Sample Size Estimation for BE Studies

1• 59

Workshop | Bucarest, 19 March 2013

Helmut Schütz

BEBAC

Helmut Schütz

BEBAC

Biostatistics

Sample Size Estimation

for BE Studies

Biostatistics

Sample Size Estimation

for BE Studies

Bine ai venit!

Wikimedia

Commons

•

2011

Korinna

•

Creative Commons Attribution

-

ShareAlike

3.0

Unported

2• 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

To bear in Remembrance...

Whenever a theory appears to you

as the only possible one, take this as

a sign that you have neither under

-

stood the theory nor the problem

which it was intended to solve.

Karl R. Popper

Even though it’s

applied

science

we’re dealin’ with, it still is

–

science!

Leslie Z. Benet

3• 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Overview

z‘Classical’ sample size estimation in BE

Patient’s & producer’s risk

Power in study planning

zUncertainties

Variability

Test/Reference-ratio

Sensitivity analysis

zRecent developments

Review of guidelines

4• 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

α

and

β

zAll formal decisions are subjected to two types

of error:



α

Probability of Error Type I (aka Risk Type I)



β

Probability of Error Type II (aka Risk Type II)

Example from the justice system:

Error type IICorrect

Presumption of innocence accepted

(not guilty)

CorrectError type I

Presumption of innocence not

accepted (guilty)

Defendant guiltyDefendant innocentVerdict

5• 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

α

and

β

zOr in more statistical terms:

zIn BE-testing the null hypothesis is

bioin

equivalence (

µ

1

≠

µ

2

)!

Error type IICorrect (H

0

)Failed to reject null hypothesis

Correct (H

a

)Error type I Null hypothesis rejected

Null hypothesis falseNull hypothesis trueDecision

Producer’s riskCorrect (not BE)Failed to reject null hypothesis

Correct (BE)Patient’s riskNull hypothesis rejected

Null hypothesis falseNull hypothesis trueDecision

6• 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

α

…

zPatient’s Risk to be treated with an inequivalent

formulation

(H

0

falsely rejected)

BA of the test compared to reference in a particular

patient is risky either

below 80% or above 125%.

If we keep the risk of particular patients at

α

0.05

(5%), the risk of the entire population of patients

(<80% and >125%) is 2×

α

(10%) – expressed as:

90% CI = 1 – 2×

α

= 0.90.

95% one-sided CI

5%

p

atients <0.8

0.5 0.6 0.8 1 1.25 1.67 2

95% one-sided CI

5%

p

atients >1.25

0.5 0.6 0.8 1 1.25 1.67 2

two 95% one-sided CIs

≈ 90% two-sided CI

p

atient

p

o

p

ulation

[

0.8

,

1.25

]

0.5 0.6 0.8 1 1.25 1.67 2

7• 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

… and

β

zProducer’s Risk to get no approval of an

equivalent formulation

(H

0

falsely not rejected)

Set in study planning to ≤0.2 (20%), where

power = 1 –

β

= ≥80%

If power is set to 80 %,

one out of five studies will fail just by chance!

β

0.20

not BE

BE

α

0.05

0.20 = 1/5

A posteriori (post hoc) power does not make sense!

Either a study has demonstrated BE or not.

8• 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Power Curves

Power to show BE

with 12 – 36

subjects for

CV

intra

20%

n 24 ↓ 16:

power 0.896 → 0.735

µ

T

/

µ

R

1.05 ↓ 1.10:

power 0.903 → 0.700

2×2 Cross-over

µT/µR

Power

20% CV

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

12

16

24

36

9• 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Power

vs.

Sample Size

zIt is not possible to calculate the required

sample size directly.

zPower is calculated instead; the smallest

sample size which fulfills the minimum target

power is used.

Example:

α

0.05, target power 80%

(

β

0.2), T/R 0.95, CV

intra

20% →

minimum sample size 19 (power 81%),

rounded up to the next even number in

a 2×2 study (power 83%).

n power

16 73.54%

17 76.51%

18 79.12%

19 81.43%

20 83.47%

10 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Power

vs.

