. At lab site B, the main problem is excessive inaccuracy in 73% with excessive imprecision being the problem in 20%. QGI provides easy insight into where improvement is required and can serve as a tool for focusing efforts on sigma quality improvement of automated analytic tests.
A complete listing of test applications, sigma metrics, and QGI results: Test Laboratory A:
APPLICATION
INSTUMENT
BIAS%
CV%
QG%
SIGMA
QGI
PROBLEM
Albumin
PPE-P1
1.40
3.40
10
2.53
0.27
Imprecision
Albumin
MOD-2
4.28
1.04
10
5.50
2.74
Inaccuracy
Alkaline Phosphatase
PPE-P1
-14.47
6.50
30
2.39
1.48
Inaccuracy
Alkaline Phosphatase
MOD-2
-13.03
6.00
30
2.83
1.45
Inaccuracy
ALT
PPE-P1
9.17
2.20
32.1
10.42
2.78
None
ALT
MOD-2
8.59
2.00
32.1
11.76
2.86
None
AST
PPE-P1
3.89
2.30
15.2
4.92
1.13
Inaccuracy/Imprecision
AST
MOD-2
0.87
1.30
15.2
11.02
0.45
None
Ammonia
PPE-P1
0.00
3.86
20
5.18
0.00
Imprecision
Ammonia
MOD-2
0.00
6.20
20
3.23
0.00
Imprecision
Total CO2
PPE-P1
0.22
1.62
10
6.04
0.09
None
Total CO2
MOD-2
4.62
2.90
10
1.86
1.06
Inaccuracy/Imprecision
Bilirubin, Direct
PPE-P1
3.99
4.90
48.5
9.08
0.54
None
Bilirubin, Direct
MOD-2
-7.65
2.00
48.5
20.43
2.55
None
Bilirubin, Total
PPE-P2
1.24
1.89
9.5
4.37
0.44
Imprecision
Bilirubin, Total
MOD-2
-3.84
2.20
9.5
2.57
1.16
Inaccuracy/Imprecision
Calcium
PPE-P1
-3.03
1.77
7.6
2.58
1.14
Inaccuracy/Imprecision
Calcium
MOD-2
-2.13
1.51
7.6
3.62
0.94
Inaccuracy/Imprecision
Chloride
PPE-P1
-0.43
1.10
5
4.15
0.26
Imprecision
Chloride
MOD-2
-0.63
1.80
5
2.43
0.23
Imprecision
Cholesterol
PPE-P1
-2.62
1.35
9
4.73
1.29
Inaccuracy
Cholesterol
MOD-2
1.99
1.29
9
5.43
1.03
Inaccuracy/ Imprecision
Creatine Kinase
PPE-P1
-1.25
1.00
30
28.75
0.83
None
Creatine Kinase
MOD-2
-1.01
1.50
30
19.33
0.45
None
Crearinine
PPE-P1
1.58
2.00
15
6.71
0.53
None
Creatinine
MOD-2
-0.06
1.40
15
10.67
0.03
None
GGT
PPE-P1
-2.21
2.20
25
10.36
0.67
None
GGT
MOD-2
-3.29
2.60
25
8.35
0.84
None
Glucose
PPE-P1
-0.20
1.09
6.3
5.60
0.12
Imprecision
Glucose
MOD-2
-1.47
0.80
6.3
6.04
1.23
None
HDL
PPE-P2
4.97
3.20
30
7.82
1.04
None
HDL
MOD-2
9.90
2.70
30
7.44
2.44
None
Hydroxybutrate
PPE-P1
-3.41
6.87
25
3.14
0.33
Imprecision
Iron
PPE-P1
6.08
2.20
30.7
11.19
1.84
None
Iron
MOD-2
5.05
1.40
30.7
18.32
2.40
None
LDH
PPE-P2
1.44
1.30
11.4
7.66
0.74
None
LDH
MOD-2
-0.27
1.30
11.4
8.56
0.14
None
Lipase
PPE-P2
-3.06
3.50
29.1
7.44
