Consideration on Japanese sample size
in multi-regional trials
Kimitoshi Ikeda, Novartis Pharma K.K.
Frank Bretz, Novartis Pharma A.G.
PKUK2010, 03Nov2010
Agenda
 Introduction
• The guidance “Basic principles on Global Clinical trials” issued by
MHLW (2007)
• Overview of Japanese sample size determination (Method 1 and
Method 2)
 Theoretical aspect of Method 1
 Alternative approach using a hypothesis test in Japanese
patients
 Numerical comparison study
 Concluding remarks
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Introduction
 In recent years, multi-regional trials have received increasing attention.
• Avoid the conduct of duplicated trials
• Reduce resources and cost
 The 11th Q&A for the ICH E5 guideline gives objectives in multiregional trials.
• To show that the drug is effective in the individual regions
• To compare the results of the study between regions and establish that the
drug is not sensitive to ethnic factors
 The sample size determination for the individual regions are not given
in the 11th Q&A for the ICH E5. These depend on scientific aspects and
regulatory requirements.
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Introduction
 In Japan, the guidance “Basic principles on Global Clinical trials” was
issued by MHLW in 2007.
 A global trial should be designed so that consistent results can be
obtained between the Japanese subpopulation and the entire
population.
 The guidance suggests how to determine the sample size of Japanese
patients when attending the multi-regional trials.
 A multi-regional trial has at least two main objectives:
• Show a significant benefit in effect of a new drug over placebo in the entire
study population.
• Demonstrate consistent results between the Japanese subpopulation and the
entire population.
 We need to consider the resulting probabilities, which lead to
interesting multiplicity problems.
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Ministry of Health, Labour and Welfare（2007）
Basic principles on Global Clinical Trials
 Q1: Basic requirements to conduct a global trial
 Q2: Appropriate timing for Japan to participate in global drug development
 Q3: Phase I trial or pharmacokinetic information in Japanese population
 Q4: Necessity of any dose finding studies in Japan
 Q5: Basic points to consider in designing a global trial
Q6: Japanese sample size determination
 Q7: Acceptability of an evaluation index used overseas
 Q8: Clinical trials performed in Japan with the identical protocol as a global trial
 Q9: Control groups in a phase III global trial
 Q10: Use of Concomitant medications or therapies
 Q11: Disease areas where conduct of a global trial
 Q12: Flow chart for determining whether or not global trial should be performed
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Ministry of Health, Labour and Welfare（2007）
Basic principles on Global Clinical Trials
Q6: When conducting a global clinical trial, how is it
appropriate to determine a sample size and a proportion
of Japanese subjects?
 In a global trial, a power to detect statistically significant
difference in Japanese subpopulation is not necessary.
 A global trial should be designed so that consistent results can
be obtained between the entire population and the Japanese
population, and by ensuring consistency of each region, it could
be possible to appropriately extrapolate the result of full
population to each region.
 Two methods are introduced to determine the Japanese sample size.
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Introduction (Japanese sample size calculation)
Guidance “Basic principles on Global Clinical trials” (2007)
Method 1
Dall = difference in the entire study population across regions
DJapan = difference within the Japanese sub-population
Determine the number of Japanese patients so that
DJapan DALL  
with a probability of 80% or higher.
The threshold ω = 0.5 or higher is generally recommended.
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Introduction (Japanese sample size calculation)
Guidance “Basic principles on Global Clinical trials” (2007)
Method 2
When assuming that three regions are included in the trial, the differences
between placebo and study drug groups in each region are D1, D2, and
D3, respectively.
Determine sample sizes so that each of the D1, D2, and D3 will exceed 0
with a probability of 80 % or higher.
Di > 0
for all region i
The method 2 is explained by Kawai et al. 2008.
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Introduction
Criteria of consistency
Method1
Method2
DJapan DALL  
Di  0 , for all i , i  1,..., I
 These criteria of consistency have different perspectives.
• The criterion of Method 1 focuses on the effect in a specific region.
• The criterion of Method 2 focuses on the difference in effect among
regions, that is, region-treatment interaction.
 In this presentation, we explain the detail of method1 and suggest a
alternative approach using a hypothesis test in Japanese patients.
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Method 1 (Joint distribution of DALL and DJapan )
Overall effect

na  nb 2 
DALL～ N   ALL ,
 
na nb


Effect in Japan

na  nb 2 

DJapan ～ N   Japan ,
 
na nb p


Let p = proportion of Japanese patients.
na= the number of patients in a study drug group,
nb= the number of patients in a placebo group. Jointly,
   ALL  na  nb 2 1 1  
 DALL 
 1 
 ～ N δ, Σ   N  
,
d  