Sample Size

2×2 cross-over, T/R 0.95, AR 80–125%, target power 80%

0

8

16

24

32

40

5% 10% 15% 20% 25% 30%

CV

intra

sample size

80%

85%

90%

95%

100%

power

sample size power power for n=12

11 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Background

zReminder: Sample Size is not directly

obtained; only power

zSolution given by DB Owen (1965) as a

difference of two bivariate noncentral

t-distributions

Definite integrals cannot be solved in closed form

‘Exact’ methods rely on numerical methods (currently

the most advanced is AS 243 of RV Lenth;

implemented in R, FARTSSIE, EFG). nQuery uses an

earlier version (AS 184).

12 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Background

zPower estimations…

‘Brute force’ methods (also called ‘resampling’ or

‘Monte Carlo’) converge asymptotically to the true

power; need a good random number generator (e.g.,

Mersenne Twister) and may be time-consuming

‘Asymptotic’ methods use large sample

approximations

Approximations provide algorithms which should

converge to the desired power based on the

t-distribution

13 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sample Size

(Guidelines)

zRecommended minimum

 12 WHO, EU, CAN, NZ, AUS, AR, MZ, ASEAN States,

RSA, Russia (2011 Draft)

 12 USA ‘A pilot study that documents BE can be

appropriate, provided its design and execution are

suitable and a sufficient number of subjects (e.g.,

12) have completed the study.’

 18 Russia (2008)

 20 RSA (MR formulations)

 24 Saudia Arabia (12 to 24 if statistically justifiable)

 24 Brazil

 ‘Sufficient number’ Japan

14 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sample Size

(Limits)

zMaximum

 NZ: If the calculated number of subjects appears to be

higher than is ethically justifiable, it may be

necessary to accept a statistical power which is

less than desirable. Normally it is not practical to

use more than about 40 subjects in a bioavailability

study.

 All others: Not specified (judged by IEC/IRB or local

Authorities).

ICH E9, Section 3.5 applies: “The number of

subjects in a clinical trial should always be large

enough to provide a reliable answer to the

questions addressed.”

15 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Power &

Sample Size

zReminder

 Generally power is set to at least 80% (

β

, error type II:

producers’s risk to get no approval for a bioequivalent

formulation; power = 1 –

β

).

1 out of 5 studies will fail just by chance!

 If you plan for power of less than 70%, probably you will face

problems with the ethics committee (ICH E9).

 If you plan for power of more than 90% (especially with

low variability drugs), problems with regulators are

possible (‘forced bioequivalence’).

 Add subjects (‘alternates’) according to the expected

drop-out rate – especially for studies with more than two

periods or multiple-dose studies.

16 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

US FDA,

Canada

TPD

zStatistical Approaches to Establishing

Bioequivalence (2001)

Based on maximum difference of 5%.

Sample size based on 80 – 90% power.

zDraft GL (2010)

*

Consider potency differences.

Sample size based on 80 – 90% power.

Do not interpolate linear between CVs (as stated in

the GL)!

* All points removed in current (2012) GL.

17 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

EU

zEMEA NfG on BA/BE (2001)

Detailed information (data sources, significance

level, expected deviation, desired power).

zEMA GL on BE (2010)

Batches must not differ more than 5%.

The number of subjects to be included in the study

should be based on an appropriate sample size

calculation.

Cookbook?

18 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Hierarchy

of Designs

zThe more ‘sophisticated’ a design is, the more

information can be extracted.

Hierarchy of designs:

Fully replicate (TRTR | RTRT, TRT | RTR) °

Partial replicate (TRR | RTR | RRT) °

Standard 2×2 cross-over (RT | RT) °

Parallel (R | T)

Variances which can be estimated:

Parallel: total variance (between + within)

2×2 Xover: + between, within subjects ®

Partial replicate: + within subjects (reference) ®

Full replicate: + within subjects (reference, test) ®

Information

19 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Coefficient(s) of Variation

zFrom any design one gets variances of

lower design levels also.