0.58
None
Lipase
MOD-2
-6.83
4.10
29.1
5.43
1.11
Inaccuracy/Imprecision
Lactate
PPE-P2
0.00
1.68
30.4
18.10
0.00
None
Lactate
MOD-2
0.00
0.86
30.4
35.35
0.00
None
Magnesium
PPE-P2
2.31
2.20
25
10.31
0.70
None
Magnesium
MOD-2
-0.98
3.90
25
6.16
0.17
None
Phosphate
PPE-P2
-0.22
1.86
4.3
2.19
0.08
Imprecision
Phosphate
MOD-2
1.38
1.70
4.3
1.72
0.54
Imprecision
Potassium
PPE-P1
-0.08
1.15
5.8
4.97
0.05
Imprecision
Potassium
PPE-P2
-0.08
0.72
5.8
7.94
0.07
None
Potassium
MOD-2
-1.50
1.12
5.8
3.84
0.89
Inaccuracy/Imprecision
Protein
PPE-P2
-0.09
1.80
10
5.51
0.03
Imprecision
Protein
MOD-2
-1.09
1.05
10
8.49
0.69
None
Sodium
PPE-P1
1.09
1.01
2.4
1.30
0.72
Imprecision
Sodium
PPE-P2
1.09
0.89
2.4
1.47
0.82
Inaccuracy/Imprecision
Sodium
MOD-2
-0.53
0.87
2.4
2.15
0.41
Imprecision
TIBC
PPE-P2
-2.57
1.80
30
15.24
0.95
None
Triglycerides
PPE-P2
10.00
1.59
27.9
11.26
4.19
None
Triglycerides
MOD-2
-1.63
3.09
27.9
8.50
0.35
None
Urea
PPE-P2
1.09
0.74
15.7
19.74
0.98
None
Urea
MOD-2
0.04
1.01
15.7
15.50
0.03
None
Uric Acid
PPE-P2
6.57
0.70
11.9
7.61
6.26
None
Uric Acid
MOD-2
5.76
1.10
11.9
5.58
3.49
Inaccuracy
A complete listing of test applications, sigma metrics, and QGI results: Test Laboratory A:
APPLICATION
INSTUMENT
BIAS%
CV%
QG%
SIGMA
QGI
PROBLEM
Albumin
PE-1
4.47
2.51
10.00
2.20
7.48
Inaccuracy
Albumin
PE-2
3.05
2.51
10.00
2.77
5.10
Inaccuracy
Alk Phos
PE-1
-13.84
2.25
30.00
7.18
20.76
None
Alk Phos
PE-2
-12.73
2.25
30.00
7.68
19.10
None
ALT
PE-1
1.37
3.05
32.10
10.08
2.79
None
ALT
PE-2
0.20
3.05
32.10
10.46
0.41
None
AST
PE-1
1.73
1.86
15.20
7.24
2.15
None
AST
PE-2
0.81
1.86
15.20
7.74
1.00
None
Bicarbonate
PE-1
-1.82
6.58
10.00
1.24
7.98
Inaccuracy
Bicarbonate
PE-2
-3.84
6.58
10.00
0.94
16.84
Inaccuracy
Bilirubin, Direct
PE-1
-20.63
4.65
44.50
5.13
63.95
Inaccuracy
Bilirubin, Direct
PE-2
-26.49
4.65
44.50
3.87
82.12
Inaccuracy
Bilirubin, Total
PE-1
0.80
3.22
9.50
2.70
1.72
Inaccuracy
Bilirubin, Total
PE-2
-1.37
3.22
9.50
2.52
2.94
Inaccuracy
Calcium, Total
PE-1
-3.18
2.42
7.60
1.83
5.13
Inaccuracy
Calcium, Total
PE-2
-2.23
2.42
7.60
2.22
3.60
Inaccuracy
Chloride
PE-1
-1.40
1.65
5.00
2.18
1.54
Inaccuracy
Chloride
PE-2
-0.89
1.65
5.00
2.49
0.98
Inaccuracy/Imprecision
Cholesterol
PE-1
1.42
1.82
9.00
4.16
1.72
Inaccuracy
Cholesterol
PE-2
-0.66
1.82
9.00
4.58
0.80
Inaccuracy/Imprecision
CK, Total
PE-1
-4.17