1

   Japan  na nb
D
Japan
p 





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Method 1 (Joint distribution of DALL and DJapan )
DJapan DALL  
DALL
DJapan DALL  
 DALL 
 ～ N δ, Σ 
d  

 DJapan 
DJapan DALL  
 ALL
DALL  Z1 
O
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 Japan
DJapan
na  nb
na nb
Probability to consider
Probability
1
Probability of detecting the statistically significant difference between
the study drug and placebo in all patients (Power).
 DALL
1  Pr
 
Probability

na nb
 Z1   1  
na  nb

2
Probability of showing consistent results between all patients and
Japanese patients.
 2  Prob(DJapan DALL   )  Prob(DJapan  DALL )

 Z1  Z1  (1   ) p 

 

2
p  2 p  1 



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(See Quan et al. 2010,
Ikeda & Bretz, 2010)
Probability to consider
Probability
3
Probability of detecting the significant difference between the study
drug and placebo in all patients and showing consistent results
between all patients and Japanese patients simultaneously.
 DALL

n
n
a
b
3  Prob
 Z1 and DJapan DALL   
na  nb
 

 

1
 1 T 1  
  Z1  Z1 (1 ) p exp x R x dx2 dx1

1  Z

1 
2

 

2
2
p


2
p


1
2 R



R 


1
p (1 )
p 2  2 p 1
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p (1 )
p 2  2 p 1
1


,


(See Ikeda & Bretz, 2010,
see also Quan et al. 2010,
Uesaka, 2009)
Probability – Method 1, Power 90% –   0.5   0.025
1
The probability of meeting the criterion
0.9
0.8
0.7
0.6
35.7%
22.4%
42.6%
2
3
0.5
0.4
0
0.05
0.1
0.15
0.2
0.25
14 | Presentation Title | Presenter Name | Date | Subject | Proportion
Business Use Only
of Japanese
patients
0.3
0.35
0.4
0.45
Proportion of Japanese patients
For Method 1, it is required in the guidance that  2  80%
Therefore, the proportion of Japanese patients can be calculated
by solving
Pr DJapan DALL     1  
0   1
The required proportion of Japanese patients is
p
Z12-
(1   ) 2 Z1  Z1    Z12-  (  2)
2
(See Quan et al. 2010, Ikeda & Bretz, 2010).
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Required proportion of Japanese patients：Method 1 DJapan DALL  0.5
  0.025
Required proportion of Japanese patients
0.4
 2  80%
0.35
0.3
28.4%
22.4%
0.25
18.7%
0.2
0.15
0.1
0.05
0
0.75
0.8
0.85
0.9
0.95
Power (Probability of showing a statistical significant
difference in entire population)
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1
Notable property of method 1
DJapan DALL  
DALL
DJapan DALL  
area a)
・Significant difference in
overall patients
area b)
d～ Nδ, Σ 
・Consistent result between
all and Japanese
area b)
・Significant difference in
overall patients
・Inconsistent result between
all and Japanese
 ALL
DALL  Z1 
area a)
O
 Japan
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na  nb
na nb
DJapan
Alternative approach
 We investigate the alternative requirement
DJapan  c
for a suitably chosen threshold c.
 One possibility of choosing the threshold c is to use a
hypothesis test for comparing a study drug and placebo
within Japanese patients.
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Alternative approach using a hypothesis test in Japanese
patients
We suggest an approach using a hypothesis test in Japanese
patients to solve the notable property in the method 1.
Null hypothesis
DJapan  0
Alternative hypothesis
DJapan  0
If the null hypothesis is rejected by doing the hypothesis test with
a significance level  , the result is regarded as a consistent
result.
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Approach using a hypothesis test in Japanese patients
–Calculation of
 2 and  3
–
Probability  2
 DJapan
Pr
 