Total CV% from a 2×2 cross-over used in planning

a parallel design study:

 Intra-subject CV% (within)

 Inter-subject CV% (between)

 Total CV% (pooled)

intra

%100 1

W

MSE

CV e

=

⋅−

2

inter

%100 1

BW

MSE MSE

CV e

−

=

⋅−

2

total

%100 1

BW

MSE MSE

CV e

+

=

⋅−

20 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Coefficient(s) of Variation

zCVs of higher design levels not available.

If only mean ± SD of reference is available…

 Avoid ‘rule of thumb’ CV

intra

=60% of CV

total

 Don’t plan a cross-over based on CV

total

 Examples (cross-over studies)

 Pilot study unavoidable, unless

 Two-stage sequential design is used

54.6

62.1

20.4

CV

total

C

max

AUC

τ

AUC

t

metric

lansoprazole DR

paroxetine MR

methylphenidate MR

drug, formulation

47.0

25.2

7.00

CV

intra

25.147SD

55.132MD

19.112SD

CV

inter

ndesign

21 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Data from

Pilot Studies

zEstimated CVs have a high degree of uncer-

tainty (in the pivotal study it is more likely that

you will be able to reproduce the PE, than the

CV)

The smaller the size of the pilot,

the more uncertain the outcome.

The more formulations you have

tested, lesser degrees of freedom

will result in worse estimates.

Remember: CV is an estimate –

not carved in stone!

22 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pilot Studies:

Sample Size

zSmall pilot studies (sample size <12)

Are useful in checking the sampling schedule and

the appropriateness of the analytical method, but

are not suitable for the purpose of sample size

planning!

Sample sizes (T/R 0.95,

power ≥80%) based on

a n=10 pilot study

ratioCV

86

68

52

36

24

uncertain

1.3036640

1.3085235

1.3004030

1.2862825

1.2002020

uncert./fixedfixed

CV%

If pilot n=24:

n=72, ratio 1.091

library(PowerTOST)

expsampleN.TOST(alpha=0.05,

targetpower=0.80, theta1=0.80,

theta2=1.25, theta0=0.95, CV=0.40,

dfCV=24-2, alpha2=0.05, design="2x2")

23 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pilot Studies:

Sample Size

zModerate sized pilot studies (sample size

~12–24) lead to more consistent results

(both CV and PE).

If you stated a procedure in your protocol, even

BE may be claimed in the pilot study, and no

further study will be necessary (US-FDA).

If you have some previous hints of high intra-

subject variability (>30%), a pilot study size of

at least 24 subjects is reasonable.

A Sequential Design may also avoid an

unnecessarily large pivotal study.

24 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pilot Studies:

Sample Size

zDo not use the pilot study’s CV, but calculate

an upper confidence interval!

Gould (1995) recommends a 75% CI (i.e., a

producer’s risk of 25%).

Apply Bayesian Methods (Julious and Owen 2006,

Julious 2010) implemented in R’s

PowerTOST/expsampleN.TOST.

Unless you are under time pressure, a Two-Stage

Sequential Design will help in dealing with the

uncertain estimate from the pilot study.

25 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Hints

zLiterature search for CV%

Preferably other BE studies (the bigger, the better!)

PK interaction studies (Cave: Mainly in steady

state! Generally lower CV than after SD).

Food studies (CV higher/lower than fasted!)

If CV

intra

not given (quite often), a little algebra

helps. All you need is the 90% geometric

confidence interval and the sample size.

26 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Algebra…

zCalculation of CV

intra

from CI

 Point estimate (PE) from the Confidence Limits

 Estimate the number of subjects / sequence (example

2×2 cross-over)

¾ If total sample size (N) is an even number, assume (!)

n

1

= n

2

= ½N

¾ If N is an odd number, assume (!)

n

1

= ½N + ½, n

2

= ½N –½(not n

1

= n

2

= ½N!)

