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: john_gordon@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 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