Biostatistics in Bioequivalence

BIOSTATISTICS IN BIOEQUIVALENCE

Dr. Bhaswat S. ChakrabortySr. VP & Chair, R&D Core Committee

Cadila Pharmaceuticals Ltd.Former Senior Clinical Reviewer, TPD (Canadian FDA)

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Presented at the IVIVC & BABE SUMMIT 2015Holiday Inn, Mumbai, Nov. 23, 2015

CONTENT GUIDELINESImportance of Biostatistics Basic concepts of biostatistics Sample size calculation Statistical aspects of Reference

scaling

Conclusion 2

BIOSTATISTICS Statistics applied to biological data (in biology and

biomedical sciences) In such data subjects (patients, mice, cells, etc.)

exhibit considerable variation in their response to stimuli may be due to different treatments or due to chance,

measurement error,  or other characteristics of subjects Biostatistics disentangles  these different sources of

variation distinguishes between correlation and causation & infers

from known samples about the populations e.g. do the results of treating patients with two therapies justify

the conclusion that one treatment is better than the other? are the products bioequivalent? 

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BIOSTATISTICS.. It applies statistical theory to real-world problems

designing and conducting biomedical experiments and clinical trials, BE trials, PK, toxicology..

Biostatisticians are specialists in the evaluation of data as scientific evidence Provide the mathematical framework that transcends

the scientific context to generalize the findings. Their expertise includes the design, conduct, data

generation and analysis of experiments Finally, the interpretation & reporting of results

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BASICS OF BIOSTATISTICS IN BE Data collection, organization & descriptive

statistics Population assumptions

Parametric or non-parametric Normal or other distribution Homogeneity of variance

Study Designs Cross over, replicate, parallel

Sample size calculation Tests of significance, ANOVA Inference on bioequivalence 5

DATA COLLECTION, ORGANIZATION & DESCRIPTIVE STATISTICS Descriptive statistics are numbers that are

used to summarize and describe data"data" refers to the information that has been

collected from an experiment, a survey, a historical record, etc.

In bioequivalnce study, DS could be summary of demographics plasma and PK ratio or geometric means and 90%CI

Descriptive statics are presented using both tables and figures 6

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POPULATION PARAMETRIC ASSUMPTIONS

Parametric and nonparametric are two broad classifications of statistical procedures

Parametric statistics assume about the shape of the distribution in the underlying population assume a normal, lognormal, Weibull distribution

Also about the form or parameters of the assumed distribution means and standard deviations

Nonparametric statistics rely on no or few assumptions about the shape or parameters of the population distribution from which the samples were drawn

If the data deviate strongly from parametric assumptions, using the parametric procedure could lead to incorrect conclusions

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PARAMETRIC & ANALOGOUS NON-PARAMETRIC PROCEDURES

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PARAMETRIC ASSUMPTIONS IN BE STUDIES Three basic assumptions

Normality random variables in BE are normally distributed

Homoscedasticity variance of the dependent variable is constant; it does not vary

with independent variables, e.g., formulation, subject, period Independence

random variables are independent lnCmax or lnAUC obtained from a volunteer plasma

levels is drawn from a population N(μ, ²) An individual observation of parameters μ & ²

defined the distribution of lnAUC can be observed in this volunteer

Data from another volunteer administeredthe same formulation is also drawn from N(μ, ²) population

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LOG TRANSFORMATION

μ is the population mean of lnX and also the population median of X

Following a log transformation, BE methods compares the median or geometric means

Log transformation stabilizes the variance and to obtain a symmetrical distribution of variables; for Tmax usually heteroscedasticity remains

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If ),(~ln 2NX

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BIOEQUIVALENCE STUDY DESIGNS For almost all generic drugs today, the

regulatory standard is “average bioequivalence (ABE)”

Concluded from 2-product, 2-period, crossover studies with fixed effects

That meansAn average patient (volunteer) will haveAn average Cmax and AUCFrom an average reference and test productThat are not significantly different

