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
Plate5
RLU
250
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
Variabil i ty C hart 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 within 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 within 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