Biological variation update_ed

1. Biological VariationBiological Variation
Dr WA BartlettDr WA Bartlett
Biochemical MedicineBiochemical Medicine
Ninewells Hospital & Medical SchoolNinewells Hospital & Medical School
Dundee Dundee
ScotlandScotland

2. ObjectivesObjectives
Identification the nature of biological Identification the nature of biological
variation.variation.
Appreciation of the significance of Appreciation of the significance of
biological variation in clinical biological variation in clinical
measurements.measurements.
Attain insight into the determination and Attain insight into the determination and
application of indices of biological application of indices of biological
variation. variation.

3. Identification the nature of Identification the nature of
biological variation.biological variation.
What is meant by the term What is meant by the term
biological variation in the context biological variation in the context
of clinical biochemistry?of clinical biochemistry?
A component of the variance in A component of the variance in
biochemical measurements biochemical measurements
determined by the physiology of determined by the physiology of
the subjects observed.the subjects observed.

4. Components of Variance in Components of Variance in
Clinical Chemistry Clinical Chemistry
MeasurementsMeasurements
Analytical variance.Analytical variance.
Within Subject biological variance.Within Subject biological variance.
Between Subject biological variance.Between Subject biological variance.

5. Biological VariationBiological Variation
All clinical chemistry measurements All clinical chemistry measurements
change with time.change with time.
Knowledge of temporal changes useful in Knowledge of temporal changes useful in
diagnosis and interpretation.diagnosis and interpretation.
Rate of change may be useful in prognosis.Rate of change may be useful in prognosis.
Understanding of the sources of biological Understanding of the sources of biological
variation in non-diseased subjects is variation in non-diseased subjects is
fundamental to the development of fundamental to the development of
reference data.reference data.

6. Sources of Biological Sources of Biological
VariationVariation
Biological Rhythms (time)Biological Rhythms (time)
HomeostasisHomeostasis
Age Age
SexSex
EthnicityEthnicity
PathologyPathology
StimuliStimuli

7. Practical significance of Practical significance of
biological variation. biological variation.
What is the significance of this result?What is the significance of this result?
Is the performance of the analytical Is the performance of the analytical
method appropriate (imprecision, method appropriate (imprecision,
accuracy)?accuracy)?
When should I measure it again?When should I measure it again?
Has this result changed significantly over Has this result changed significantly over
time?time?
Changes in variability be used as a tool?Changes in variability be used as a tool?

8. Models of Biological VariationModels of Biological Variation
Assume values represent random Assume values represent random
fluctuation around a homeostatic setting fluctuation around a homeostatic setting
point.point.
More general model allows correlation More general model allows correlation
between successive results. (between successive results. (Time series Time series
and non-decayed biological variationand non-decayed biological variation))

9. Quantifying Biological Quantifying Biological
VariationVariation
How are you going to quantify biological How are you going to quantify biological
variation?variation?
You have to dissect out the You have to dissect out the
components of variance:components of variance: - -
ss
22
total total = = ss
22
Analytical Analytical ++
ss
22
Individual Individual + + ss
22
GroupGroup

10. Quantifying Biological Quantifying Biological
VariationVariation
s
2
Analytical
=
s
2
Individual
=
s
2
Group
=
Average variance of replicate assaysAverage variance of replicate assays
within run analytical variancewithin run analytical variance
Average biological within subject Average biological within subject
variance.variance.
Average Variance around the Average Variance around the
homeostatic setting pointhomeostatic setting point
Variance of true means among subjects.Variance of true means among subjects.
Variance in homeostatic setting pointsVariance in homeostatic setting points

11. Analytical
Variance
Within Subject
Variance
**
**
**Subject 1
**
**
**
**
**
**
**
**Subject 2
**
**
**
Between Subject
Variance
**
**
**Subject 3
**
**
**
**

12. Quantifying Biological Quantifying Biological
VariationVariation
How do you do the experiment?How do you do the experiment?
SubjectsSubjectsHow many?How many?
Collect specimensCollect specimensNumber? Frequency?Number? Frequency?
Analyse specimensAnalyse specimens MinimiseMinimise ss
22
Analytical Analytical ??
Analyse dataAnalyse dataOutliers? Statistics?Outliers? Statistics?
Apply results of analysis.Apply results of analysis.