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DESIGN OF 2-PRODUCT, 2-PERIOD, CROSSOVER STUDIES

Subjects

Sequence 1

Sequence 2

Test

Reference

Reference

Test

Period I W

A

S

H

O

U

T

Randomizaion

Period II

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TESTS OF SIGNIFICANCE

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Interval hypothesis

Two one-sided t tests

ANOVA

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ANALYSIS OF CROSS-OVER DESIGNS Need a computer software and validated procedure

especially when the experimental design is unbalanced

Need of a model to analyse data Steps

Write the model to analyse the cross-over Check at least graphically the parametric assumptions Check the absence of a carry-over effect Estimate the mean for each formulation, estimate the

within subjects variance for each PK parameter Carry out ANOVA for each PK parameter Compute 90% CI for each PK parameter 18

19A MODEL FOR THE 22 CROSSOVER DESIGN

lkjijljikjiljikji SANPSFAUC ,,,),(),,(,,

Y1,1,1,1= 98.3µ = population meanFi = effect of the ith formulationSj = effect of the jth sequencePk(i,j) = effect of the kth periodAnl|Sj = random effect of the lth subject of sequence j,they are assumed independent distrib according a N(0,²)ei,j,k,l = indep random effects assumed to be drawn from N(0,s²)

d.concordet@envt.fr

INFERENCE ON BIOEQUIVALENCE

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AN EXAMPLE

.251ln lnln8.0ln:25.1lnlnlnor 8.0lnlnln:

1

0

RT

RTRT

HH

.251 8.0:

25.1or 8.0:

1

0

R

T

R

T

R

T

H

H

Seq

uenc

e 1

Seq

uenc

e 2

ln AUC PER 1 PER 24.37 4.834.21 4.553.88 4.192.68 3.294.09 4.414.56 4.523.94 4.283.74 4.313.16 3.733.61 4.063.60 3.213.77 3.755.29 4.604.25 3.913.50 2.543.30 2.203.91 3.093.29 2.203.64 2.364.80 4.21

lkjijljikjiljikji SANPSFAUC ,,,),(),,(,,ln

Homoscedasticity seems reasonableNo (differential) carryover effect

0.0508ˆ 2 3.51TX 08.4RX

nT=10 ; nR=10 ; df = nT+nR -2 = 18 734.195.018 t

d.concordet@envt.fr

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SAMPLE SIZE CALCULATION: Where does the General Formula come from?

UNDERSTANDING VARIABLES & TYPES OF ERROR μ0 and μA

Means under Null & Alternate Hypotheses σ0

2 and σA2

Variances under Null & Alternate Hypotheses (may be the same) N0

and NA Sample Sizes in two groups (may be the same)

H0: Null Hypothesis μ0 – μA = 0

HA: Alternate Hypothesis μ0 – μA = δ

Type I Error (α): False +ve Probability of rejecting a true H0

Type II Error (β): False –ve Probability of rejecting a true HA

Power (1-β): True +ve Probability of accepting a true HA

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α/2

UNDERSTANDING SAMPLE SIZE DETERMINATION

H0: μ0 – μA = 0 HA: μ0 – μA = δ

α/2

Power = 1-ββ

S.Error =σ(√2/N) S.Error =σ(√2/N)

0+Z1-α/2σ√(2/N)

0

δ–Z1-βσ√(2/N)

δX0–XA

Critical Value

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FROM THE PREVIOUS GRAPH, WE HAVE

0+Z1-α/2σ√(2/N) = δ–Z1-βσ√(2/N)

Upon simplification,

N =2 σ2 [Z1-α/2 + Z1-β/2]2

δ 2

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PLANNING STATISTICAL ANALYSIS:ANSWER THOSE FIVE KEY QUESTIONS1. What is the main purpose of the trial?

2. What is the principal measure of patient outcome?

3. How will the data be analysed to detect a treatment difference?

4. What type of results does one anticipate with standard treatment?

5. How small a treatment difference is it important to detect and with what degree of certainty?

Stuart Pocock in Clinical Trials, Wiley Int.