 Difference between one CL and the PE in log-scale; use

the

CL which is given with more significant digits

ln ln ln ln

CL lo CL hi

PE CL or CL PE∆= − ∆= −

lo hi

P

ECLCL=⋅

27 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Algebra…

zCalculation of CV

intra

from CI (cont’d)

 Calculate the Mean Square Error (MSE)

 CV

intra

from MSE as usual

12

2

12 , 2

12

2

11

CL

nn

MSE

t

nn

α

−⋅ + −





∆



=







+⋅





intra

%100 1

MSE

CV e

=

⋅−

28 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Algebra…

zCalculation of CV

intra

from CI (cont’d)

 Example: 90% CI [0.91 – 1.15], N 21 (n

1

= 11, n

2

= 10)

0.91 1.15 1.023PE =⋅=

ln1.15 ln1.023 0.11702

CL

∆= − =

2

0.11702

2 0.04798

11

1.729

11 10

MSE





==





+×





0.04798

intra

% 100 1 22.2%CV e=× −=

29 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Algebra…

zProof: CI from calculated values

 Example: 90% CI [0.91 – 1.15], N 21 (n

1

= 11, n

2

= 10)

ln ln ln 0.91 1.15 0.02274

lo hi

PE CL CL=⋅=×=

2 2 0.04798

= 0.067598

21

MSE

SE

N

∆

⋅×

==

ln

0.02274 1.729 0.067598

PE t SE

CI e e

∆

±⋅

±×

==

0.02274 1.729 0.067598

0.91

1.15

lo

hi

CI e

−×

+×

==

9

30 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sensitivity to Imbalance

zIf the study was more imbalanced than

assumed, the estimated CV is conservative

 Example: 90% CI [0.89 – 1.15], N 24 (n

1

= 16, n

2

= 8, but

not reported as such); CV 24.74% in the study

24.74816

25.43915

25.911014

26.201113

26.291212

CV%n

2

n

1

Sequences

in study

Balanced Sequences

assumed…

31 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

No

Algebra…

zImplemented in R-package PowerTOST,

function

CVfromCI (not only 2×2 cross-over,

but also parallel groups, higher order cross-

overs, replicate designs). Example:

library(PowerTOST)

CVfromCI(lower=0.91, upper=1.15, n=21, design="2x2", alpha=0.05)

[1] 0.2219886

32 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Literature data

Doxicycline (37 studies from Blume/Mutschler, Bioäquivalenz: Qualitätsbewertung wirkstoffgleicher

Fertigarzneimittel, GOVI-Verlag, Frankfurt am Main/Eschborn, 1989-1996)

10

15

20

25

30

200 mg

100 mg

total

0

2

4

6

8

10

12

frequency

CVs

studies

33 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pooling of CV%

zIntra-subject CV from different studies can be

pooled

(LA Gould 1995, Patterson and Jones 2006)

In the parametric model of log-transformed data,

additivity of variances (not of CVs!) apply.

Do not use the arithmetic mean (or the geometric

mean either) of CVs.

Before pooling variances must be weighted

acccording to the studies’ sample size and

sequences

 Larger studies are more influentual than smaller ones.

 More sequences (with the same n) give higher CV.

34 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pooling of CV%

zIntra-subject CV from different Xover studies

Calculate the variance from CV

Calculate the total variance weighted by df

Calculate the pooled CV from total variance

Optionally calculate an upper (1–

α

) % confidence

limit on the pooled CV (recommended

α

= 0.25)

2

W

df

σ

∑

2

1

W

df df

CV e

σ

∑∑

=

−

22

,

1

Wdf

df

CV

CL e

α

σχ

∑

=

−

22

intra

ln( 1)

W

CV

σ

=

+

35 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pooling of CV%

zDegrees of freedom of various Xover designs

2x4x43n – 42×4×4 replicate design

4x43n – 64×4 Latin Squares, Williams’

2x2x32n – 32×2×3 replicate design

2x2x43n – 42×2×4 replicate design

3n – 4

2n – 4

n – 2

df

2x3x22×3×3 partial replicate

3x6x36 sequence Williams’ design

3x33×3 Latin Squares

2x22×2×2 cross over

Name in PowerTOSTName

36 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pooling of CV%

zExample: 3 studies, different Xover designs

CV

intra

nseq.df

σ

W

σ

²

W

σ

²

W

× df

15% 12 6

20 0.149 0.0223 0.4450

25% 16 2

14 0.246 0.0606 0.8487

20% 24 2

22 0.198 0.0392 0.8629

σ

pooled

σ

²

pooled

N52

Σ

56

Σ

2.1566 0.196 0.0385

CV

pooled

CV

g.mean

19.81% 19.57%

α

1 –

αχ

²

(

α

,df)

