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Statistical Comparison of Immunogenicity Cutpoint Factors Using Log Transformation Dingzhou (Dean) Li PharmaTx Statistics, Pfizer Global R&D MBSW, 2010 Definitions • Immunogenicity: – Causing or capable of producing an immune response. – Unwanted for target-binding drugs – Desired for vaccines – Assay required for FIH • Anti-drug antibody (ADA) : – Binds to a portion of the drug thus preventing the drug from binding to its target – Affects the conformation of the drug so that when it binds to its target it is not functional. – Cross reactivity with endogenous proteins; greatest regulatory concern Immunoassays Bridging ELISA Bridging ECL Sandwich (nonbridging ELISA) SA-HRP Biotinlabeled drug Detection Antibody/reagent:HRP ADA ADA ADA Drug Biotin Drug Drug Fab From Quantitative to Qualitative • Quantitative – Continuous units of reference standard • Qualitative – Reference standard is not available – Ordinal or nominal • Quasi-quantitative – Continuous units of signals Endpoint Titer: A quasi-quantitative method • A way of expressing [Ab] in blood or serum • Related to the number of times you can dilute a sample of serum and still detect Ab • Titer = Reciprocal of the last dilution of a titration giving a measurable effect. – Reported log2 of the titer. Endpoint Titer Example 2000 1000 Plate 1 RLU 800 600 500 400 300 Titer=1894222 200 cutpoint 0 1000000 2000000 Dilution 3000000 Cutpoint • Cutpoint: Positive vs. Negative • How to calculate cutpoint? – Pooled negative controls (PNC) – Cutpoint = Mean(PNC) + cα*SD(PNC) – cα : Critical value at significance level α, depending on underlying distribution (e.g. c0.05 = 1.645 for normal distribution) – Parametric or nonparametric • Screening vs. Confirmatory Cutpoint Factor • For each plate in production, want to readily get the plate-specific cutpoint • Multiply the mean PNC by a factor – Cutpoint = Mean(PNC) * CPF • Need two steps… Two Steps • Step 1: Cutpoint factor determination – Negative control only • Step 2 : Production – Negative control, positive control, patient samples on the same plate – Endpoint titer, inference, sensitivity, etc Step 1: Cutpoint Factor Determination • 150 samples distributed on 6 plates – Sample: a serum sample from a subject • For each plate, – CPF (Plate) = Cutpoint (Plate)/Mean(Plate) • Average CPF for all the plates to get an overall CPF – This is the CPF for Step 2 Step 1: Pooled Negative Controls 275 250 Plate5 RLU 225 cutpoint 200 175 150 125 0 10 20 30 Negative Control Sample 40 50 Determination of CPF from PNC Cutpoint CPF Overall CPF Plate 1 Plate 2 Plate 3 Plate 4 Plate 5 Plate 6 Sub 1 Rep 1 Sub 26 Rep 1 Sub 1 Rep 2 Sub 26 Rep 2 Sub 1 Rep 3 Sub 26 Rep 3 Sub 2 Rep 1 Sub 27 Rep 1 Sub 2 Rep 2 Sub 27 Rep 2 Sub 2 Rep 3 Sub 27 Rep 3 … … … … … … Sub 25 Rep 1 Sub 50 Rep 1 Sub 25 Rep 2 Sub 50 Rep 2 Sub 25 Rep 3 Sub 50 Rep 3 275 1.19 150 1.25 1.15 1.21 209 1.19 1.17 1.31 Step 2: Typical Production Plate Layout 1 ID 2 3 4 5 6 7 8 9 10 11 12 A Rep 1 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 1000 B Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 2000 C Rep 3 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 4000 D Rep 4 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 8000 E Rep 5 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 16000 F Rep 6 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 32000 G Rep 7 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 64000 H Rep 8 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2 128000 NC PC sample1 sample2 sample3 sample4 • Cutpoint = Mean(NC) * Overall CPF (from Step 1) • Use the cutpoint for endpoint titer calculation Comparing Cutpoint Factors • Are CPFs the same at different setups? – Reagent lot, serum type, etc – Important for process improvement – Decision making • How to compare CPF with repeated measures? – A subject may contribute multiple samples Statistical Treatment of CPF • Note for a certain plate, CPF = (Mean+ cα*SD)/Mean = 1+ cα*CV • CV has a noncentral t-distribution (Johnson and Welch, 1967) – Computationally difficult (though tools do exist) – Hard to extend to repeated measure scenarios • Alternative: Log-transform – In many cases, the signals (relative light units) are approximately log-normal Example: 25 Samples 130 140 150 160 170 180 190 200 210 Normal(158.68,17.8202) LogNormal(5.06118,0.10533) • Goodness of fit – Normal: p = 0.02 (S-W test) – LogNormal: p = 0.10 (Kolmogorov’s D) Log-transform Approach 2 log normal ( , ) • It is well known that if X ~ then CV(X) = exp( 2 ) 1 • When σ is small, exp( 2 ) 1 • So statistical inference can be based upon variability of the logged data Example: 25 Samples 130 140 150 160 170 180 190 200 210 Normal(158.68,17.8202) LogNormal(5.06118,0.10533) • Noncentral t-distribution – CV = (0.088, 0.157) – CPF= (1.145, 1.258) • Log-transform – CV = (0.084, 0.150) – CPF = (1.138, 1.247) Homogeneity of Variability • Levene’s test – Fit 1st ANOVA to get residual variability estimate – Fit 2nd ANOVA on abs(residual) to test equal variance – Readily extends to repeated-measure cases • Models: – i: Lot; j: replicate; k: subject – 1st ANOVA: RLUijk = μ + replicatekj(i) + subjectk + εijk => Get residuals rijk – 2nd ANOVA • Within-lot: • Between-lot: rijk = μ + replicatej(i) + εijk rijk = μ + loti + εijk Example Variability Chart for Log(RLU) 10.0 Log(RLU) • Two different reagent lots • Three plates at each lot • Samples from 30 subjects 10.5 9.5 9.0 8.5 • Results: a2 a3 b1 1 b2 b3 2 Rep w ithin Lot 0.20 0.15 Std Dev – In Lot 1, Plate a2 has higher variability than other plates – No significant difference in variability between Lots 1 and 2 a1 0.10 0.05 0.00 a1 a2 1 Rep w ithin Lot a3 b1 b2 2 b3 Discussions • Cutpoint analysis is crucial in various applications of the endpoint titer method • Cutpoint in most cases depends on the plate, experimental parameters, etc. So using a fixed cutpoint is not recommended • Uncertainty in CPF will translate to error in the endpoint titer Acknowledgements • Daniel Baltrukonis – Immunotox CoE • Jessica Duffy – Immunotox CoE • David Potter – PharmaTx Statistics