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SAMPLE SIZE FOR A T TESTInput variables you will needα The Type I error probability for a two sided test. n For independent t-tests n is the number of experimental subjects. For pair test n is the number of pairs.power For independent tests power is probability of correctly rejecting the null hypothesis of equal population meansδ A difference in population meansσ For independent tests σ is the within group standard deviation. For paired designs it is the standard deviation of difference in the response of matched pairs.m For independent tests m is the ratio of control to experimental patients. m is not defined for paired studies.

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SAMPLE SIZE FOR A T TEST• A study with 1 control(s) per experimental

subject. • In a previous study the response within each

subject group was normally distributed with standard deviation 20.

• SAMPLE SIZE: If the true difference in the experimental and control means is 15, we will need to study 38 experimental subjects and 38 control subjects

• Power of 0.9• The Type I error of 0.05 28

SAMPLE SIZE VS EFFECT SIZE: T TEST

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SAMPLE SIZE VS POWER: T TEST

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• The hypotheses to be tested:

• The equivalence interval : [0.8, 1.25]• The experimental design : crossover (22) with the same

number of subjects per sequence N• The consumer risk (α = 5%)• The producer/trialist risk (β = 20%)• A log transformation is required• An estimate of intra-subject variation from

log-transformed data)• An estimate of µT/µR

DETERMINING BE SAMPLE SIZE

25.18.0 R

T

multiplicative

Acceptance Probability

0

0.2

0.4

0.6

0.8

1

1.2

0.8 0.9 1 1.1 1.2

T/R

Prob

abili

ty

Accept Prob (n=24) Accept Prob (n=36) Accept Prob (n=12)

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SAMPLE SIZE BE

µT/µR

CV % 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.205.0% 12 6 4 4 4 6 8 227.5% 22 8 6 6 6 8 12 4410.0% 36 12 8 6 8 10 20 7612.5% 54 16 10 8 10 14 30 11815.0% 78 22 12 10 12 20 42 168

Number of subjects per sequence for a 22 crossover, log transformation, equivalence interval : [0.8, 1.25], α=5%, β = 20%

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BIOEQUIVALENT DRUG PRODUCTS Pharmaceutical Equivalent

Same dose and dosage form, ideally same assay and content uniformity

Could be pharmaceutical alternative dose or form

BioequivalentStatistical and pharmacokinetic equivalentEquivalent rate and extent of absorption

90% CI of relative mean Cmax and AUC: 80-125%

Interpretation: Therapeutic equivalence35

CURRENTLY PRACTICED BE For almost all generic drugs today, the regulatory

standard is “average bioequivalence (IBE)” Concluded from 2-product, 2-period, crossover

studies with fixed effects That means

An average patient (volunteer) will have An average Cmax and AUC From an average reference and test product That are not significantly different

Problem: cannot individualize or generalize for population 36

THREE MAIN CONCERNS WITH ABE Safety

Generic N– as safe as the Brand?

Prescribability Can a physician have an

equal choice of prescribing Brand or Generic N to drug-naïve patients?

Switchability Can a patient stabilized

on Generic1 be switched to Generic N?

Brand

Gen 1Gen 2

Gen 3 Gen N

?

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LIMITATIONS OF ABE FROM A 2X2 STUDY Produces medical dilemma Ignores distribution of Cmax and AUC Within subject variation is not accurate Ignores correlated variances and subject-by-

formulation interaction One criteria irrespective of inherent patterns of

product, drug or patient variations Although rare, but may not be therapeutic

equivalent 38

OTHER CHOICES IN BE AND THEIR CONDITIONS Individual Bioequivalence (IBE)

Addresses switchability

Population Bioequivalence (PBE) Addresses prescribability

Design and statistics of IBE & PBE Take into account both population mean

and variance Address switchability and thereby subject-fomulation interaction Provide same level of confidence (consumer’s risk of 5%) and

power Accept formulations with reduced within subject variability 39

INDIVIDUAL BIOEQUIVALENCE (IBE) METRIC

2 2 2 2

2 20

( ) ( )max( , )

T R D WT WRI

WR W

2

20

(ln1.25)I

W

Where

WhereµT = mean of the test product

µR = mean of the reference product

σD2 = variability due to the subject-by-formulation interaction

σWT2 = within-subject variability for the test product

σWR2 = within-subject variability for the reference product

σW02 = specified constant within-subject variability

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POPULATION BIOEQUIVALENCE (PBE) METRIC