 Z1    Z1  Z1   p  Z1

n p  na


n p na p

Probability  3
D
Pr All
 


 Z1 / 2 and
 Z1 

n p  na

n p  na


 
1
 1 T 1  

exp
 w R s w dw2 dw1
 Z1 Z1  Z1  p
1  Z
1 
 2
 

2 R s 2
n p na
DJapan
n p na p
The required proportion of Japanese patients is

Z
p
Z
1
1
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 Z1 
2
 Z1 
2
Selection of  in the proposed approach
We set  so that the proposed approach needs almost same
number of Japanese patients compared with method 1.
Method 1
When   0.5 and the overall power is 0.8 - 0.9, the 22.4 – 28.4%
of total patients is needed as Japanese patients to show the
consistent result with a 80% probability.
Proposed approach
When   0.25 and the overall power is 0.8 - 0.9, the 21.9 –
29.3% of total patients is needed as Japanese patients to show
the consistent result with a 80% probability.
0.25 or less than 0.25 should be used as
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 .
Simulation for the probability of obtaining a consistent results
 2 , 3 are investigated by a simulation study under the following setting.
We compare the method1 and the proposed approach.
Effect size
0.125 …
( ALL ,  Japan ) T  (1,1) T
 8
Power
0.8, 0.9, 0.95
Value of
 and 
Method 1
  0.5
Proposed approach
  0.25
Number of Japanese patients
The number of Japanese patients is determined so that the probability of
consistency is 80 % or higher in the method 1.
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Simulation results for the probability of obtaining a consistent
results
T
T
Effect size = 0.125, ( ALL ,  Japan )  (1,1)   8 ,   0.5 ,   0.25 , Unit：%
Power,
sample size
Method
1
2
3
Power = 0.8
Proposed
approach
79.89
79.29
68.61
n=1006, nJapan=288
Method 1
79.89
79.92
66.58
Power = 0.9
Proposed
approach
89.93
80.57
75.40
n=1336, nJapan=303
Method 1
89.93
80.02
73.47
Power=0.95
Proposed
approach
95.00
81.50
78.99
n=1665, nJapan=312
Method 1
95.00
80.21
76.97
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Numerical study for false-positive error rates
Error rate (  2) are calculated under the following setting. We compare
the method1 and the proposed approach.
Mean and SD
( Other ,  Japan ) T  (1,0) T
 8
Nominal power under assumption that the effect size is 0.125.
0.8, 0.9, 0.95
Value of

Method 1
and

  0.5
Proposed approach   0.25
Number of Japanese patients
The number of Japanese patients is determined so that the probability of consistency is
T
T
80 % or higher in the method 1 under assumption of ( ALL ,  Japan )  (1,1) .
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Results for false-positive error rates
( Other ,  Japan ) T  (1,0) T
 8
  0.5
  0.25
Error rate (%)
Nominal
power
Proposed
approach
Method 1
0.80
25.00
27.10
0.90
25.00
25.62
0.95
25.00
24.68
Error rate: Probability of obtaining the consistent result despite the study
drug has no effect in Japanese patients or all patients.
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Concluding remarks
 We focused on Method 1 and derived closed form expressions for the
resulting probabilities.
 We proposed an alternative method, which has better operating
characteristics compared with Method 1.
 The proposed approach provides higher probabilities to achieve
statistical significance in all patients and consistent results between
Japanese and entire patients, when the study drug is effective in both
Japanese and entire patients.
 The error rates of the proposed approach are comparable or even
lower than those of Method 1, when the study drug has no effect in
Japanese patients.
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Concluding remarks
 Other choices of

are possible and need to be investigated in
future.
 The problem of showing effectiveness remains a difficult problem. We
considered necessary sample sizes to demonstrate the effectiveness
for Japanese patients. In addition, we would need to compare the
results across the regions as well. If differences in treatment effect exist
across regions, we need to investigate the reason for the difference.
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Reference
 International Conference on Harmonization. Q&A for the ICH-E5 Guideline on ‘Ethnic
Factors in the Acceptability of Foreign Clinical Data’, 2006. Available at
www.ich.org/cache/compo/475-272-1.html.
 Ministry of Health, Labour and Welfare. Basic Principles on Global Clinical Trials. 2007.
 Kawai N, Chuang-Stein C, Komiyama O, Ii Y. An approach to rationalize partitioning
sample size into individual regions in a multiregional trial. Drug Information Journal 2008;
42: 139-147.
 Quan H, Zhao P-L, Zhang J, Roessner M, Aizawa K. Sample size considerations for
Japanese patients in a multi-regional trial based on MHLW Guidance. Pharmaceutical
Statistics 2010; 9(2): 100-112.
 Ikeda K, Bretz F. Sample size and proportion of Japanese patients in multi-regional trials.
Pharmaceutical Statistics 2010; 9(3): 207-216.
 Uesaka H. Sample size allocation to regions in a multiregional trial. Journal of
Biopharmaceutical Statistics 2009; 19: 580-594.
PKUK2010 | Kimitoshi Ikeda | 03NOV20010|