Appendix 2.
Scenario 2. Estimation of MU for a glucose measurement procedure including bias uncertainty (artificial data for illustrative purposes).
| Parameter | Data | Calculations | Comment |
|---|---|---|---|
| Imprecision (uImp) | 0.11 mmol/L | Data from scenario 1. QC Level 1: plasma glucose 4.80 mmol/L. | |
| Bias | Evaluated | Level 3 CRM (certified reference material) 965a measured under replicate conditions (n=10). | |
| CRM 965a: Glucose. | Data from CRM certificate includes assigned value and expanded uncertainty U (k = 2). | ||
| Level 3 value: | 6.777 mmol/L | ||
| U: | 0.073 mmol/L | Calculate uCRM from expanded uncertainty. | |
| uCRM | 0.0365 mmol/L | Calculated as U/2 | |
| CRM 965a value using routine procedure (n=10) | 6.9, 7.0, 6.9, 6.8, 7.2, 7.1, 6.9, 6.8, 7.2, 6.9 | 10 measurements of SRM glucose using routine procedure under repeatability conditions (N.B. artificial data for illustration only). | |
| Mean value | 6.97 mmol/L | ||
| SD | 0.149 mmol/L | ||
| SEM | 0.047 mmol/L | SEM = 0.149/√10 = uRep | Standard error of mean. |
| Bias * | 0.193 mmol/L | 6.970–6.777 mmol/L | Mean of replicate measurements by routine procedure minus CRM assigned value. |
| uBias | uCRM: 0.0365 mmol/L | uBias is uncertainty of value used for bias correction (0.193 mmol/L). | |
| uRep: 0.047 mmol/L | |||
| uBias: 0.0595 mmol/L | uBias = (0.03652 + 0.0472) 1/2 | uBias calculated by combining uCRM and SEM of mean CRM value estimated by routine procedure (uRep). | |
| Is Bias significant? | t = Bias/uBias | t test; use distribution table for t (2 tailed) values | |
| t = 3.24 | 0.193/0.0595 | df = degrees of freedom. | |
|
0.01<P<0.02 |
df = 10−1 = 9 | Bias is significant; hence, procedure re-calibration should include offset of −0.193 mmol/L. | |
| Is uBias significant? | uBias/uImp = 0.54 | 0.0595/0.11 | uBias is of significant magnitude relative to imprecision, therefore include in MU estimate. |
| Measurement Uncertainty | Combined standard uncertainty for whole procedure by combining uBias and uImp. | ||
| uProc | uProc = (uBias2 + uImp2)1/2 | ||
| 0.125 mmol/L
0.1 mmol/L (rounded) |
(0.05952 + 0.112)1/2 = 0.125 | uProc is rounded to same number of decimal places as reported results (unless calculating U). | |
| Expanded Uncertainty: U | 0.25 mmol/L
0.3 mmol/L (rounded) |
k = 2; 2 x 0.125 = 0.250 | Coverage factor 2 to calculate U. U is rounded to same number of significant figs as reported results. |
| Coverage interval: 5.0–10.0 mmol/L | ± 0.3 mmol/L | Rounded data for general use by lab staff and ‘handbook’. Coverage probability 95%. |
*
Bias evaluated and procedure adjusted to minimise estimated bias.