Download P16_Zhang_QT - American Statistical Association

Regulatory Perspectives on the Thorough
QT/QTc Study
2005 FDA/Industry Workshop
Washington DC
September 16, 2005
Juan (Joanne) Zhang, Ph.D.
CDER/FDA
*Acknowledgement: Drs. Stella Machado & George Rochester
Disclaimer
• This presentation represents the opinions of the
author, and not necessarily those of the U.S. Food
and Drug Administration.
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Outline
I. Thorough QT/QTc Study
- Introduction
II. Design Considerations
III. Statistical Test for a Negative ‘Thorough QT/QTc
Study’
- Statistical Hypothesis & Test
- Intersection-Union Tests
IV. False Positive and False Negative Probabilities
V. Assay Sensitivity
VI. Summary
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Thorough QT/QTc Study
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Introduction
• QT interval represents
the time between start
of ventricular
depolarization and end
of ventricular
repolarization (QT).
• QTc is the QT-interval
corrected for heart
rates
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Introduction (2)
• QT/QTc prolongation may cause ventricular arrhythmias
including ventricular fibrillation and Torsade de Pointes,
which can be fatal even though the degree of this
association is not known
• Current ICH E 14 Guidance requests all sponsors
submitting new drug applications to conduct a thorough
QT/QTc study
– Generally conducted in early clinical development after
some knowledge of the pharmacokinetics of the drug
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Introduction (3)
• ICH E14 Guidance (Step 4, Adopted May 2005)
“The ‘thorough QT/QTc study’ is intended to determine
whether the drug has a threshold pharmacologic effect on
cardiac repolarization, as detected by QT/QTc prolongation.”
“The study is typically carried out in healthy volunteers (as
opposed to individuals at increased risk of arrhythmias) and
is used to determine whether or not the effect of a drug on
the QT/QTc interval in target patient populations should be
studied intensively during later stages of drug development.”
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Negative ‘Thorough QT/QTc Study’
• ICH E14 Guidance (Step 4, Adopted May 2005)
“…a negative ‘thorough QT/QTc study’ is one in which the
upper bound of the 95% one-sided confidence interval for
the largest time-matched mean effect of the drug on the
QTc interval excludes 10 ms.”
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Non-negative ‘Thorough QT/QTc Study’
• If a ‘thorough QT/QTc study’ is not negative, i.e., if at least
one upper bound of the one-sided 95% confidence interval
of the time-matched difference exceeds the threshold of 10
ms, the study is termed “Non-negative”.
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Implications of Results from the ‘Thorough
QT/QTc Study’
ICH E 14:
• IF the ‘thorough QT/QTc study’ is negative – “the
collection of baseline and periodic on-therapy ECGs in
accordance with the current investigational practices in
each therapeutic field is almost always sufficient
evaluation during subsequent stages of drug development.”
• IF ‘thorough QT/QTc study’ is non-negative – “additional
evaluation in subsequent clinical studies should be
performed.” Hence, expanded ECG safety evaluation
during later stages of drug development are needed.
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Design Considerations
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Design Considerations
• To better control variability and potential bias
– Randomized, double blinded, placebo and active controlled,
single or multiple doses of the drug, crossover or parallel
study
– Healthy volunteers, it is better to have similar number of
males and females in the study (randomization stratified by
gender)
– Crossover design recommended if possible
– For a crossover study, baseline at each period is
recommended
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Design Considerations (2)
• QT data are highly variable, so control of all sources of
variability is critical
• Replicated QT measurements at each time-point are
recommended. Typically ≥3 replicates. The mean of these
replicates is used.
• The baseline QT measurements should be taken as close to
the treatment date as possible; typically either
– At matching time-points on the day prior to drug treatment; or
– At time 0 before dosing, the same day of treatment
• QT interval data are adjusted for heart rate (HR) to obtain
QTc values which are correlated with HR as little as
possible.
– Fridericia’s corrected values
– Individual corrected values
– Bazett’s corrected values
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Crossover Design
• A crossover QT/QTc study is recommended as opposed to
a parallel study if possible since
– It requires smaller number of subjects
– The precision of estimated treatment differences is