13. Quantifying Biological Quantifying Biological
VariationVariation
Estimates of biological variation are Estimates of biological variation are
similar regardless of: -similar regardless of: -
Number of subjectsNumber of subjects
Time scale of study (Short v Long?)Time scale of study (Short v Long?)
GeographyGeography
A lot of information can be obtained A lot of information can be obtained
from small studies.from small studies.

14. Within Subject Variation (CVWithin Subject Variation (CV
II,%) for Serum Sodium and Urea,%) for Serum Sodium and Urea
No. ofNo. ofTimeTime SexSex
bb
statusstatusNaNa
++
UreaUrea
subjectssubjects
11110.5 h0.5 h mm HH 0.60.62.22.2
11118 h8 h mm HH 0.50.56.06.0
62621 d1 d HH 0.60.64.84.8
11112 weeks2 weeks mm HH 0.70.712.312.3
10104 weeks4 weeks mm HH 0.90.914.314.3
14148 weeks8 weeks FF HH 0.50.511.311.3
11111115 weeks15 weeksmm HH 0.60.615.715.7
373722 weeks22 weeksmm HH 0.50.511.111.1
2742746 months6 months-- HH 0.50.511.211.2
151540 weeks40 weeks-- HH 0.70.713.913.9
99 2 d2 d-- RFRF0.80.86.56.5
15156 weeks6 weeks FF HPHP0.80.814.514.5
16168 weeks8 weeks mm DMDM0.80.813.013.0

15. Collection of Specimens.Collection of Specimens.
Conditions should minimise pre-analytical Conditions should minimise pre-analytical
variables.variables.
Healthy subjects.Healthy subjects.
Usual life styles.Usual life styles.
No drugs (alcohol, smoking?).No drugs (alcohol, smoking?).
Phlebotomy by same person.Phlebotomy by same person.
Same time of day at regular intervals.Same time of day at regular intervals.
Set protocol for sample transport, processing & Set protocol for sample transport, processing &
storage.storage.

16. Analysis of SpecimensAnalysis of Specimens
Need to minimise analytical imprecision.Need to minimise analytical imprecision.
Ideal : -Ideal : -
Single lots of reagents and calibrants.Single lots of reagents and calibrants.
Single analyst and analytical system.Single analyst and analytical system.
Single or very small number of Single or very small number of
batches.batches.

17. Preferred Protocol: Preferred Protocol: CotloveCotlove et alet al
Healthy subjects.Healthy subjects.
Specimens taken at set time intervals.Specimens taken at set time intervals.
Specimens processed & stored frozen.Specimens processed & stored frozen.
When ALL specimens are available: -When ALL specimens are available: -
Analysis of all samples in a single run.Analysis of all samples in a single run.
Simultaneous replicate analysis.Simultaneous replicate analysis.
Quality control to monitor driftQuality control to monitor drift

18. Preferred Protocol: Preferred Protocol: CotloveCotlove et alet al
Advantage: -Advantage: -
Minimisation of Minimisation of ss
22
AnalyticalAnalytical
Disadvantages: -Disadvantages: -
Limits the number of specimens and subjects Limits the number of specimens and subjects
that can be studied.that can be studied.
Analyte must be stable on storage.Analyte must be stable on storage.