1.93
30.00
13.38
5.37
None
CK, Total
PE-2
-3.77
1.93
30.00
13.59
4.85
None
Creatinine
PE-1
-3.25
2.98
15.00
3.94
6.46
Inaccuracy
Creatinine
PE-2
-1.96
2.98
15.00
4.38
3.89
Inaccuracy
GGT
PE-1
-3.25
2.27
25.00
9.58
4.92
None
GGT
PE-2
-2.48
2.27
25.00
9.92
3.75
None
Glucose
PE-1
1.26
2.10
6.30
2.40
1.76
Inaccuracy
Glucose
PE-2
-0.22
2.10
6.30
2.90
0.31
Imprecision
HDL-C
PE-1
1.69
2.15
30.00
13.17
2.42
None
HDL-C
PE-2
3.45
2.15
30.00
12.35
4.95
None
Hydroxybutrate
PE-1
2.34
3.85
25.00
5.89
6.01
Inaccuracy
Hydroxybutyrate
PE-2
2.04
3.85
25.00
5.96
5.24
Inaccuracy
Iron
PE-1
0.45
2.58
30.70
11.72
0.77
None
Iron
PE-2
3.98
2.58
30.70
10.36
6.85
None
LDH
PE-1
-0.72
1.28
11.40
8.34
0.61
None
LDH
PE-2
0.28
1.28
11.40
8.69
0.24
None
Lipase
PE-1
0.54
4.58
29.10
6.24
1.65
None
Lipase
PE-2
-0.31
4.58
29.10
6.29
0.95
None
Magnesium
PE-1
0.62
2.86
25.00
8.52
1.18
None
Magnesium
PE-2
1.29
2.86
25.00
8.29
2.46
None
Phosphate
PE-1
-0.59
3.23
4.30
1.15
1.27
Inaccuracy
Phosphate
PE-2
1.06
3.23
4.30
1.00
2.28
Inaccuracy
Potassium
PE-1
-1.08
13.7
5.80
0.34
9.86
Inaccuracy
Potassium
PE-2
-0.71
13.7
5.80
0.37
6.48
Inaccuracy
Protein, Total
PE-1
-0.59
1.52
10.00
6.19
0.60
None
Protein, Total
PE-2
-0.14
1.52
10.00
6.49
0.14
None
Sodium
PE-1
-0.63
1.79
2.40
0.99
0.75
Imprecision
Sodium
PE-2
-0.17
1.79
2.40
1.25
0.20
Imprecision
UIBC/TIBC
PE-1
-10.00
8.70
30.00
2.30
58.00
Inaccuracy
UIBC/TIBC
PE-2
-3.24
8.70
30.00
3.08
18.79
Inaccuracy
Triglycerides
PE-1
4.21
2.27
27.90
10.44
6.37
None
Triglycerides
PE-2
-2.35
2.27
27.90
11.26
3.56
None
Urea
PE-1
0.00
2.80
15.70
5.61
0.00
Imprecision
Urea
PE-2
-0.91
2.80
15.70
5.28
1.70
Inaccuracy
Uric Acid
PE-1
5.93
1.62
11.90
3.69
6.40
Inaccuracy
Uric Acid
PE-2
5.31
1.62
11.90
4.07
5.73
Inaccuracy
Summary of Laboratory Performance Problems
SITE
NUMBER OF PERFORMANCE PROBLEMS (PERCENT)
NONE
IMPRECISION
INACCURRACY
BOTH
Lab A
32 (54%)
14 (23%)
5 (8%)
9 (15%)
Lab B
24 (43%)
4 (7%)
26 (46%)
2 (4%)
Sigma Quality Improvement
One cause of difficulty in reducing inaccuracy of automated tests is the variable error introduced when switching from one lot of calibrator to another. The manufacturer of the multi-test calibrator we use claims a variability limit of +/-5%. A tolerance of 10% is not adequate for achieving long-term accuracy for six sigma quality performance of automated analytic tests.
