Hitch-hiker’s Guide to Interpreting Serial Results
Transcript of Hitch-hiker’s Guide to Interpreting Serial Results
Hitch-hiker’s Guideto
Interpreting Serial Results
Graham WhiteSA Pathology
Flinders Medical CentreBedford Park 5042
Is the difference between consecutive serial results explained by
inherent variability of the results ?
OR
Is the magnitude of the difference larger than can be explained
by inherent variation?
i.e. a real biological change that may be clinically significant?
Can the assay reliably measure thedifference in concentration between the two specimens?’.
PSA QC results for 3 months
Precision under intermediate reproducibility conditions
Can use data to estimate MU of each result
PSA QC results for 3 months
Mean value: 2.34 μg/L
SD (uQC): 0.09 μg/L
CV: (urel): 3.8 %
CV: 3.8 % of 7.3 = SD = 0.28; 2 SD = 0.56 = 0.6 μg/L
8.6 = SD = 0.33; 2 SD = 0.66 = 0.7 μg/L
7.3 ± 0.6 μg/L 8.6 ± 0.7 μg/L
6.7 - 7.9 μg/L 7.9 - 9.3 μg/LInterval of possible values (95 % probability):
PSA μg/L7.97.96.7
8.6
7.9 9.3
7.3
2 SD0.6
2 SD0.7
X
1.3 μg/L
Cannot add or subtract SDs – must use variances
SD2 = variance
Combining SDA and SDB:
Combined SD = (SDA2 + SDB
2)
Combined SD = (SDA2 + SDB
2)1/2
Variance
or using alternative notation for
PSA μg/L
7.3
?
SD = 0.28Variance = 0.282 = 0.078
SD = 0.33Variance = 0.332 = 0.109
Combined variance = 0.187
Combined SD = 0.187 = 0.43 μg/L
For 95 % probability: 0.43 x 1.96 = 0.84 μg/L
Bi-directional probability: Allows possibility that the 2 results
could have been up/down due to analytical imprecision.
PSA μg/L7.3
≥0.8
8.1
8.6 μg/L
MP can reliably distinguish 7.3 and 8.6 μg/L
Information of limited use because wrongly assumed
PSA concentration is constant at all times
Most measurand concentrations show significant
inherent variability over time
Biological variation
Biological variation
Within-individual biological variation
Between-individual biological variation
Concentration of many measurands
in a presumed healthy individual fluctuate with time
MinutesHoursDaysWeeksMonths
Within-individual biological variation
Biological variation within the individual
Endogenous factors:
gender, biological age, genes, ethnicity,
homeostatic mechanisms e.g. serum TSH, calcium
anabolic/catabolic balance, compartment distribution
Exogenous factors:
lifestyle and environment e.g. nutritional intake, activity,
alcohol/drugs, season
Many causes e.g.
Quantifying within-individual biological variation
Presumed healthy’ subjects– gender & age range?
Standardise specimen collection:
Specimens: same time & day, same phlebotomist etc
Frequency: each week/fortnight/month
Analysis: Single run to reduce imprecision
Fraser CG. Biological variation, 2001, AACC Press
Sub
ject
s
Total variability of results for each individual: CVT
Repeatability imprecision of assay: CVA
Within-individual biological variation: CVI
CVT = (CVA2 + CVI
2)1/2
CVI = (CVT2 - CVA
2)1/2
For each individual:
Calculate Mean, total SD & total CVT %
Mean value = personal homeostatic set pointfor analyte concentration/enzyme activity
CVT % = combined analytical imprecision & within subject BV
Calculate CVI for each individual
CVI % = (CVT2 % - CVA
2 %)1/2
Express this relationship as relative variances
Calculate the mean CVI % for the total individuals
Mean CVI:
quantifies average variability of results
due to within-individual biological variation
Limitation:
Calculations assumes distribution of values around
personal set-point is Gaussian – often not true
(ANOVA – ANalysis Of VAriance often used for calculations)
Fraser CG. Biological variation, 2001, AACC Press
Between-individual biological variation
Total biological variation = (CVI2 + CVG
2)1/2
Personal mean
Andersen S et al. J Clin Endo Metab 2002, 87: 1068
12 monthly measurements of serum TSH in healthy subjects
Pickup JF et al. Clin Chem 1977, 23: 842
Andersen S et al. J Clin Endo Metab 2002, 87: 1068
Index of Individuality (II) = CVICVG
II >0.6:– RI relatively sensitive to abnormal values in the individual
II <0.6:– RI relatively insensitive to abnormal values in the individual
Westgard Biological Database
Lists the extensive studies by Ricos et al - many measurands
www.westgard.com/biodatabase1
or
Google westgard biological
PSA
CVI: ~18 %
CVA: ~ 2-3 %
Summary so far
Analytical imprecision (CVA):unavoidable cause of result variability
Within-individual biological variation (CVI):
unavoidable cause of result variability
Comparing 2 serial results for a patient:
Must consider: Combined effect of CVA and CVI on each result
Combining SDs or CVs:
requires conversion to variances, relative variances
PSA μg/L
7.3
? – combined effect
CVA = 3.8 %
CVI = 18 %
CVA = 3.8 %
CVI = 18 %
(CVA2 + CVI
2)1/2
First result (7.3) Second result (8.6)
(CVA2 + CVI
2)1/2
1.96 x (CVA2 + CVI
2)1/2 1.96 x (CVA2 + CVI
2)1/2
[1.96 x (CVA2 + CVI
2)1/2]2 + [1.96 x (CVA2 + CVI
2)1/2]2
{[1.96 x (CVA2 + CVI
2)1/2]2 + [1.96 x (CVA2 + CVI
2)1/2]2}1/2
CVA2 + CVI
2Combine the 2 variances: CVA2 + CVI
2
Convert each to total CV:
Combine both terms
Take square root to give combined CVT
{[1.96 x (CVA2 + CVI
2)1/2]2 + [1.96 x (CVA2 + CVI
2)1/2]2}1/2
21/2 x 1.96 x (CVA2 + CVI
2)1/2
1.41 x 1.96 x (CVA2 + CVI
2)1/2
2.77 x (CVA2 + CVI
2)1/2 = 2.77 x CVT
Reference Change Value (RCV)
Above simplifies to:
PSA μg/L
7.3
CVA = 3.8 %
CVI = 18 %
CVA = 3.8 %
CVI = 18 %
2.77 x (CVA2 + CVI
2)1/2
2.77 x (3.82 + 18.02)1/2
PSA μg/L
7.3
2.77 x (CVA2 + CVI
2)1/2
2.77 x (3.82 + 18.02)1/2
2.77 x 18.4
Reference Change Value = 51 %
?