19. Other Protocols: Other Protocols: Costongs Costongs et alet al
Collection and storage as before.Collection and storage as before.
Singleton assay of all samples in a single Singleton assay of all samples in a single
run.run.
Duplicate assay of QC or patient pool to Duplicate assay of QC or patient pool to
estimate estimate ss
22
AnalyticalAnalytical

20. Other Protocols: Other Protocols: Costongs Costongs et alet al
Disadvantages: -Disadvantages: -
True estimate of True estimate of ss
22
AnalyticalAnalytical ? ?
Integrity of QC materialsIntegrity of QC materials
 Viral infections of poolsViral infections of pools
Vial to vial variability in QCVial to vial variability in QC

21. Other Protocols: Other Protocols: Costongs/Moses Costongs/Moses et alet al
Samples assayed once or in duplicate on Samples assayed once or in duplicate on
the day of collectionthe day of collection
Disadvantage: -Disadvantage: -
s s
22
individual individual confounded by between batch confounded by between batch
variance.variance.
Advantage: -Advantage: -
Useful if analyte is unstableUseful if analyte is unstable..

22. Analysis of DataAnalysis of Data
2 Stages2 Stages
–Identification of outliersIdentification of outliers
–Nested analysis of varianceNested analysis of variance

23. Analytical
Variance
Within Subject
Variance
**
**
**Subject 1
**
**
**
**
**
**
**
**Subject 2
**
**
**
Between Subject
Variance
**
**
**Subject 3
**
**
**
**

24. Applications of BV DataApplications of BV Data
Setting of analytical goals.Setting of analytical goals.
Evaluating the significance of change in Evaluating the significance of change in
serial results.serial results.
Assessing the utility of reference Assessing the utility of reference
intervals.intervals.
Assessing number of specimens required Assessing number of specimens required
to estimate homeostatic set points.to estimate homeostatic set points.

25. Applications of BV DataApplications of BV Data
Assessment of reporting strategies.Assessment of reporting strategies.
Selecting the best specimen.Selecting the best specimen.
Comparing utility of available tests.Comparing utility of available tests.

26. Setting of analytical goals.Setting of analytical goals.
Accepted analytical goal for imprecision: -Accepted analytical goal for imprecision: -
CVCV
GoalGoal = ½ CV = ½ CV
II
therefore: -
CVCV
AnalyticalAnalytical = CV = CV
GoalGoal
= = ¼ of the ¼ of the ss
22
Individual if achieved.Individual if achieved.
(Harris. Am J Clin Pathol 1979:72;274)

27. Utility of Analytical GoalsUtility of Analytical Goals
Assessment of methods and equipment.Assessment of methods and equipment.
Should be addressed in early stages of Should be addressed in early stages of
method development.method development.
Index of Fiduciality: -Index of Fiduciality: -
CVCV
AnalyticalAnalytical /CV /CV
GoalGoal
If <1 analytical goal metIf <1 analytical goal met
(Fraser Clin Chem 1988:34;995)(Fraser Clin Chem 1988:34;995)

28. Evaluating the significance Evaluating the significance
of change in serial results.of change in serial results.
Critical Difference or Reference Change value Critical Difference or Reference Change value
indicates the value by which 2 serial results indicates the value by which 2 serial results
must differ to be considered statistically must differ to be considered statistically
significant: -significant: -
CD = 2CD = 2
½½
* Z * (CV * Z * (CV
AA
22
+ CV + CV
II
22
))
½½

Probabilty = 95% Z = 1.96Probabilty = 95% Z = 1.96
Probability = 99% Z = 2.58Probability = 99% Z = 2.58
Only valid if the variance of Only valid if the variance of ss
22
IndividualIndividual is is
homogenous.homogenous.
(Costongs J Clin Chem Clin Biochem 1985;23:7-16)(Costongs J Clin Chem Clin Biochem 1985;23:7-16)

29. Multipliers for (CVMultipliers for (CV
AA
22
+ CV + CV
II
22
) )
½ ½
to Obtain Criticalto Obtain Critical
Difference at Different Levels of ProbabilityDifference at Different Levels of Probability
MultiplierMultiplier 3.643.642.772.772.332.331.811.811.471.471.191.190.950.95
(2 (2
½ ½
* Z)* Z)
Probability ofProbability of 0.010.010.050.050.100.100.200.200.300.300.400.400.500.50
false alarmfalse alarm
ProbabilityProbability 99%99%95%95%90%90%80%80%70%70%60% 60% 50%50%

