Biological VariationBiological Variation

Dr WA BartlettDr WA Bartlett

Biochemical MedicineBiochemical Medicine

Ninewells Hospital & Medical SchoolNinewells Hospital & Medical School

Dundee Dundee

ScotlandScotland

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.

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 the determined by the physiology of the subjects observed.subjects observed.

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.

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.

Sources of Biological Sources of Biological VariationVariation

Biological Rhythms (time)Biological Rhythms (time)HomeostasisHomeostasisAge Age SexSexEthnicityEthnicityPathologyPathologyStimuliStimuli

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?

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))

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: - -

total total = = Analytical Analytical ++

Individual Individual + + GroupGroup

Quantifying Biological Quantifying Biological VariationVariation

Analytical =

Individual =

Group =

Average variance of replicate assaysAverage variance of replicate assayswithin 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

A n a l y t i c a lV a r i a n c e

W i t h i n S u b j e c tV a r i a n c e

* ** ** * S u b j e c t 1* ** ** ** *

* ** ** ** * S u b j e c t 2* ** ** *

B e t w e e n S u b j e c t

V a r i a n c e

* ** ** * S u b j e c t 3* ** ** ** *

Quantifying Biological Quantifying Biological VariationVariation

How do you do the experiment?How do you do the experiment? SubjectsSubjects How many?How many? Collect specimensCollect specimens Number? Frequency?Number? Frequency?

Analyse specimensAnalyse specimens MinimiseMinimise Analytical Analytical ??

Analyse dataAnalyse data Outliers? Statistics?Outliers? Statistics? Apply results of analysis.Apply results of analysis.

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.

Within Subject Variation (CVWithin Subject Variation (CVII,%) for Serum Sodium and Urea,%) for Serum Sodium and Urea No. ofNo. of TimeTime SexSexbb statusstatus NaNa++ UreaUrea subjectssubjects

1111 0.5 h0.5 h mm HH 0.60.6 2.22.21111 8 h8 h mm HH 0.50.5 6.06.06262 1 d1 d HH 0.60.6 4.84.81111 2 weeks2 weeks mm HH 0.70.7 12.312.31010 4 weeks4 weeks mm HH 0.90.9 14.314.31414 8 weeks8 weeks FF HH 0.50.5 11.311.3111111 15 weeks15 weeks mm HH 0.60.6 15.715.73737 22 weeks22 weeks mm HH 0.50.5 11.111.1274274 6 months6 months -- HH 0.50.5 11.211.21515 40 weeks40 weeks -- HH 0.70.7 13.913.999 2 d2 d -- RFRF 0.80.8 6.56.51515 6 weeks6 weeks FF HPHP 0.80.8 14.514.51616 8 weeks8 weeks mm DMDM 0.80.8 13.013.0

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.

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.

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

Preferred Protocol: Preferred Protocol: CotloveCotlove et alet al

Advantage: -Advantage: -

Minimisation of Minimisation of 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.

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 AnalyticalAnalytical

Other Protocols: Other Protocols: Costongs Costongs et alet al

Disadvantages: -Disadvantages: - True estimate of True estimate of

AnalyticalAnalytical ? ? Integrity of QC materialsIntegrity of QC materials Viral infections of poolsViral infections of poolsVial to vial variability in QCVial to vial variability in QC

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: -

individual individual confounded by between batch confounded by between batch

variance.variance.

Advantage: -Advantage: -

Useful if analyte is unstableUseful if analyte is unstable..

Analysis of DataAnalysis of Data

2 Stages2 Stages

– Identification of outliersIdentification of outliers

– Nested analysis of varianceNested analysis of variance

A n a l y t i c a lV a r i a n c e

W i t h i n S u b j e c tV a r i a n c e

* ** ** * S u b j e c t 1* ** ** ** *

* ** ** ** * S u b j e c t 2* ** ** *

B e t w e e n S u b j e c t

V a r i a n c e

* ** ** * S u b j e c t 3* ** ** ** *

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.

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.

Setting of analytical goals.Setting of analytical goals.

Accepted analytical goal for imprecision: -Accepted analytical goal for imprecision: -CVCVGoalGoal = ½ CV = ½ CVII

therefore: -

CVCVAnalyticalAnalytical = CV = CVGoalGoal

= = ¼ of the ¼ of the Individual if achieved.Individual if achieved.

