Kyiv, 2005-10-06 1
TRAINING WORKSHOP ON PHARMACEUTICAL QUALITY,
GOOD MANUFACTURING PRACTICE & BIOEQUIVALENCE
Statistical Considerations for
Bioequivalence Studies
Prepared by John Gordon, Ph.D.
Presented by Hans Kemmler
White Sands, 23 August 2006
e-mail: [email protected]
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Introduction
Performance will never be identical– Two formulations– Two batches of the same formulation?– Two tablets within a batch?
Purpose of bioequivalence (BE)– Demonstrate that performance is not
“significantly” different– Same therapeutic effect– What constitutes a ‘significant’
difference?
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Introduction cont.
Agencies must define a standard
consisting of the following:– Bioavailability metrics– One or more acceptance criteria for
each metric– Number and type of metrics may vary
• Dependent on drug formulation
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Metrics for BE studies
Concentration vs. time profiles– Area under the curve (AUC)– Maximal concentration (Cmax)– Time to Cmax (Tmax)
Statistical measures of BE metrics– Mean– Variance
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Logarithmic Transformations
Distribution of BE metrics– Skewed to the right– Consistent with lognormal distribution
Proportionate effects
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Example
What would be the expected drop in AUC if a patient received 20% less drug?
Subject 1– Original AUC = 100 units– 20% drop = 20 units
Subject 2– Original AUC = 1000 units– 20% drop = 200 units
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Example cont.
Log transformation – Absolute intrasubject differences
become independent of patient’s AUC
Log(80) – log(100) = log(800) – log(1000)
Log transformation for concentration
dependent measures– Accepted by regulatory agencies
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Analysis of Variance
ANOVA
Most common technique of analysis and
estimation
Lognormal distribution– Raw data must be log transformed– Comparison of means and variances of
transformed data– Geometric mean– Results reported in original scale
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ANOVAHypothesis Testing
Null hypothesis test– No formulation difference
Convey little detail
Statistically significant difference– Clinically significant?
Imprecise estimates (high variability)– No statistically significant difference
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Confidence Intervals (CI)
Inference from study to wider world
Range of values within which we can
have a chosen confidence that the
population value will be found
Study findings expressed in scale of
original data measurement
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Confidence Intervals cont.
Width of CI indication of (im)precision
of sample estimates
Width partially dependent on:– Sample size– Variability of characteristic being
measured• Between subjects• Within subjects• Measurement error• Other error
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Confidence Intervals cont.
Degree of confidence required– More confidence = wider interval
In other words, width of CI dependent
on:– Standard error (SE)
• Standard deviation, sample size
– Degree of confidence required
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Confidence Intervals cont.
Statistical analysis of pharmacokinetic
measures– Confidence intervals– Two one-sided tests
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Typical BEAssessment Criteria
90% confidence interval
Ratio of geometric means
Acceptance criteria: 80 – 125%
Log transformed AUCT & Cmax
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Statistical Approaches for BE
Average bioequivalence
Population bioequivalence
Individual bioequivalence
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Statistical approaches cont.
Average BE– Conventional method– Compares only population averages– Does not compare products variances– Does not assess subject x formulation
interaction
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Statistical approaches cont.
Population and individual BE– Include comparisons of means and
variances
Population BE– Assesses total variability of the
measure in the population
Individual BE– Assesses within subject variability– Assesses subject x formulation
interaction
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Design Considerations
Non-replicated designs– Most common– Crossover designs– Two-formulation, two-period, two-
sequence, crossover design– Average or population BE approaches– Parallel designs
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Design Considerations
Replicated designs– Can be used for all approaches– Critical for individual BE approach– Suggested replicated design
• Two-formulation, four-period, two-sequence
• T R T R• R T R T
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Statistical effects in model
Sequence effect
Subject (SEQ) effect
Formulation effect
Period effect
Carryover effect
Residual
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Outliers
Statistical outliers
Valid clinical/physiological justification
Re-testing?
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Add-on designs
All studies should be powered appropriately
If study fails the standard– Reformulate– Undertake larger study– Add-on study
• Consistency testing
Group-sequential designs– Penalty for ‘peeking’ at results