TRAINING WORKSHOP ON PHARMACEUTICAL QUALITY, GOOD MANUFACTURING PRACTICE

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TRAINING WORKSHOP ON PHARMACEUTICAL QUALITY, GOOD
MANUFACTURING PRACTICE BIOEQUIVALENCE

• Statistical Considerations for Bioequivalence
  Studies
• Presented by
• John Gordon, Ph.D.
• Consultant to WHO
• e-mail john_gordon_at_hc-sc.gc.ca

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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 patients 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