Statistical considerations Drs. Jan Welink Training workshop: Assessment of Interchangeable...

Statistical considerations

Drs. Jan Welink

Training workshop: Assessment of Interchangeable Multisource Medicines, Kenya, August 2009

Assessment of Interchangeable Multisource Medicines, Kenya, August 20092 |

Statistical considerationsStatistical considerations


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]



Reference Test

2 pharmaceutical products

Bioequivalent??



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



How similar is similar?





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)





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%



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



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



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(



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”





)( 05.0,exp.100%90 abdfbA SEtLSMLSMCIGeometric

Least SquareMeans from ANOVA

t-statistic with0.05 in one

tail

StandardError



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%



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)



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



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



ANOVA CV

intra-subject variability

unexplained random

variability

subject by formulation interaction

analytical

variability



80 100 125



why log-transformation:



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


OutliersOutliers

‘Outliers’

Definition:

♦ aberant/irregular values (e.g. no plasma concentration, ‘late’ high concentrations….)


OutliersOutliers

‘Outliers’

Explanation: ♦ vomiting?♦ non-compliant volunteers?♦ bioanalytical failure?♦ individual pharmacokinetics?♦ protocol violations?♦ ……


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)


Power calculationPower calculation


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