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1 Parallelism in practice USP Bioassay Workshop August 2010 Ann Yellowlees Kelly Fleetwood Quantics Consulting Limited.

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Presentation on theme: "1 Parallelism in practice USP Bioassay Workshop August 2010 Ann Yellowlees Kelly Fleetwood Quantics Consulting Limited."— Presentation transcript:

1 1 Parallelism in practice USP Bioassay Workshop August 2010 Ann Yellowlees Kelly Fleetwood Quantics Consulting Limited

2 2 Contents What is parallelism? Approaches to assessing parallelism  Significance  Equivalence Experience Discussion

3 3 Setting the scene: Relative Potency RP: ratio of concentrations of reference and sample materials required to achieve the same effect RP = C ref / C samp

4 4 Parallelism  One curve is a horizontal shift of the other  These are ‘parallel’ or ‘similar’ curves  Finney: A prerequisite of all dilution assays

5 5 Real data: continuous response

6 6 Linear model (4 concentrations) Parallel when the slopes β equal Linear: Y = a + β log (C)

7 7 Four parameter logistic model 4PL: Y = γ + (δ - γ) / [1 + exp (β log (C) – α)] Parallel when asymptotes γ, δ slope β equal

8 8 Five parameter logistic model Parallel when asymptotes γ, δ slope β asymmetry φ equal 5PL: Y = γ + (δ - γ) / [1 + exp (β log (C) – α) ] φ

9 9 Tests for parallelism Approach 1 Is there evidence that the reference and test curves ARE NOT parallel? Compare unrestricted vs restricted models  Test loss of fit when model restricted to parallel  ‘p value’ approaches 1.Traditional F test approach as preferred by European Pharmacopoeia 2.Chi-squared test approach as recommended by Gottschalk & Dunn (2005)

10 10 Approach 2 Is there evidence that the reference and test curves ARE parallel? Equivalence test approach as recommended in the draft USP guidance (Hauck et al 2005)  Fit model allowing non-parallel curves  Confidence intervals on differences between parameters Pharmacopoeial disharmony exists!! (existed?)

11 11 In practice... Four example data sets  Data set 1: 60 RP assays (96 well plates, OD: continuous)  Data set 2: 15 RP assays (96 well plates, OD : continuous)  Data set 3: 12 RP assays (96 well plates, OD : continuous)  Data set 4: 60 RP assays (in vivo, survival at day x: binary*) * treated as such for this purpose; wasteful of data

12 12 In practice... We have applied the proposed methods in the context of individual assay ‘pass/fail’ (suitability): Data set 1  Compare 2 ‘significance’ approaches  Compare ‘equivalence’ with ‘significance’ Data sets 2, 3  Compare 2 ‘significance’ approaches Data set 4  Compare ‘F test’ (EP) with ‘equivalence’ (USP)

13 13 Data set 1 60 RP assays 8 dilutions 2 independent wells per dilution 4PL a good fit (vs 5PL) NB precision

14 14 Data set 1: F test and chi-squared test F test: straightforward Chi-squared test:  need to establish mean-variance relationship

15 15 Data set 1: F test and chi-squared test F test:  12/60 = 20% of assays have p < 0.05  Evidence of dissimilarity? – OR –  Precise assay? Chi-squared test:  58/60 = 97% of assays have p < 0.05!  Intra-assay variability is low  differences between parallel and non-parallel model are exaggerated

16 16 Data set 1: Comparison of approaches to parallelism

17 Some evidence of ‘hook’ in model Residual SS inflated 17

18 18 Data set 1: Comparison of approaches to parallelism

19 19 Data set 1: F test and chi-squared test RSS parallel = 159 RSS non-parallel = 112 RSS p – RSS np = 47 Pr(  2 3 >47) < 0.01 F test: P = 0.03

20 20 Data set 1: F test and chi-squared test RSS parallel = 100.2 RSS non-parallel = 99.0 RSS p – RSS np = 1.2 Pr(  2 3 >1.2) = 0.75

21 Data set 1: USP methodology Prove parallel Lower asymptote:

22 22 Data set 1: USP methodology Upper asymptote:

23 23 Data set 1: USP methodology Scale:

24 24 Data set 1: USP methodology Criteria for 90% CI on difference between parameter values:  Lower asymptotes: (-0.235, 0.235)  Upper asymptotes: (-0.213, 0.213)  Scales: (-0.187, 0.187) Applying the criteria:  3/60 = 5% of assays fail the parallelism criteria No assay fails more than one criterion

25 25 Data set 1: Comparison of approaches to parallelism

26 This plate ‘fails’ all 3 tests  USP: Lower asymptote 26

27 27 Data set 1: Comparison of approaches to parallelism Equivalence test: scales not equivalent F test p-value = 0.60 Chi-squared test p-value < 0.001

28 28 Data set 2: Comparison of approaches to parallelism

29 29 Data set 3: Comparison of approaches to parallelism

30 30 In practice... Data set 4:  Compare ‘F test’ with ‘equivalence’ Methodology for Chi-squared test not developed for binary data

31 31 Data set 4 60 RP assays 4 dilutions 15 animals per dilution

32 32 Data set 4: Comparison of approaches to parallelism

33 33 Data set 4: Comparison of approaches to parallelism

34 34 Broadly... F test  Fail (?wrongly?) when very precise assay  Pass (?wrongly?) when noisy  Linear case: p value can be adjusted to match equivalence Chi-squared  Fail when very precise assay (even if difference is small)  If model fits badly – weighting inflates RSS (e.g. hook)  2 further data sets supported this USP  Limits are set such that the extreme 5% will fail They do! Regardless of precision, model fit etc

35 35 Stepping back… What are we trying to do?  Produce a biologic to a controlled standard that can be used in clinical practice  For a batch we need to know its potency With appropriate precision In order to calculate clinical dose

36 36 Some thoughts 1.Establish a valid assay Use all development assay results unless a physical reason exists to exclude them  Statistical methodology can be used to flag possible outliers for investigation  USP applies this to individual data points Parallelism / similarity  Are the parameter differences fundamentally zero? Or is there a consistent slope difference (e.g)?  Equivalence approach + judgment for acceptable margin

37 37 Some thoughts 2. Set number of replicates to provide required precision  Combine RP values plus confidence intervals for reportable value 3.Per assay, use all results unless physical reason not to  (They are part of the continuum of assays)  Flag for investigation using statistical techniques Reference behaviour Parallelism 4. Monitor performance over time (SPC) Reference stability Parallelism

38 38 Which parallelism test? Our view:  Chi squared test requires too many complex decisions and is very sensitive to the model  F test not generally applicable to the assay validation stage Does not allow examination of the individual parameters Does not lend itself to judgment about ‘How parallel is parallel?’  The equivalence test approach fits in all three contexts With adjustment of the tolerance limits as appropriate

39 39 Thank you USP the invitation Clients use of data  BioOutsource: www.biooutsource.comwww.biooutsource.com  Other clients who prefer to remain anonymous Quantics staff analysis and graphics  Kelly Fleetwood (R), Catriona Keerie (SAS)

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