0.25 0.75 48.546 21.31% +7.6%

2.1566 56

2×n- 4

n-2

0.0385

100 e -1

56×0.0385 48.546

100 e -1

37 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pooling of CV%

zR package PowerTost function CVpooled,

example’s data.

library(PowerTOST)

CVs <- ("

PKmetric | CV | n | design | source

AUC | 0.15 | 12 | 3x6x3 | study 1

AUC | 0.25 | 16 | 2x2 | study 2

AUC | 0.20 | 24 | 2x2 | study 3

")

txtcon <- textConnection(CVs)

CVdata <- read.table(txtcon, header=TRUE, sep="|",

strip.white=TRUE, as.is=TRUE)

close(txtcon)

CVsAUC <- subset(CVdata,PKmetric=="AUC")

print(CVpooled(CVsAUC, alpha=0.25), digits=4, verbose=TRUE)

Pooled CV = 0.1981 with 56 degrees of freedom

Upper 75% confidence limit of CV = 0.2131

38 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pooling of CV%

zOr you may combine pooling with an estimated

sample size based on uncertain CVs (we will

see later what that means).

R package PowerTost function expsampleN.TOST,

data of last example.

CVs and degrees of freedom must be given as

vectors:

CV = c(0.15,0.25,0.2), dfCV = c(20,14,22)

39 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pooling of CV%

library(PowerTOST)

expsampleN.TOST(alpha=0.05,

targetpower=0.8, theta0=0.95,

CV=c(0.15,0.25,0.2),

dfCV=c(20,14,22),

alpha2=0.25, design="2x2",

print=TRUE, details=TRUE)

++++++++ Equivalence test - TOST ++++++++

Sample size est. with uncertain CV

-----------------------------------------

Study design: 2x2 crossover

Design characteristics:

df = n-2, design const. = 2, step = 2

log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8

BE margins = 0.8 ... 1.25

Null (true) ratio = 0.95

Variability data

CV df

0.15 20

0.25 14

0.20 22

CV(pooled) = 0.1981467 with 56 df

one-sided upper CL = 0.2131329 (level = 75%)

Sample size search

n exp. power

16 0.733033

18 0.788859

20 0.832028

40 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Pooling of CV%

z‘Doing the maths’ is just part of the job!

Does it make sense to pool studies of different

‘quality’?

 The reference product may have been subjected to many

(minor only?) changes from the formulation used in early

publications.

 Different bioanalytical methods are applied. Newer (e.g.

LC/MS-MS) methods are not necessarily better in terms of

CV (matrix effects!).

 Generally we have insufficient information about the clinical

setup (e.g. posture control).

 Review studies critically; don’t try to mix oil with water.

41 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Tools

zSample Size Tables (Phillips, Diletti, Hauschke,

Chow, Julious, …)

zApproximations (Diletti, Chow, Julious, …)

zGeneral purpose (SAS, S+, R, StaTable, …)

zSpecialized Software (nQuery Advisor, PASS,

FARTSSIE, StudySize, …)

zExact method (Owen – implemented in R-

package

PowerTOST )

*

* Thanks to Detlew Labes!