30. Significance of Change?Significance of Change?
63 year old patient: Cholesterol 1 = 6.60 mmol/L63 year old patient: Cholesterol 1 = 6.60 mmol/L
Cholesterol 2 = 5.82 mmol/LCholesterol 2 = 5.82 mmol/L
Significant change ?Significant change ?
Cva = 1.6% CVCva = 1.6% CV
II = 6.0% = 6.0%
RCV = 2RCV = 2
½½
* Z * (CV * Z * (CV
AA
22
+ CV + CV
II
22
))
½½
95%RCV = 1.414 * 1.96 * (1.6 95%RCV = 1.414 * 1.96 * (1.6
½ ½
+ 6.60 + 6.60
½½
) )
½ ½
= 17.2%= 17.2%
99%RCV = 99%RCV = 1.414 * 2.58 * (1.6 1.414 * 2.58 * (1.6
½ ½
+ 6.60 + 6.60
½½
) )
½ ½
= 22.6%= 22.6%
Actual Change = ((6.60 – 5.82)/6.60)*100= 11.8%

31. Dispersion =Z* (SDDispersion =Z* (SD
22
A A + SD+ SD
22
II) )
Dispersion of first result = result Dispersion of first result = result ± 1.96 SD± 1.96 SD : - : -
95% level 6.60 95% level 6.60 = 5.80 –7.40= 5.80 –7.40
99% level 6.60 = 5.54 – 7.6699% level 6.60 = 5.54 – 7.66
Dispersion of 2 resultDispersion of 2 result
95% level = 5.82 = 5.11 – 6.5395% level = 5.82 = 5.11 – 6.53
99% level = 5.82 = 4.89 – 6.7599% level = 5.82 = 4.89 – 6.75
Overlap: therefore neither significantly or highly Overlap: therefore neither significantly or highly
significantly differentsignificantly different
Can use the formula to ascertain the probability that Can use the formula to ascertain the probability that
change is significant. Calculate Z using the (((6.6-change is significant. Calculate Z using the (((6.6-
5.82)/6.6)*100%) as RCV and look up in tables. 82% in 5.82)/6.6)*100%) as RCV and look up in tables. 82% in
this case.this case.

32. USE of RCVUSE of RCV
Handbooks reports, 95% and 99%
probabilities that change is significant.
(> or >> * or **)
Delta checking, exemption reporting.
–95% auto validate, 99% refer for clinical
validation or renanalysis.

33. Index of HeterogeneityIndex of Heterogeneity
Measure of the heterogeneity of variance Measure of the heterogeneity of variance
within within
the study population: -the study population: -
ratio of the observed CV of the set of subjects ratio of the observed CV of the set of subjects
variances variances (SD(SD
A+IA+I
22
)) to the to the theoretical theoretical CV ( / 2/n-1) CV ( / 2/n-1)
for the set.for the set.
The ratio should =1The ratio should =1 (1SD = 1/ /2n )(1SD = 1/ /2n )
Large ratio = more heterogeneity.Large ratio = more heterogeneity.
(Costongs J Clin Chem Clin Biochem 1985;23:7-16)(Costongs J Clin Chem Clin Biochem 1985;23:7-16)

34. Assessing the utility of Assessing the utility of
reference intervalsreference intervals..
Utility of population based reference data?Utility of population based reference data?
Ratio of Within to Between subject variances.Ratio of Within to Between subject variances.
Index of Individuality = CVIndex of Individuality = CV
II / CV / CV
GG
Population Ref Intervals: -Population Ref Intervals: -
Index Index <<0.6 = Limited in Value 0.6 = Limited in Value
Index Index >>1.4 = Applicable1.4 = Applicable

35. Biological Variation &Utility of Reference Biological Variation &Utility of Reference
IntervalsIntervals

36. Number of specimens Number of specimens
required to estimate required to estimate
homeostatic set pointshomeostatic set points..
n = ( Z. CVn = ( Z. CV
A+A+
II/D)/D)
where: -where: -
Z = Z = number of Standard deviates for a number of Standard deviates for a
stated probablity (e.g. 1.96 for 95%).stated probablity (e.g. 1.96 for 95%).
D = D = desired % closeness homeostatic set desired % closeness homeostatic set
point.point.