greater since subjects act as their own control
• Methods and practice applicable in any cross-over trial
should be applied in a crossover QT/QTc trial.
• Some issues encountered in a crossover-trial need to be
considered here; including period effect and carry-over or
residual effect.
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Crossover Design (2)
•
•
Suppose a 4 TRT arm study
– DH: drug, high dose
– DL: drug, low dose
– P: placebo
– PC: positive control
Some designs we have seen:
(Example 1)
Period 1
PC
•
Period 2
P
Period 3
DL
Period 4
DH
Problems? – Can’t distinguish the period effect from the
treatment effect.
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Crossover Design (3)
Example 2
Group
Period 1 Period 2 Period 3 Period 4
A
B
C
D
DL
DL
P
P
DH
P
DL
DH
P
DH
DH
DL
PC
PC
PC
PC
E
F
DH
DH
DL
P
P
DL
PC
PC
Problems? – Period effect is confounded with the treatments. This
concern only pertains to PC though.
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Crossover Design (Continued)
• One recommended design for a 4 treatment study (a
Williams Square)
Group
Period 1
Period 2
Period 3
Period 4
A
DL
DH
P
PC
B
DH
PC
DL
P
C
P
DL
PC
DH
D
PC
P
DH
DL
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Parallel
Parallel group studies may have to be used under
certain circumstances:
• For drugs with long elimination half-lives
• For drugs whose carryover effects are
prominent
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Sample Size Required for a Crossover
Design and a Parallel Design
Notations:
• N1 - # of subjects in a crossover study
• N2 - # of subjects per arm in a parallel study
•  - observed difference in treatment (adjusted for baseline) for an individual
• SD() = 1 for a crossover;
2 for a parallel
• D – SD for the drug
• P – SD for placebo
• 12 – Correlation coefficient between the drug and placebo for the same
individual (>0)
Relation between N1 and N2
• In order to make Var(mean of ) the same for both crossover and parallel
studies, we have
N2 = (2/ 1)2N1
• Relation between 1 and 2: 22 = 12 + 212DP
• For a 4 arm trial, sample needed for a parallel study can be at least 4 times
more than a crossover study
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Statistical Test for a Negative ‘Thorough
QT/QTc Study’
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Calculating Time-matched Mean
Difference
• How to estimate the time-matched population mean
effect?
Qit: (Baseline adjusted) QT/QTc value for the ith
subject at time t after receiving the drug
Pit: (Baseline adjusted) QT/QTc value for the ith
subject at time t after receiving placebo
Time-matched mean difference at time t (suppose
equal sample size N in both the drug and placebo
groups)
 Qit/N -  Pit/N = (For a crossover) i (Q it  Pit ) / N
N is the number of subjects
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Statistical Hypotheses
• Hypotheses:
H0: t(D) - t(P) ≥  ms for at least one t
H1: t(D) - t(P) <  ms for all t
•  is the non-inferiority margin (10 ms in the
guidance)
• t(D) and t(P) are the population means for the
drug and placebo at time t, t=1,2,…,K. K is the total
number of time points where QT has been
measured.
• Claim a negative QT/QTc study if H0 is rejected
• Use  = 0.05
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Statistical Test
• Let  be the observed average time-matched drug placebo difference
t
after baseline adjusted at time t. Let Tt be the test statistic at time t,
then
Tt = (  t - )/SD( t )
Reject H0 if Tt < -t, N-1 for all t, where t, N-1 is the upper tail 
level critical value for the t distribution with N-1 df, and N is the
sample size.
The above procedure is
to test if all one sided 95% CI upper
bounds are <  ms at each time point.
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Intersection-Union Tests
• Suppose Rt is the rejection region of a level- test for H0t:
t(D) - t(P) ≥  ms, t=1,2,…,K, then the IntersectionUnion Test with rejection region R= Kt 1 R t is still a level-
 test for H0
• No need for multiplicity adjustment to test for a negative
thorough QT/QTc study
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False Positive & False Negative Probabilities
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Definitions
• Type I error: False Negative Probability (FNP)
FNP = P(Tt < - t, N-1 for all t | at least one true difference ≥ )
By IUT, FNP can be controlled under  (0.05) level
• Type II error: False Positive Probability (FPP)
FPP = P(Tt ≥ - t, N-1 for at least one t | true difference < 5 ms at
each time point)
Why 5 ms chosen: “… drugs that prolong the mean QT/QTc
interval by around 5 ms or less do not appear to cause TdP” –
ICH E14
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Simulation Study
• Purpose: to evaluate the FNP and FPP
• Assumptions:
–  = 8 ms, 10 ms
– SD () = 8.5 ms based on a crossover study in house
– # of times evaluated K = 5 and 15
– Multi-normal assumption: NK(, )

