statistical considerations drs. jan welink training workshop: assessment of interchangeable...
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Statistical considerations
Drs. Jan Welink
Training workshop: Assessment of Interchangeable Multisource Medicines, Kenya, August 2009
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Statistical considerationsStatistical considerations
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BioequivalenceBioequivalence
The primary concern in bioequivalence assessment
is to limit the risk of a false declaration of equivalence.
Statistical analysis of the bioequivalence trial should
demonstrate that the clinically significant difference
in bioavailability is unlikely…..
[WHO working document multisource (generic) pharmaceutical products: Guidelines on registration requirements to establish interchangeability, Nov. 2005]
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BioequivalenceBioequivalence
Reference Test
2 pharmaceutical products
Bioequivalent??
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BioequivalenceBioequivalence
Important PK parameters
AUC :
area under the concentration-time curve measure of the extent of absorption
Cmax :the observed maximum concentration of a drug
measure of the rate of absorption
tmax: time at which Cmax is observed
measure of the rate of absorptionCmax
Tmax
AUC
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Statistical considerationsStatistical considerations
How similar is similar?
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Statistical considerationsStatistical considerations
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Statistical considerationsStatistical considerations
Statistical test should take into account…
The consumer (patient) risk of erroneously accepting bioequivalence (primary concern health authorities)
Minimize the producer (pharmaceutical company) risk of erroneously rejecting bioequivalence
Choice:- two one-side test procedure- confidence interval ratio T/R 100 (1-2)- set at 5% (90% CI)
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Statistical considerationsStatistical considerations
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Statistical considerationsStatistical considerations
Consumer Risk
The risk of declaring two product BE when they’re not is called the ‘consumer risk’
In statistical terms, this is a Type I error– The risk of rejecting the null hypothesis when it’s true
The consumer risk is set at 5%
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Statistical considerationsStatistical considerations
Producer Risk
The risk of declaring two products NOT BE when they truly are BE is called the ‘producer risk’
In statistical terms, this is a Type II error– The risk of accepting the null hypothesis
when it’s false
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Statistical considerationsStatistical considerations
The risks are related
If the consumer risk is reduced, the producer risk increases
In statistical terms, if you lower the acceptable risk of making a Type I error, the risk of making a Type II error increases
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Statistical considerationsStatistical considerations
Average Bioequivalence:
two drug products are bioequivalent ‘on the average’ when the (1-2α)
confidence interval around the Geometric Mean Ratio falls
entirely within 80-125%) regulatory control of specified limit(
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Statistical considerationsStatistical considerations
Some International Criteria
Country/RegionAUC 90% CI
Criteria
Cmax 90% CI
Criteria
Canada (most drugs)80 – 125%none (point estimate
only)
Europe (some drugs)80 – 125%75 – 133%
South Africa (most drugs)
80 – 125%75 – 133% (or broader if justified)
Japan (some drugs)80 – 125%Some drugs wider than 80 – 125%
Worldwide (WHO)80 – 125%“acceptance range for Cmax may be
wider than for AUC”
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Statistical considerationsStatistical considerations
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Statistical considerationsStatistical considerations
)( 05.0,exp.100%90 abdfbA SEtLSMLSMCIGeometric
Least SquareMeans from ANOVA
t-statistic with0.05 in one
tail
StandardError
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Statistical considerationsStatistical considerations
BE Limits
The concept of the 20% difference is the basis of BE limits (goal posts)
If the concentration dependent data were linear, the BE limits would be 80-120%
On the log scale, the BE limits are 80-125%
The 90%CI must fit entirely within specified BE limits e.g. 80-125%
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Statistical considerationsStatistical considerations
Variables:..
Log transformation:– For all concentration dependent pharmacokinetic variables
(AUC and Cmax)
Analysis of log-transformed data by means of ANOVA (analysis of variance)– includes usually formulation, period, sequence or carry-over, and subject factors– parametric test (normal theory)
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Statistical considerationsStatistical considerations
The sources of variance in the model are– Product– Period– Sequence– Subject (Sequence)
– Residual variance
These accountfor all the inter-subjectvariability
This estimatesIntra-subject variability
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Statistical considerationsStatistical considerations
The width of the 90%CI depends on – The magnitude of the WSV (ANOVA-CV (residual variance))– The number of subjects in the BE study
The bigger the WSV (within- or intra-subject variability), the wider the CI
If the WSV is high, more subjects are needed to give statistical power compared with when the WSV is low
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Statistical considerationsStatistical considerations
ANOVA CV
intra-subject variability
unexplained random
variability
subject by formulation interaction
analytical
variability
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Statistical considerationsStatistical considerations
80 100 125
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Statistical considerationsStatistical considerations
why log-transformation:
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Statistical considerationsStatistical considerations
Why parametric testing and not non-parametric:
applicant: after log transformation not normal distributed!
based upon test for normality, however these are insensitive and it concerns a small study
normally after log transformation AUC and Cmax are normal distributed
reason for non-normality should be explained
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OutliersOutliers
‘Outliers’
Definition:
♦ aberant/irregular values (e.g. no plasma concentration, ‘late’ high concentrations….)
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OutliersOutliers
‘Outliers’
Explanation: ♦ vomiting?♦ non-compliant volunteers?♦ bioanalytical failure?♦ individual pharmacokinetics?♦ protocol violations?♦ ……
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OutliersOutliers
‘Outliers’
Handling:
♦ “…pharmacokinetic data can only be excluded based on non-statistical reasons that have been defined previously in the protocol.
♦ Exclusion of data can never be accepted on the basis of statistical analysis or for pharmacokinetic reasons alone, because it is impossible to distinguish between formulation effects and pharmacokinetic effects.
♦ Results of statistical analyses with and without the excluded subjects should be provided.” (excerpt from Q&A Doc Ref: EMEA/CHMP/EWP/40326/2006)
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Power calculationPower calculation
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EndEnd
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