1 Is it potent? Can these results tell me? Statistics for assays
Ann Yellowlees PhD Quantics Consulting Limited Slide 2 2 Contents
Role of statistics in bioassay Regulations Estimating Relative
Potency Choice of model for RP estimation Parallelism Case study
Slide 3 3 Role of statistics in bioassay Design / optimisation
Analysis Validation Slide 4 4 Why use statistics - regulations
Validation of routine and custom assays: ICH Q6B SPECIFICATIONS:
TEST PROCEDURES AND ACCEPTANCE CRITERIA FOR
BIOTECHNOLOGICAL/BIOLOGICAL PRODUCTS Assessment of biological
properties constitutes an....essential step in establishing a
complete characterisation profile Appropriate statistical analysis
should be applied Methods of analysis, including justification and
rationale, should be described fully A relevant, validated potency
assay should be part of the specifications for a biotechnological
or biological drug substance and/or drug product Slide 5 5 Why use
statistics - regulations Stability testing, more defined by ICH:
ICH Q5C QUALITY OF BIOTECHNOLOGICAL PRODUCTS At time of submission,
applicants should have validated the methods that comprise the
stability-indicating profile and the data should be available for
review ICH Q1A (R2) STABILITY TESTING An approach for analyzing
data of quantitative attribute that is expected to change with time
is to determine the time at which the 95% one-sided confidence
limit for the mean curve intersects the acceptance criterion Slide
6 6 Estimating Relative Potency Analysis of dose response data
Choosing the best model for estimating RP Checks for parallelism
Estimating RP Calculations: RP and its precision Improving
precision Slide 7 7 Data types Response per unit (animal, welI,
etc): Binary Dead / alive at a given time point Diseased / disease
free at a given time point Summarised as % or proportion Continuous
Antibody level Time of death Optical density Slide 8 8 Continuous
response Note: Log concentration S shape Noise level varies Slide 9
9 Continuous response means Slide 10 10 What is Relative Potency?
Potency of the sample in comparison with the reference
Mathematically this is the same as: Slide 11 11 Estimating RP Slide
12 12 When is it valid to calculate RP? When the bioassay is a
dilution assay the unknown preparation to be assayed is supposed to
contain the same active principle as the standard preparation, but
in a different ratio of active and inert compounds ** Implies RP
constant across concentrations One curve is a horizontal shift of
the other i.e. parallel curves ** European Pharmacopoeia 3.1.1
Slide 13 13 Check for parallelism 1.Ph. Eur approach: Residual sum
of squares (RSS) and the F-test Arbitrary p value Penalises good
data 2.USP Confidence intervals on differences between parameters
Arbitrary confidence level Arbitrary limits on width Penalises bad
data 3.Others Chi squared test Similar to (1) Slide 14 14 Check for
parallelism EP, USP are guidance only No simple, generally
applicable statistical solution exists to overcome these
fundamental problems. The appropriate action has to be decided on a
case-by-case basis USP Workshop 2008 Slide 15 15 Estimating RP from
data 1.Choose a model; fit to each material 2.Check system
suitability reference is behaving as expected parallel models are
appropriate 3.Calculate RP and 95% confidence interval Slide 16 16
Choose a model Slide 17 17 Choose a model Slide 18 18 Linear model
(4 concentrations) Assume: Middle 4 concentrations of interest
Parallel when the same for both materials Slide 19 19 Four
parameter logistic model Note: If A = 0 and B = 1 this is a simple
logistic model: proportions. Slide 20 20 Four parameter logistic
model Parallel: when A, B and scale are the same for both materials
Slide 21 21 Five parameter logistic model Parallel: when A, B scale
and asym are the same for both materials Slide 22 22 Which model to
use? Slide 23 23 Which model to use? Consider the relevant range of
concentrations How much do you need to know about the ends? Pros
and cons Need more data to fit curves More data = more precision?
Weighting / variability at ends Formal statistical tests for fit Is
a 5PL model really necessary or is it a statistical remedy for a
bad assay? R Capen Chair, USP workshop 2008 Slide 24 24 4 PL
parallel model chosen Slide 25 25 Calculate RP and 95% CI Parallel
model provides an estimate of log e RP Horizontal distance between
the curves log e RP = 0.233 Back-transform for RP RP = e 0.233 =
1.26 95% confidence interval for RP (1.26) (0.84, 1.90) Slide 26 26
Assay development / optimisation Choose statistical model Design
assay Number of replicates per concentration Operators, days etc to
achieve required precision for RP Set suitability criteria for
assay Reference behaviour Parallelism Slide 27 27 Model selection
for an assay Model must: Fit the data Allow RP calculation most of
the time i.e. the curves are parallel Provide precise estimates of
RP Slide 28 28 Example with 12 plates 12 development plates run
Wide range of concentrations 0.001 2000 IU/ml Reference and sample
3 replicates 4 statistical models examined Linear (4), Linear (6),
4PL, 5PL Parallelism Precision Fit Slide 29 29 Slide 30 30 Summary:
Parallelism test (F) ModelN failing (P < 0.05)% parallel * LM
40100% LM 6187% 4PL467% 5PL375% * Denominator = 12 Slide 31 31
Summary: Precision Slide 32 32 Linear model: 4 points, parallel
Slide 33 33 Summary: Model selection Linear model based on 4
concentrations All 12 pairs passed linearity test All 12 pairs
passed parallelism test Provided the best precision No apparent
bias Slide 34 34 Improving precision If the linear model can be
justified: Allows extra replication Better precision within plate ?
fewer plates required How low can you go? 2 doses: test for
linearity cannot be done 3 doses: test for linearity has low power
Slide 35 35 Summary System software provides most of the required
statistics per plate When do you need a statistician? Choosing
model Appropriate statistical analysis should be applied Methods of
analysis, including justification and rationale, should be
described fully Designing and validating assay Assessing sources of
variation Simulation Setting suitability criteria A relevant,
validated potency assay should be part of the specifications for a
biotechnological or biological drug substance and/or drug product
Slide 36 36 Thank you Quantics staff Kelly Fleetwood, Catriona
Keerie Analysis and graphics Slide 37 37