 1


1
2
 


 T1
T 2



  T1 

T 2
  
  

 1 
–  = 0.1 and 0.9
– Sample size 65
– 10000 simulations per scenario
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Results: False Negative Probability
Table 1
K=5
K=15


(0,0,8,0,0)
(0,0,8,8,0)
(0-0,8,0-0)
(0-0,8,8,0-0)
8
0.1
0.044
0.005
0.051
0.004
8
0.9
0.041
0.036
0.047
0.028
(0,0,10,0,0)
(0,0,10,10,0)
(0-0,10,0-0)
(0-0,10,10,0-0)
10
0.1
0.037
0.002
0.051
0.002
10
0.9
0.052
0.036
0.046
0.031
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Results: Power (1-FPP) Curves
(=(2,3,4,4,3)’, =0.1)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
6
8
10
12
14
Theta=8, N=30
Theta=8, N=60
Theta=8, N=90
Theta=8, N=200
Theta=10, N=30
Theta=10, N=60
Theta=10, N=90
Theta=10, N=200

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Results: Power (1-FPP) Curves
(=(2,3,4,4,3)’, =0.9)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
6
7
8
9
10
11
12
13
14
15
Theta=8, N=30
Theta=8, N=60
Theta=8, N=90
Theta=8, N=200
Theta=10, N=30
Theta=10, N=60
Theta=10, N=90
Theta=10, N=200

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Conclusions
This simulation example shows:
• FNP is well controlled under the  level
• FPP (or 1 - Power) is driven by
– The true mean difference of the drug and placebo
– The Non-inferiority margin
– Variability of the data
– Sample size
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Is it true the greater the number of time
points, the higher the type II error? (N=65)
Table 2
Scenario
, K
Assumed True Mean Difference
r=0.1
r=0.9
a
8, 5
(3,4,4.9,4,1)
0.134
0.109
b
8, 15
(0,0,0,1,1,3,4,4.9,4,1,1,1,0,0,0)
0.132
0.103
c
8, 5
(1,1,1,4.9,1)
0.101
0.106
d
8, 15
(0,0,0,1,1,1,1,1,4.9,1,1,1,0,0,0)
0.112
0.097
e
10, 5
(3,4,4.9,4,1)
0.001
0.001
f
10,15
(0,0,0,1,1,1,1,1,4.9,1,1,1,0,0,0)
0.001
0.001
g
10, 5
(1,1,1,4.9,1)
0.001
0.001
h
10, 15
(0,0,0,1,1,1,1,1,4.9,1,1,1,0,0,0)
0.001
0.001
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Findings
Focus on top half of table 2.
• As long as the time points chosen can capture the relatively
big QT/QTc effect, the number of time points does not
change FPP (Scenarios (a) vs. (b), (c) vs. (d))
• FPP can increase with the number of time points (Scenario
(c) vs. (b))
• FPP can decrease with the number of time points (Scenario
(a) vs. (d)).
• Conclusion: It is not always true that the FPP is an increasing
function of the time points when QT/QTc are evaluated
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Assay Sensitivity
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Assay Sensitivity
ICH E14:
“The positive control should have an effect on the mean
QT/QTc interval of about 5 ms”
The positive control “should be well-characterized and
consistently produce an effect on the QT/QTc interval that
is around the threshold of regulatory concern (5 ms,
section 2.2.).”
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Statistical Procedures to Assess Assay
Sensitivity
• H0: t(PC) - t(P) < c ms for all t
H1: t(PC) - t(P) ≥ c ms for at least one t
• How to choose c? Under discussion.
• Challenge: Multiple endpoint issues (can’t apply IUT
here)
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Summary
• A ‘thorough QT/QTc study’ is negative when the study
drug is non-inferior to placebo in terms of the effect of
QT/QTc interval.
• If all the one-sided 95% upper limits of the time-matched
mean difference between the drug and placebo after
baseline adjustment are below  (the non-inferiority
margin, 10 ms) at each time point, then we can claim a
negative ‘thorough QT/QTc study’.
• By the Intersection-Union test, there is no need for the
multiplicity adjustment to claim the drug is non-inferior to
placebo.
• If possible, a crossover design should be considered.
• Need more thoughts on assay sensitivity issues.
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