Achieving and maintaining six sigma quality performance requires a rigorous approach to calibrator lot changes, one linked to a bias reference point or “anchor”. To accomplish this, the current biases of our “anchor tests” are incorporated into the decision making process during new calibrator lot evaluation. This concept is easiest to understand when described by the procedural steps involved as follows:
TEST EXAMPLES Creatinine Urea 1 Obtain assigned value for new calibrator 331.0 15.1 2 Assay new calibrator over a one month period to establish assayed mean value 322.34 15.28 3 Subtract assayed mean value from calibrator assigned value to determine % difference from assigned value 2.62 -1.19 4 Obtain % bias from RIQAS 0.41 1.03 5 Calculate % combined error (% difference + % bias) 3.03 -0.17 6 Calculate accuracy goal (1.5TEa/6) 3.8 3.9 7 Determine ratio % bias / accuracy goal (B/AG) 0.11 0.26 8 Determine ratio % combined error / accuracy goal (CE/AG) 0.89 -0.04 9 Select either assigned value or assayed mean value for new calibrator setpoint depending on which ratio is numerically lower. If B/AG < CE/AG, use assayed mean value. If CE/AG < B/AG, use new calibrator assigned value 322.34 15.1 In the accompanying test examples, the assayed mean value is selected as calibrator setpoint for creatinine, whereas the assigned value is selected for urea. Each of these choices gives best calibrator cross-over accuracy on the RIQAS quality assessment program. Using this approach for twenty-three “anchor tests” at laboratory site A, it was determined that best cross-over accuracy was achieved by using the assigned values for new calibrator setpoints for 12 of these tests (Table 3). Assayed means provided better cross-over accuracy for the remaining 11 tests. In addition, the number of tests exceeding their six sigma accuracy goals decreased from five with the old lot to three with the new lot of calibrator, which is expected to improve further with successive lot changes.
APPLICATION
ASSIGNED VALUE
ASSAYED MEAN
%DIFFERENCE
BIAS%
CE%
AG%
B/AG
CE/AG
NEW SETPOINT
Albumin
28.00
28.44
-1.57
1.77
0.20
2.5
0.71
0.08
28.0
Alkaline Phosphatase
227.00
217.50
4.19
-14.60
-10.41
7.5
-1.95
-1.39
227.0
ALT
113.00
122.39
-8.31
9.88
1.57
8.0
1.23
0.20
113.0
AST
111.00
115.50
-4.05
2.78
-1.27
3.8
0.73
-0.33
111.0
Bilirubin, Direct
40.50
37.56
7.26
3.03
10.29
11.1
0.27
0.92
37.56
Bilirubin, Total
84.00
73.11
12.96
-0.13
12.84
2.4
-0.05
5.41
73.11
Calcium
2.220
2.140
3.60
-3.12
0.48
1.9
-1.64
0.25
2.22
Choloesterol
3.990
3.960
0.75
-1.85
-1.09
2.3
-0.82
-0.49
3.99
Creatine Kinase
350.00
334.87
4.32
-1.44
2.88
7.6
-0.19
0.38
334.87
Creatinine
331.00
322.34
2.62
0.41
3.03
3.8
0.11
0.81
322.34
Iron
38.50
39.09
-1.53
5.51
3.97
7.7
0.72
0.52
38.5
GGT
93.60
91.94
1.77
-1.97
-0.20
6.3
-0.32
-0.03
93.6
Glucose
11.30
11.56
-2.30
-0.18
-2.48
1.6
-0.11
-1.57
11.56
Lactate
2.99
3.04
-1.67
0.00
-1.67
7.6
0.00
-0.22
3.04
LDH
237.00
239.56
-1.08
1.50
0.42
2.9
0.53
0.15
237.0
Lipase
72.50
74.50
-2.76
-3.46
-6.22
7.3
-0.48
-0.86
74.5
Magnesium
1.050
1.110
-5.71
2.32
-3.39
6.3
0.37
-0.54
1.11
Phosphorus
1.490
1.460
2.01
-0.51
1.50
1.1
-0.47
1.40
1.46
Salicylate
145.00
140.40
3.17
0.00
3.17
6.3
0.00
0.51
140.4
Triglycerides
1.540
1.550
-0.65
8.96
8.31
7.0
1.28
1.19
1.54
Total Protein
50.60
49.67
1.84
-0.76
1.08
2.5
-0.30
0.43
49.67
Uric Acid
290.00
293.99
-1.38
4.67
3.29
3.0
1.57
1.11
290.0
Urea
15.10
15.28
-1.19
1.03
-0.17
3.9
0.26
-0.04
15.1
Application of the above concepts based on six sigma principles is a “project-in-progress” in Winnipeg, Manitoba, Canada. It has already served to bring attention and interest in six sigma methodology in our region. Expectantly, it is a system to objectively assess how our automated analytic tests are doing, to determine where improvement is still needed and to measure where progress has been made. As such, it is fundamental to achieving six sigma quality performance.
References
1. www.westgard.com/essay36.htm
2. www.westgard.com/biodatabase1.htm
3. Westgard JO. Six Sigma Quality Design & Control, Westgard QC, Inc., 2001, Appendix 2, page 276