42 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Approximations obsolete

zExact sample size tables still useful in

checking plausibility of software’s results

z Approximations based on

noncentral

t (FARTSSIE17)

http://individual.utoronto.ca/ddubins/FARTSSIE17.xls

or / S+ →

z Exact method (Owen) in

R-package PowerTOST

http://cran.r-project.org/web/packages/PowerTOST/

require(PowerTOST)

sampleN.TOST(alpha=0.05,

targetpower=0.80, theta0=0.95,

CV=0.30, design='2x2')

alpha <- 0.05 # alpha

CV <- 0.30 # intra-subject CV

theta1 <- 0.80 # lower acceptance limit

theta2 <- 1/theta1 # upper acceptance limit

theta0 <- 0.95 # expected ratio T/R

PwrNeed <- 0.80 # minimum power

Limit <- 1000 # Upper Limit for Search

n <- 4 # start value of sample size search

s <- sqrt(2)*sqrt(log(CV^2+1))

repeat{

t <- qt(1-alpha,n-2)

nc1 <- sqrt(n)*(log(theta0)-log(theta1))/s

nc2 <- sqrt(n)*(log(theta0)-log(theta2))/s

prob1 <- pt(+t,n-2,nc1); prob2 <- pt(-t,n-2,nc2)

power <- prob2-prob1

n <- n+2 # increment sample size

if(power >= PwrNeed | (n-2) >= Limit) break }

Total <- n-2

if(Total == Limit){

cat('Search stopped at Limit', Limit,

' obtained Power', power*100, '%\n')

} else

cat('Sample Size', Total, '(Power', power*100, '%)\n')

43 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Comparison

CV%

original values Method Algorithm 5 7.5 10 12 12.5 14 15 16 17.5 18 20 22

PowerTOST 1.1-02 (2013

)

exact Owen’s Q

4 688 10 12 12 14 16 16 20 22

Patterson & Jones (2006)

noncentr.

t

AS 243

45 7 8 9111213 15161922

Diletti

et al.

(1991) noncentr.

t

Owen’s Q

45 7

NA

9

NA

12

NA

15

NA

19

NA

nQuery Advisor 7 (2007)

noncentr.

t

AS 184

4 688 10 12 12 14 16 16 20 22

FARTSSIE 1.7 (2010)

noncentr.

t

AS 243

45 7 8 9111213 15161922

noncentr.

t

AS 243

45 7 8 9111213 15161922

brute force ElMaestro

45 7 8 9111213 15161922

StudySize 2.0.1 (2006)

central

t

?NA

5 7 8 9111213 15161922

Hauschke

et al.

(1992) approx.

t

NA NA

8 8 10 12 12 14 16 16 20 22

Chow & Wang (2001)

approx.

t

NA

6 6 8 81012 12 14 16 18 22

Kieser & Hauschke (1999)

approx.

t

2

NA

6 8

NA

10 12 14

NA

16 20 24

EFG 2.01 (2009)

CV%

original values MethodAlgorithm22.524252627.528303234363840

PowerTOST 1.1-02 (2013

)

exact Owen’s Q

24 26 28 30 34 34 40 44 50 54 60 66

Patterson & Jones (2006)

noncentr.

t

AS 243

23 26 28 30 33 34 39 44 49 54 60 66

Diletti

et al.

(1991) noncentr.

t

Owen’s Q

23

NA

28

NA

33

NA

39

NA NA NA NA NA

nQuery Advisor 7 (2007)

noncentr.

t

AS 184

24 26 28 30 34 34 40 44 50 54 60 66

FARTSSIE 1.7 (2010)

noncentr.

t

AS 243

23 26 28 30 33 34 39 44 49 54 60 66

noncentr.

t

AS 243

23 26 28 30 33 34 39 44 49 54 60 66

brute force ElMaestro

23 26 28 30 33 34 39 44 49 54 60 66

StudySize 2.0.1 (2006)

central

t

?

23 26 28 30 33 34 39 44 49 54 60 66

Hauschke

et al.

(1992) approx.

t

24 26 28 30 34 36 40 46 50 56 64 70

Chow & Wang (2001)

approx.

t

24 26 28 30 34 34 38 44 50 56 62 68

Kieser & Hauschke (1999)

approx.

t

NA

28 30 32

NA

38 42 48 54 60 66 74

EFG 2.01 (2009)

44 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sample size tables

zDiletti E, Hauschke D and VW Steinijans

Sample size determination for bioequivalence assessment by means of confidence intervals

Int J Clin Pharmacol Ther Toxicol 29/1, 1–8 (1991)

