Article Figures & Data
Figures
- Fig. 1. The Westgard-like algorithm and the aggregation of Z-values under simplified conditions.
Z(x) indicates Z-transformation. An out-of-control (OOC) condition may affect Z-values of both QCs equally (A) or unequally (B). The OOC condition shifts both QCs by 2 Z-values on average (C). ΔZ is the difference between the Z-transformed shifts of both QCs. Performance of control rules on simulated stable and OOC conditions with increasing ΔZ (D).
- Fig. 2. Steps of simulation.
In each phase, true and measured values were generated (A). If 5% of measurements exceeded the allowable total error (TEa), the day was marked as out-of-control (OOC). Parameters for Z-values were calculated in a stable phase (B). Decision thresholds were determined and tested in independent error-prone phases. For 5 analytes, 200 runs were conducted (C).
- Fig. 3. Example of biases in 1 simulation of albumin.
The top lane shows constant biases with constantly increasing and random parts. The middle lane depicts relative biases again with constantly increasing and random parts. The interaction of various biases creates a broad range of realistic out-of-control situations (bottom lane).
- Fig. 4. AUC values of quality control rules and simple quality control parameters.
zWAggr, zAggr – weighted and unweighted aggregation of Z-values; west – Westgard-like algorithm; zWAggr.QC, zAggr.QC – weighted and unweighted aggregation of Z-values from control measurements only; west.QC – Westgard-like algorithm from internal QC measurements only; median - patient medians; QC_1, …, QC_4 - internal QC measurements.
- Fig. 5. AUC values of quality rules and simple quality control parameters from disturbed simulations.
zWAggr, zAggr – weighted and unweighted aggregation of Z-values; west – Westgard-like algorithm; zWAggr.QC, zAggr.QC – weighted and unweighted aggregation of Z-values from control measurements only; west.QC – Westgard-like algorithm from control measurements only; median - patient medians (median); QC_1, …, QC_4 - QC measurements. Outliers are removed for better clarity. “x” marks mAUC values from the undisturbed simulation.
Tables
Albumin HbA1c Testosterone Troponin I Vitamin D3 Description Many measurements per day; normal distribution of true values Low sigma value; four QC measurements Bimodal distribution of true values based on sex Many measurements close to limit of detection Seasonal variation of true values Measurements per day (SD) 500 (50) 70 (6) Male: 50 (5) Female: 30 (4) 120 (20) 200 (20) Distribution of values Normal; centerb: 3.474 spread: 0.886 (unit: g/dl) Lognormal; center: 5.504 spread: 0.892 (unit: %) Male: lognormal; center: 3.505 spread: 2.402 female: lognormal; center: 0.366 spread: 0.532 (unit: ng/mL) Lognormal; center: 0.160 spread: 0.656 (unit: ng/mL) Lognormal; center: 19.585 ± 7.5% seasonal variation; spread: 11.382 (unit: ng/mL) Allowable total error [on interval] 12.5% [2–7] 10% [4.89– 14.96] 20.5% [0.2– 20] 20% [0.1–35] 25% [5–50] Precision αc 0.067 0.1 0.008 0.003 0.5 ßd 0.031 0.029 0.034 0.033 0.05 Quality controls QC_1 3 5 3 0.05 10 QC_2 6 6 8 0.95 30 QC_3 8 QC_4 10 ↵a α and ß are parameters of the characteristic function.
↵b Center and spread denote mean and standard deviation for normal distribution.
↵c α expresses constant imprecision at low concentration.
↵d ß expresses relative imprecision similar to the coefficient of variation. For lognormal distribution, respective values are also provided on a non-logarithmized scale for better comparability.
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