37. Number of specimens required to Number of specimens required to
estimate homeostatic set pointsestimate homeostatic set points: -: -
Cholesterol testingCholesterol testing
How many samples (n) required to How many samples (n) required to
estimate set point within ±5% given: -estimate set point within ±5% given: -
CVCV
I I = 4.9% = 4.9%CVCV
AA = 3% (Recommended) = 3% (Recommended)
Substitute equationSubstitute equation: -: -
n = ( Z. CVn = ( Z. CV
A+A+
II/D)/D)
n =n =

[1.96·(3[1.96·(3
22
+ 4.9 + 4.9
22
))
½½
/5]/5]
22
= 5.07 = 5.07

38. RCV at 95% and Number. of Specimens Required RCV at 95% and Number. of Specimens Required
to Assess the Homeostatic Set Point at Different Levels of Imprecisionto Assess the Homeostatic Set Point at Different Levels of Imprecision
CVCV
AA CVCV
I I RCVRCV
aa
Number of Number of
(%)(%) (%)(%) (%)(%) specimens specimens
bb

2.02.0 4.74.7 14.1 14.1 4 4
3.03.0 4.74.7 15.4 15.4 5 5
4.04.0 4.74.7 17.1 17.1 6 6
5.05.0 4.74.7 19.0 19.0 7 7
6.06.0 4.74.7 21.1 21.1 9 9
7.07.0 4.74.7 23.4 23.4 11 11
8.08.0 4.74.7 25.7 25.7 13 13
9.09.0 4.74.7 28.1 28.1 16 16
10.010.0 4.74.7 30.6 30.6 19 19
15.015.0 4.74.7 43.5 43.5 38 38
20.020.0 4.74.7 56.9 56.9 65 65
aa
RCV (pRCV (p < <0.05) = 2.77 (CV0.05) = 2.77 (CV
AA
22
+ CV + CV
II
22
))
½½
, assuming no statistical evidence of heterogenity, assuming no statistical evidence of heterogenity
bb
Number = mean result is within Number = mean result is within ±±5%of homeostatic set point1.965%of homeostatic set point1.96
22
x (CV x (CV
AA
22
+ CV + CV
II
22
) )
½½
/25./25.

39. Assessment of reporting Assessment of reporting
strategiesstrategies
Results may be reported in different Results may be reported in different
formats formats
e.g. 24h Urinary creatinine output: -e.g. 24h Urinary creatinine output: -
CVCV
I I for concentration = 23.8% for concentration = 23.8%
CVCV
I I for output per collection = 13.0%for output per collection = 13.0%
CD for concentration = 66.0%CD for concentration = 66.0%
CD for output = 36.2%CD for output = 36.2%

40. Selecting best Specimen.Selecting best Specimen.
e.g early morning urines for albumin e.g early morning urines for albumin
versus 24h collections.versus 24h collections.
Random hormone measurements versus Random hormone measurements versus
timed measurements.timed measurements.

41. Comparing Available TestsComparing Available Tests
Creatinine v Creatinine ClearanceCreatinine v Creatinine Clearance
FT4 v TSH in replacement situationsFT4 v TSH in replacement situations
FT4 v Total T4FT4 v Total T4

42. Reference IntervalsReference Intervals
Dr WA BartlettDr WA Bartlett
Birmingham Heartlands & Solihull Birmingham Heartlands & Solihull
NHS Trust (Teaching)NHS Trust (Teaching)