(Harris. Am J Clin Pathol 1979:72;274)

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: -

CVCVAnalyticalAnalytical /CV /CVGoalGoal

If <1 analytical goal metIf <1 analytical goal met

(Fraser Clin Chem 1988:34;995)(Fraser Clin Chem 1988:34;995)

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 = 2½½ * Z * (CV * Z * (CVAA22 + CV + CVII

22))½½

Probabilty = 95% Z = 1.96Probabilty = 95% Z = 1.96Probability = 99% Z = 2.58Probability = 99% Z = 2.58

Only valid if the variance of Only valid if the variance of 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)

Multipliers for (CVMultipliers for (CVAA22 + CV + CVII

22) ) ½ ½ to Obtain Criticalto Obtain Critical

Difference at Different Levels of ProbabilityDifference at Different Levels of Probability

MultiplierMultiplier 3.643.64 2.772.77 2.332.33 1.811.81 1.471.47 1.191.19 0.950.95(2 (2 ½ ½ * Z)* Z)Probability ofProbability of 0.010.01 0.050.05 0.100.10 0.200.20 0.300.30 0.400.40 0.500.50false alarmfalse alarm

ProbabilityProbability 99%99% 95%95% 90%90% 80%80% 70%70% 60% 60% 50%50%

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% CVII = 6.0% = 6.0%

RCV = 2RCV = 2½½ * Z * (CV * Z * (CVAA22 + CV + CVII

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%

Dispersion =Z* (SDDispersion =Z* (SD22A A + SD+ SD22

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 result95% 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 change is significant. Calculate Z using the (((6.6-5.82)/6.6)*100%) as RCV and look up in tables. (((6.6-5.82)/6.6)*100%) as RCV and look up in tables. 82% in this case.82% in this case.

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.

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(SDA+IA+I22)) 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)

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 = CVII / CV / CVGG

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

Biological Variation &Utility of Reference Biological Variation &Utility of Reference IntervalsIntervals

Number of specimens Number of specimens required to estimate required to estimate

homeostatic set pointshomeostatic set points..

n = ( Z. CVn = ( Z. CVA+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.

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: -

CVCVI I = 4.9% = 4.9% CVCVAA = 3% = 3% (Recommended)(Recommended)

Substitute equationSubstitute equation: -: -

n = ( Z. CVn = ( Z. CVA+A+ II/D)/D)

n =n = [1.96·(3[1.96·(322 + 4.9 + 4.922))½½/5]/5]22 = 5.07 = 5.07

RCV at 95% and Number. of Specimens Required RCV at 95% and Number. of Specimens Required to Assess the Homeostatic Set Point at Different to Assess the Homeostatic Set Point at Different Levels of ImprecisionLevels of Imprecision

CVCVAA CVCVI I RCVRCVaa Number of Number of(%)(%) (%)(%) (%)(%) specimens specimensbb

2.02.0 4.74.7 14.1 14.1 4 43.03.0 4.74.7 15.4 15.4 5 54.04.0 4.74.7 17.1 17.1 6 65.05.0 4.74.7 19.0 19.0 7 76.06.0 4.74.7 21.1 21.1 9 97.07.0 4.74.7 23.4 23.4 11 118.08.0 4.74.7 25.7 25.7 13 139.09.0 4.74.7 28.1 28.1 16 1610.010.0 4.74.7 30.6 30.6 19 1915.015.0 4.74.7 43.5 43.5 38 3820.020.0 4.74.7 56.9 56.9 65 65

aaRCV (pRCV (p < <0.05) = 2.77 (CV0.05) = 2.77 (CVAA 22 + CV + CVII22))½½, assuming no statistical evidence of , assuming no statistical evidence of

heterogenityheterogenity

bbNumber = mean result is within Number = mean result is within 5%of homeostatic set point1.965%of homeostatic set point1.9622 x (CV x (CVAA22 + +

CVCVII22) ) ½½/25./25.

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: -

CVCVI I for concentration = 23.8% for concentration = 23.8%

CVCVI 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%

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.

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

Reference IntervalsReference Intervals

Dr WA BartlettDr WA Bartlett

Birmingham Heartlands & Solihull Birmingham Heartlands & Solihull NHS Trust (Teaching)NHS Trust (Teaching)