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Dear Colleagues,
For those who are familiar with Classical and Westlake methods in calculation of
Confidence Interval (CI) in Bioequivalence study, please kindly explain the
difference between the two methods.
Is it compulsory to calculate CI using both methods ?
Kindly suggest articles or references that we can refer to for more information.
Thank you.
Regards,
Ken Peh
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The following message was posted to: PharmPK
Dear Kean, I would like to advice you to send this query to Bebac website. According, my
experience Westlake provides a larger confidence interval than classical approach. Best
regards, Daniel Campos
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The following message was posted to: PharmPK
Dear Ken Peh,
Westlake's method results in confidence intervals symmetric around unity,
while classical confidence intervals are symmetric around the point
estimate.
The Westlake's method was initially thought as more understandable by
"non-statisticians" with the confidence interval being expressed as e.g.
"Test = 100 +/- 15% of the Reference" (rather than e.g. "Test = 88 - 107% of
the reference" as given by the classical approach).
To my knowledge, Westlake's method is obsolete (at least in the field of
bioequivalence) and is not required anymore by any Regulatory Agency.
Best regards,
Fabrice
--
Fabrice Nollevaux,
Pharmacometrics and Statistics Team Manager
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Ken,
The idea between the Westlake method was to compute a confidence interval on the
ration of means (test/reference) such that the interval was centered about 100%.
The thought being that clinicians would prefer to quote the bioavailability of
a test formulation as being +/- 15% (say) of the reference. At one time I
believe this was required by FDA OGD but is no longer requested nor required
today. For historical purposes, WinNonlin's bioequivalence routinely includes
the Westlake CI as part of the textual output (as well as many other measures).
Note that classical CIs are symmetric on ln scale about the difference in the ln
means for the two formulations, but symmetry is lost when then taking the
anti-logs.
Here is sample output from WinNonlin. Note the computation of the Westlake
intervals. These formulations are clearly not bioequivalent no matter what
method you use!
Hope this helps,
Dan Weiner
-
Formulation variable: Form
Reference: t LSMean= 1.179502 SE= 0.152106 GeoLSM= 3.252753
-
Test: c LSMean= 1.520851 SE= 0.152106 GeoLSM= 4.576117
Difference = 0.3413, Diff_SE= 0.1854, df= 16.0
Ratio(%Ref) = 140.6844
Classical Westlake
CI 80% = ( 109.7991, 180.2575) ( 34.8546, 165.1454)
CI 90% = ( 101.7746, 194.4699) ( 19.7490, 180.2510)
CI 95% = ( 94.9545, 208.4378) ( 5.5450, 194.4550)
Failed to show average bioequivalence for confidence=90.00 and percent.0.
Two One-Sided T-tests
Prob(< 80%)=0.0039 Prob(> 125%)=0.7336 Max=0.7336 Total=0.7375
Anderson-Hauck Procedure
A.H. p-value = 0.729756
Power of ANOVA for Confidence Level 90.00
Power at 20% = 0.302114
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dear Ken,
the classical confidence interval is derived from a two sample t statistic. it
is not symmetric about '0' (for the difference b/w means ) and not symmetric
about '1' (for ratio of means) As the equivalence limits are always given in a
symmetric form , Westlake C.I was developed which is adjusted to be symmetric
about 0 for difference( and unity for ratio of means).. hope this helps
thanks
shikha
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Dear Weiner,
Thank you for your clarification.
I would like to know further if you mean that both Westake and Classical methods can be
used for untransformed and ln-transformed data ?
As we do not have WinNonlin, we calculate using computer software such as Microsoft Excel.
For BE study, we run statistical analysis using ANOVA on AUC and Cmax for the
untransformed and ln-transformed data. We follow the method given in the following text
book:-
Wagner JG. Fundamentals of Clinical Pharmacokinetics, 1st ed., Drug Intelligence
Publication, Inc. Hamilton, IL, 1975, 285-305.
Once we have the ANOVA table, we calculate the confidence interval using the Westlake
method (0.82 - 1.25).
As for the calculation of Classical method, we follow the text book :
DESIGN & ANALYSIS OF BIOAVAILABILITY AND BIOEQUIVALENCE STUDIES', by 'Chow & Liu'.
(chapter -4 for CI).
So far, we thought that in classical method, the AUC and Cmax are untransformed. After we
create the ANOVA table, we calculate the confidence interval on the untransformed AUC and
Cmax.
I would be grateful if clarification could be given.
Thank you.
Regads,
Ken Peh
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The following message was posted to: PharmPK
Dear Ken,
Mathematically speaking: yes, both methods (Westlake and Classical) can be
used on untransformed and ln-transformed data.
=46rom a regulatory point of view, only an analysis using the classical method
on ln-transformed data is generally required, based on the following steps:
1) Calculation of a classical 90%CI on the test-reference difference for the
ln-transformed PK parameters
2) Transformation of this 90% CI back into the original scale (i.e. by
taking the exponential of each limit), which gives a (classical) 90%CI
around the test/reference geometric means ratio
3) Comparison of the back-transformed 90% CI to the regulatory acceptance
range (80.00-125.00% in most situations)
Regards,
Fabrice
--
Fabrice Nollevaux,
Pharmacometrics and Statistics Team Manager
www.arlenda.com
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