PSA μg/L
7.3
If Reference Change Value = 51 %
8.6
8.6 – 7.3 = 1.3 = only ~18 % of 7.3 μg/L
PSA μg/L
7.3
2.77 x (CVA2 + CVI
2)1/2
If Reference Change Value = 51 %
Or: 51 % of 7.3 = 3.7 μg/L
≥11.0+ 3.7
(95 % probability)
SUMMARY
when calculating a Reference Change Value that is bi-directional
Use RCV = 2.77 x (CVA2 + CVI
2)1/2
From Lab QC data From Westgard BV website
i.e. Inherent variability of both results could be up or down
Assuming Z-score of 1.96 used (95 % probability)
Uni-Directional Changes
Used to answer questions such as:
Is a result is definitely above a clinical decision value?
Is a result is definitely below a clinical decision value?
Is a serial result biologically higher than the previous result?
Is a serial result biologically lower than the previous result?
PSA μg/L4.34.0
?
Is the result biologically different from a clinical decision value?
Requires different Z score
Fraser CG. Biological variation, 2001, AACC Press
PSA μg/L4.34.0
?
Is the result biologically different from a clinical decision value?
Z score: 1.65
1.65 x (CVA2 + CVI
2)1/2
= 1.65 x 18.4 = 30.4 %
RCV = 30 % of 4.0 = 1.2 μg/L
PSA μg/L4.0 5.2
1.2
For result to be biologically higher
from the fixed clinical decision value (95 % confidence)
Z score: 1.65
RCV = 5.2 μg/L
PSA μg/L
?
7.3 8.6
Is 8.6 biologically higher than 7.3?
OR
Is 7.3 biologically lower than 8.6?
PSA μg/L
?
7.3
21/2 x 1.65 x (CVA2 + CVI
2)1/2
1.41 x 1.65 x (3.82 + 18.02)½ =
2.33 x 18.4 = ~42.9 %
RCV = 7.3 x 43/100 = 3.1 μg/L
PSA μg/L
3.1
7.3
RCV= 3.1 μg/L
10.4
Second result needs to be ≥10.4 μg/L to have ≥95 %
confidence it has biologically increased from 7.3 μg/L
PSA μg/L
?
8.6
21/2 x 1.65 x (CVA2 + CVI
2)1/2
1.41 x 1.65 x (3.82 + 18.02)½ =
2.33 x 18.4 = ~42.9 %
RCV = 8.6 x 43/100 = 3.7 μg/L
PSA μg/L
3.7
4.9
RCV= 3.7 μg/L
8.6
Second result needs to be ≤4.9 μg/L to have ≥95 %
confidence it has biologically decreased from 8.6 μg/L
SUMMARY
Bi-directional changes: 2.77 x CVT
Uni-directional changes: 2.33 x CVT
For RCV with 95 % probability
CVI often dominant cause of result variability
Aspects not discussed
Variable quality of CVI data – often only one study
Need to standardise study protocols; data means vs. medians
Applicability of CVI data to disease states
Use of more than two serial results
Reporting biological changes in results
Validity of Gaussian distributions
Validity of specimen timing
REFERENCES
Essential reading:
Biological Variation: From Principles to Practice. Fraser CG.AACC Press, 2001
Biological variation: a still evolving facet of laboratory medicineSimundic A-M, Bartlett WA, Fraser CG.
Ann Clin Biochem 52(2);19-190, 2015
www.westgard.com/biodatabase
Rationale for using data on biological variation. C Ricós.Stockholm Conference on Quality Specifications in LaboratoryMedicine 2014. Clin Chem Lab Med 2015:56(6)
REFERENCES
Calculation of limits for significant bidirectional changes in twoor more serial results of a biomarker based on a computersimulation model Ann Clin Biochem 52(4);434-440, 2015
Calculation of limits for significant unidirectional changes in twoor more serial results of a biomarker based on a computersimulation model Ann Clin Biochem 52(2);237-244, 2015
Lund F, Petersen PH, Fraser CG, Sölétormos G.