0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20

5.01154445722

7.521755571244

10.03511 7 6 7102075

12.5 54 16 9 8 9 14 30 117

15.0 77 22 12 10 12 19 41 167

17.5103291513152556226

20.0134371916183272293

22.5168462319233990368

25.02065628232748110452

27.52476733273357132543

30.02927939323867155641

α

0.05,

∆

0.2 [0.80 – 1.25], Power 80%

CV%

PE (GMR, T/R)

0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20

5.01464445828

7.528965681660

10.0 48 14 8 7 8 13 26 104

12.5742111 9111840161

15.0106291512152557231

17.5142392015193475312

20.0185502619244399405

22.52326331233054124509

25.02847737283665151625

27.53429244344378181751

30.0 403 108 52 39 51 92 214 888

α

0.05,

∆

0.2 [0.80 – 1.25], Power 90%

PE (GMR, T/R)

CV%

45 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sample size tables

zTóthfalusi L and L Endrényi

Sample Sizes for Designing Bioequivalene Studies for Highly Variable Drugs

J Pharm Pharmaceut Sci 15/1, 73–84 (2011)

0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20

301945327222645104>201

35127512925294584>201

40 90 44 29 27 30 42 68 139

45 77 40 29 27 29 37 57 124

50 75 40 30 28 30 37 53 133

55 81 42 32 30 32 40 56 172

60 88 46 36 33 36 44 63 >201

65 99 53 40 37 40 50 71 >201

70109584541455680>201

75136675046506289>201

80144725451556897>201

α

0.05, ABEL (EMA), partial repl., Power 80%

CV%

PE (GMR, T/R)

0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20

30 145 45 24 21 24 39 82 >201

35 74 37 24 22 25 34 54 109

40 60 33 24 22 24 31 47 104

45 59 31 23 22 24 29 43 116

50 66 30 24 22 23 28 41 133

55 80 30 24 22 24 28 44 172

60 88 31 24 23 24 30 50 >201

65 98 32 25 24 25 31 53 >201

70 106 35 26 25 26 31 62 >201

75 136 38 27 26 27 34 70 >201

80 144 40 40 27 29 37 76 >201

α

0.05, RSABE (FDA), partial repl., Power 80%

PE (GMR, T/R)

CV%

46 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sample size tables

zNever interpolate!

zUse the most conservative cell entry

(higher CV, PE away from 1)

Example: Sample size for CV 18%, PE 0.92, 80% power?

0.90 0.95 1.00

17.5 29 15 13

20.0 37 19 16

CV%

PE (GMR, T/R)

0.90 0.95 1.00

17.5 29 15 13

20.0 37 19 16

CV%

PE (GMR, T/R)

Round up to next

even number (38)

47 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Tables

vs.

calculations

zThe penalty to be paid using tables might be

high – especially if uprounding has to be

applied.

Sample sizes of the example: CV 18%, PE 0.92, 80% power

zTable: n = 38

zApproximations

z Hauschke et al. 1992: n = 24

z Chow and Wang 2001: n = 22

z FARTSSIE.xls: n = 22

zExact: n = 22

48 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Tables

vs.

calculations

zIf we planned the study in 38 subjects (tables)

instead of the required 22 (exact) we gain a lot

of power, but how much?

zn = 22: power 80.55%

zn = 38: power 95.56%

zIf step sizes to wide calculations mandatory

zPowerTOST supports simulations for ABEL and

RSABE

49 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Tables

vs.

calculations

library(PowerTOST)

sampleN.scABEL(CV=0.40, details=F)

library(PowerTOST)

sampleN.RSABE(CV=0.40, details=F)

++++ Reference scaled ABE crit. ++++

Sample size estimation

-------------------------------------

Study design: 2x3x3

log-transformed data (multiplicative

model)

1e+05 studies simulated.

alpha = 0.05, target power = 0.8

CVw(T) = 0.4; CVw(R) = 0.4

Null (true) ratio = 0.95

ABE limits/PE constraints = 0.8…1.25

Regulatory settings: FDA

Sample size

n power

24 0.808640

++++++ scaled (widened) ABEL +++++++

Sample size estimation

------------------------------------

Study design: 2x3x3

log-transformed data (multiplicative

model)

