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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)
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
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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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