WhereµT = mean of the test product

µR = mean of the reference product

σTT2 = total variability (within- and between-subject) of the test product

σTR2 = total variability (within- and between-subject) of the reference product

σ02 = specified constant total variance

≤θP

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DESIGN OF 4-PERIOD, REPLICATE STUDIES

Subjects

Sequence 1

Sequence 2

T

R

PI W

A

S

H

O

U

T

1

Randomizaion

PII PIII PIVW

A

S

H

O

U

T

2

W

A

S

H

O

U

T

3R

RR

TT

T

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SAMPLE SIZE FOR IBE

Source: US FDA Guidelines for Industry

Minimum 1243

SAMPLE SIZE FOR PBE

Source: US FDA Guidelines for Industry

Minimum 1844

CONDUCT OF REPLICATE STUDIES Generally dosing, environmental control, blood sampling

scheme and duration, diet, rest and sample preparation for bioanalysis are all the same as those for 2-period, crossover studies

Avoid first-order carryover (from preceding formulation) & direct-by-carryover (from current and preceding formulation) effects Unlikely when the study is single dose, drug is not endogenous,

washout is adequate, and the results meet all the criteria

If conducted in groups, for logistical reasons, ANOVA model should take the period effect of multiple groups into account

Use all data; if outliers are detected, make sure that they don’t indicate product failure or strong subject-formulation interaction 45

Standards for IBE and PBE2 ' 2

' 2

2 ' 2

20

( ) ( )( ) / 2

( ) ( )

R T R R

R R

R T R R

E y y E y yE y y

E y y E y y

' 2 20( ) / 2R RE y y

' 2 20( ) / 2R RE y y

Where σ0 is constant variability.For IBE, YT, YR and YR

’ are PK responses from the test and two reference formulations to the same individual For PBE, YT, YR and YR’ are PK responses from the test and two reference formulations to the different individuals

if

if

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REFERENCE SCALING A general objective in assessing BE is to compare the log-

transformed BA measure after administration of the T and R products

Population and individual approaches are based on the comparison of an expected squared distance between the T and R formulations to the expected squared distance between two administrations of the R formulation

An acceptable T formulation is one where the T-R distance is not substantially greater than the R-R distance

In both population and individual BE approaches, this comparison appears as a comparison to the reference variance, which is referred to as scaling to the reference variability 47

REFERENCE SCALING.. Population and individual BE approaches, but not the average BE

approach, allow two types of scaling reference-scaling constant-scaling.

Reference-scaling means that the criterion used is scaled to the variability of the R product, which effectively widens the BE limit for more variable reference products

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Reference Test

PI PII PI PII

Declaring IBE and PBE

IBE or PBE is claimed when 95% confidence upper bound of θ is less than θI or θP and the observed ratio of geometric means is within bioequivalence limits of 80 – 125%.

H0: θ ≥ θI or θP; HA: < θI or θP

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ANALYSIS BY SAS PROC MIXED

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EXAMPLE: TWO CYCLOSPORINE FORMULATIONSTEST: OPEN CIRCLES; REF.: CLOSED CIRCLES; N = 20

Canafax et al.(1999) Pharmacology 59:78–88

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ABE – TWO CYCLOSPORINE FORMULATIONSN = 20

Canafax et al.(1999) Pharmacology 59:78–88

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IBE – TWO CYCLOSPORINE FORMULATIONSN = 20

Canafax et al.(1999) Pharmacology 59:78–88

εI=0.04-0.05;Constant Scaled σW02 = 0.2; θI = 2.245; IBE

declared

<θI

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ANOTHER EXAMPLE: TWO ALVERINE FORMULATIONS HIGHLY VARIABLE DRUG, INTRA-SUBJECT CV ~35%; N = 48

Chakraborty et al.(2010) Unpublished Data

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ABE, IBE & PBE: TWO ALVERINE FORMULATIONSHIGHLY VARIABLE DRUG, INTRA-SUBJECT CV ~35%; N = 48

Chakraborty et al.(2010) Unpublished Data

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Thank You Very Much

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