1e+05 studies simulated.

alpha = 0.05, target power = 0.8

CVw(T) = 0.4; CVw(R) = 0.4

Null (true) ratio = 0.95

ABE limits/PE constraints = 0.8…1.25

Regulatory settings: EMA

- CVswitch = 0.3, cap on ABEL

if CV > 0.5

- Regulatory constant = 0.76

Sample size

n power

30 0.827170

50 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sensitivity Analysis

zICH E9 (1998)

Section 3.5 Sample Size, paragraph 3

 The method by which the sample size is calculated

should be given in the protocol […]. The basis of

these estimates should also be given.

 It is important to investigate the sensitivity of the

sample size estimate to a variety of deviations from

these assumptions and this may be facilitated by

providing a range of sample sizes appropriate for a

reasonable range of deviations from assumptions.

 In confirmatory trials, assumptions should normally

be based on published data or on the results of

earlier trials.

51 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sensitivity Analysis

zExample

nQuery Advisor:

σ

22

intra

ln( 1); ln(0.2 1) 0.198042

w

CV=+ +=

20% CV, PE 90%:

power 90% → 67%

20% CV:

n=26

20% CV, 4 drop outs:

power 90% → 87%

25% CV:

power 90% → 78%

25% CV, 4 drop outs:

power 90% → 70%

52 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sensitivity Analysis

zExample

PowerTOST, function sampleN.TOST

library(PowerTOST)

sampleN.TOST(alpha=0.05, targetpower=0.9, theta0=0.95,

CV=0.2, design="2x2", print=TRUE)

+++++++++++ Equivalence test - TOST +++++++++++

Sample size estimation

-----------------------------------------------

Study design: 2x2 crossover

log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.9

BE margins = 0.8 ... 1.25

Null (true) ratio = 0.95, CV = 0.2

Sample size

n power

26 0.917633

53 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sensitivity Analysis

zTo estimate Power for a given sample size,

use function power.TOST

library(PowerTOST)

power.TOST(alpha=0.05, theta0=0.95, CV=0.25, n=26, design="2x2")

[1] 0.7760553

power.TOST(alpha=0.05, theta0=0.95, CV=0.20, n=22, design="2x2")

[1] 0.8688866

power.TOST(alpha=0.05, theta0=0.95, CV=0.25, n=22, design="2x2")

[1] 0.6953401

power.TOST(alpha=0.05, theta0=0.90, CV=0.20, n=26, design="2x2")

[1] 0.6694514

power.TOST(alpha=0.05, theta0=0.90, CV=0.25, n=22, design="2x2")

[1] 0.4509864

54 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Sensitivity Analysis

zMust be done before the study (a priori)

zThe Myth of retrospective (a posteriori)

Power…

High values do not further support the claim of

already demonstrated bioequivalence.

Low values do not invalidate a bioequivalent

formulation.

Further reader:

RV Lenth (2000)

JM Hoenig and DM Heisey (2001)

P Bacchetti (2010)

55 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

Thank You!

Sample Size Estimation

for BE Studies

Open Questions?

Helmut Schütz

BEBAC

Consultancy Services for

Bioequivalence and Bioavailability Studies

1070 Vienna, Austria

[email protected]

56 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

To bear in Remembrance...

Power. That which statisticians are always calculating

but never have.

Power: That which is wielded by the priesthood

of

clinical trials, the statisticians, and a stick which they

use

to beta their colleagues.

Power Calculation

–

A guess masquerading

as mathematics.

Stephen Senn

You should treat as many patients as possible with the

new drugs

while they still have the power to heal.

Armand Trousseau

57 • 59

Workshop | Bucarest, 19 March 2013

Sample Size Estimation for BE Studies

The Myth of Power

There is simple intuition behind

results like these: If my car made

it to the top of the hill, then it is

powerful enough to climb that hill;

if it didn’t, then it obviously isn’t

powerful enough. Retrospective

power is an obvious answer to a

rather uninteresting question. A