Overview–Courses

1、Biological variation Introduction Estimation (ANOVA application) Index-of-individuality Comparison of a result with a reference interval (Grey-zone) Reference change value (RCV)Biological variationBiological variation25Statistics & graphics for the laboratoryReference interval and biological variati

2、onReference interval encompasses: pre-analytical imprecision analytical imprecision within-subject biological variation between-subject biological variationUsefulness of reference intervalsReference intervals are of most use when the between-subject variation is smaller than the within-subject varia

3、tion:CVB-S 1If not, individuals may have values which lie within reference limits but are highly unusual for them: See also later: Index of individualityUses of biological variation Setting desirable analytical goals Assessing significance of changes in serial results Assessing utility of population

4、 based reference values Deciding number of specimens required to assess homeostatic set point of an individual Determining optimum mode for result reporting Comparing available tests Assessing clinical utility of testsAbbreviations for biological variation CVW-S = Within-subject CVB-S = Between-subj

5、ect CVG = Group = SQRT(CV2W-S + CV2B-S) = of the reference intervalNote: sometimes CVG is used to designate CVB-S (e.g. in the Westgard database on analytical specifications)Biological variationBiological variation26Statistics & graphics for the laboratoryEstimation of biological variation (ANOVA-ap

6、plication)Approaches One overall analysis using nested ANOVA based on dedicated software (SAS, SPSS, BMDP etc.). Stepwise approach with computation of variances at each level.General requirement: Repeated measurements at each level, i.e. at least duplicates, in order to resolve the variance componen

7、ts.a time period.Inspection of data on biological variationGenerally, ANOVA is robust towards moderate deviations from normality, but it is sensitive towards outliers.Occurrence of outliersWithin subgroups or one subgroup versus the bulk of the rest of subgroups Within-subject variationHomogeneity/h

8、eterogeneityWithin- & between subject biological variationExample CreatinineBiological variation27Statistics & graphics for the laboratoryAnalytical & biological variationEstimation of biological variationRemark Consider the importance of analytical imprecision.Inter (B-S)/intra (W-S) -individual bi

9、ological variationAnalytical variation (A)Total dispersion of a single measurement of individuals*:T2 = B-S2 + (W-S2 + A2) = B-S2 + T, W-S2Index of individuality (Ii) (see also later):T,W-S/B-S W-S/B-S*Ignoring pre-analytical variationComponents of variation-ANOVABetween (B-S)- and within-individual

10、(W-S) biological variation* Inclusive analytical variation (T,W-S)The within-biological variation is here obtained as an average value for all the studied individuals, which generally is preferable.Biological variation28Statistics & graphics for the laboratoryAnalytical & within biological variation

11、Analytical variation can be minimized by collecting and running the samples within one run.Shortcut computational principlesDuplicate sets of measurementsSD = d2/2n0.5 for n duplicate measurements, where d is the difference between pairs of measurements.Examples Measurements of duplicate samples to

12、derive the SDA Duplicate samples from each individual to derive SDT,W-S Practical approachObtain repeated samples over a suitable time period, e.g. 5 samples, from a collection of individuals, e.g. 10-20 subjects, and measure each sample in duplicate. Inspect/test data for outliers and variance homo

13、geneity. Carry out a simple ANOVA on the means of duplicates and derive SDB-S and SDT,W-S Derive SDA from duplicates Derive SDW-S from the relation: SDT,W-S2 = 0.5 SDA2 + SDW-S2(the factor 0.5 enters because the means of duplicate measurements entered the analysis)Biological variationCochran&Bartlet

14、t; ANOVA29Statistics & graphics for the laboratoryIndex-of-individuality (II)Index-of-individuality (II)CVW-S/CVB-Sis calledIndex-of-individuality =Ratio between within- and between-subject variationOften, the analytical variation is included, to giveII = (CVW-S2 + CVA2)/CVB-SHarris EK Clin Chem 197

15、4;20:1535-42ExamplesCalculation of CVGRange = 27Mean = 18 of the RI in % of the mean = 36%Biological variation30Statistics & graphics for the laboratoryIndex-of-individuality (II)II = CVW-S/CVB-SIf II 1.4low degree of individualityreference ranges are more usefulMost analytes have II 1.4 !ExamplesBi

16、ological variation31Statistics & graphics for the laboratoryComparison of a result with a reference-intervalThe grey-zoneExample2 measurement results for serum glucose: (1) 88 mg/100 ml (2) 109 mg/100 ml with a reference-interval: 60 - 100 mg/100 ml.Question: Is result (1) actually inside, result (2

17、) outside the reference-interval?Data :CVa = 2 %; CVi = 6.1 %CVtot = SQRT(CVa2 +CVi2) = SQRT(2 2 + 6.1 6.1) = 6.4%Transform CVtot into stot: 6.4 mg/100 ml (at 100 mg/100 ml)Calculate the “grey-zone” around the limit of 100 mg/100 ml with 95 (90) % probability (Note: one-sided):1.65 (1.29) stot or 1.

18、65 (1.29) 6.4 mg/100 ml = 10.6 (8.3) mg/100 ml.Grey zone at 95 % = 89.4 - 110.6 mg/100 ml Grey zone at 90 % = 91.7 - 108.3 mg/100 ml.Thus, result (1) lies inside the reference-interval in both cases.Result (2) lies outside the reference-interval only in the case of 90% probability.Conclusion: If one

19、 wants to miss few pathological cases, one would calculate the grey zone below the limit with 95 % probability, the one above the limit with 90 %.Glucose Grey-zoneAlternative approachWith the statistical concept of Power: How big is the chance that we decide healthy, when the patient is sick, in fac

20、t (-error; false negatives).Biological variationThe power concept will be explained later. It is important for: Sample size method comparison Limit of detection (LOD) IQC32Statistics & graphics for the laboratoryP = 95%Biology, only1.65 CVW-SGrey zone for results at reference limitsP = 95%Total1.65

21、UA2+CVW-S2UAAnalytical uncertainty(see Goals)Biological variation33Statistics & graphics for the laboratoryReference Change Value (RCV), or Medically significant difference (Dmed)95 % interval for difference between two samplings and measurementsDmed = 1.96 2 (CV2W-S + CV2Anal)The RCV is particular

22、important for analytes with high CVB-S.med for the “creatinine clearance”C: ml plasma cleared per min per standard body surface Ucr: concentration of creatinine in urine (mg/ml)Pcr: concentration of creatinine in plasma (mg/ml)V: volume urine flow in ml per min A: body surface in m2 ForUcr: 1 mg/mlP

23、cr: 0.01mg/mlV: 1 ml/minA: 1.88 m2 (man of 70 kg and 1.75 m tall)is C = 92 ml/min/1.73 m2Calculation of sa:When CVa = 2% for Ucr=1 mg/ml, then sa = 0.02 mg/ml.When CVa = 2% for Pcr= 0.01 mg/ml, then sa = 0.0002 mg/ml. CVa for V is not considered. Note: in our example, sy = sa; y = Csa = 92 0.0283 = 2.6 ml/min/1.73m2Biological variation34Statistics & graphics for the laboratorymed for the “creatinine clearance”Calculation:CVi = 15 % or at C = 92 ml/min/1.73 m2 , si = 13.8 ml/min/1.73 m2 (*)stot = SQRT2.62 + 13.82 = 14 ml/min/1.73m2Thus:Dmed = 1.96