Hitch-hiker’s Guideto

Interpreting Serial Results

Graham WhiteSA Pathology

Flinders Medical CentreBedford Park 5042

Graham.White@health.sa.gov.au

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.