Transcript n/2

臨床試驗
對照組、盲性作業、隨機分派
Control, Blinding, and Randomization
授課老師: 劉仁沛教授
國立台灣大學
與 國家衛生研究院
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Jen-pei Liu, PhD
1
Basic Design Considerations

Methods to eliminate bias and to
reduce variability



Use of a control
Blinding
Randomization
Jen-pei Liu, PhD
2
Types of controls

Three components contained in an observed response

The true pharmacological activity of the active ingredient

The symptomatic relief provided by the placebo

The natural reversible healing process
The last two components can not be unbiasedly estimated without
inclusion of a concurrent placebo.
Jen-pei Liu, PhD
3
Examples of placebo and active
treatment controls

Canadian Beclomethasone Dipropoinate Salmethrol Xinafoate
Study Group (NEJM, 1997; 337:1659-65)
Patient population: 241 children, 6-14 years old with stable asthma
 Test treatment
Long-acting β2-adrenergic-receptor agonist
Salmethrol Xinafoate (50 ug twice daily)
Active treatment concurrent control
Glucocorticoid
Beclomethasone (200 ug twice daily) / Placebo concurrent control

Jen-pei Liu, PhD
4
Examples of no-treatment control

Barst, et al. (NEJM 1996; 334:296-301)

Patient population: 81 patients with primary pulmonary
hypertension

Treatment
Epoprostenol + conventional therapy
Concurrent no treatment control + conventional therapy
Jen-pei Liu, PhD
5
Examples of dose-response controls

Wernicke, et al (1987, PschB, 23:164-8)
Patient population:345 patients satisfied DSMⅢcriteria and HamD>=20

Test treatments
Fluoxetine:20, 40, and 60 mg
Placebo concurrent control
Jen-pei Liu, PhD
6
Bias

Bias




The systematic tendency to make the estimate of a
treatment effect deviate from its true value.
Design, conduct, analysis, evaluation and interpretation of
the results.
Operational bias: deviations in conduct
Statistical bias: deviations in all others
Jen-pei Liu, PhD
7
Selection Bias
The Blackwell-Hodges Diagram
for Selection Bias
Investigator’s guess
Test Drug (a’)
Placebo (b’)
Random Assignment (p=1/2)
Test Drug (a)
Placebo (b)

n/2 – 
n/2 – 

n/2
n/2
Jen-pei Liu, PhD
8
Selection Bias



Under random assignment E(na) = n/2
Under Ho: E(Y|a) = E(Y|b) = 
Under investigator’s guest


E(Y|a’) =  - /2
E(Y|b’) =  + /2
Jen-pei Liu, PhD
9
Selection Bias

The expected selection bias



2( +  - n/2) = 2E(F)
2: Investigator’s bias
E(F): the expected bias factor
# of correct guesses - # of incorrect guesses

2
Jen-pei Liu, PhD
10
Selection Bias


Random assignment is independent of patient
characteristics and past assignments  E(F) = 0.
Investigator’s bias: subjective judgment in the
conduct, management, and assessment of patients if
he or she knew the treatment assignment of the
treatment.
Jen-pei Liu, PhD
11
Blinding
Blinding is the only way to prevent subjective judgment bias in the
management, conduct, and evaluations of the trial.
The inference for the treatment effect can be only unbiasedly made
only if all aspects of patient characteristics, management, conduct,
and evaluations except for the intervention are identical between
the treatment groups.
Jen-pei Liu, PhD
12
Double dummies

Occasions



No matching placebo available
Different frequencies
Example
Treatment A
Time 6:00
A
B Pla
Treatment B
Time 6:00
B
12:00
B Pla
18:00
A
B Pla
24:00
B Pla
12:00
A Pla
B
18:00
B
24:00
A Pla
Jen-pei Liu, PhD
-
13
Correct Guesses for BHAT Study
Propranolol Placebo
Patient
79.9%
42.8%
Investigator
69.9%
68.6%
Clinic Coordinator 67.1%
70.6%
Expected
Bias Factor
380(N=3230)
568(N=3398)
669(N=3552)
Morgan (1985)
Jen-pei Liu, PhD
14
Accidental Bias

The bias of an estimate of the treatment effect from a
model in which one or more important covariates,
either known or unknown, is ignored
(Efron, 1971, Biometrika; 58: 403-417)
Jen-pei Liu, PhD
15
Accidental Bias
An ANCOVA Model:
Yi = μ + τTi + βX i + ε i , i=1 ,..., n.
 =  E -  C ; n = n E + n C.
Ti =  1 for experimental drug and control group;
X i : an unobserved covariate.
Assume that
 Xi = 0 and
2
X
 i 1
Jen-pei Liu, PhD
16
Accidental Bias
A wrong model without the covariate:
Yi = μ* + τ*Ti + ε*i .
The LSE under the wrong model is
* =
 (T - T)(Y - Y) ,
 (T - T)
i
i
2
i
and
Yi - Y   (Ti - T) +  (X i - X) + ( i -  ).
Jen-pei Liu, PhD
17
Accidental Bias
 *- =
  (Ti  T)(X i  X)   (Ti  T)( i   )
 (T
i
 T)
2
.
Under equal allocation when n  ,
T  0 and
 (T
i
 T) 2 /n=1.

 *- =
  Ti X i   Ti i
n
.
Jen-pei Liu, PhD
18
Accidental Bias
{Ti } and { i } are independent 
E[Ti i ] = 0.
E[ *
TX

-  ] =  E[
i
n
i
].
 * is a consistent estimator of  in a linear model
for which the assignment of {Ti } are unconditionally
orthogonal to {X i }.
Jen-pei Liu, PhD
19
Accidental Bias
TX

lim E[
i
n 
i
] = 0.
n
Randomization procedure that is independent of
patient's characteristics gurantees that the estimator
of  , asymptotically, is free of accidental bias,
even for unmeasured, or unknown covariates.
Jen-pei Liu, PhD
20
Randomization

Goals

To introduce a deliberate element of chance into assignment of treatments to
patients.

To avoid bias in selection and allocation of subjects from the predictability of
treatment assignments.

To minimize the differences in relevant characteristics of the treatment groups
and to produce similar distributions of prognostic factors between groups.

To provide a sound statistical basis for the quantitative evaluation of the
evidence relating to treatment effects.
Jen-pei Liu, PhD
21
Randomization

Methods

Unrestricted randomization


imbalances
p = 0.5.

E(nE) = n/2

V(nE) = n/4

When n=100, a 60/40 imbalance or greater occurs 5% of the
time.
Jen-pei Liu, PhD
22
Randomization

Methods

Permuted-block randomization
Patients characteristics may change over time.
Block length of 4 to 8 and not specified in the protocol

Assign E to patient (bE + bc +1) in a block with probability
P(E) = (BE – bE)/(BE + BC - bE - bc), where BE are BC the total
number of assignments in a block and bE + bc the number of
assignments already made in a block.
Jen-pei Liu, PhD
23

Example：
Generation of random codes by the method of
permuted-block randomization




# of treatment：2 –– A and B
Length of blocks：4
Possible arrangements：
1. AABB, 2. BBAA, 3. ABAB,
4. BABA, 5. ABBA, 6. BAAB
Generate a random permutation of 1-6：361425
ABAB BAAB AABB
BABA BBAA ABBA
Jen-pei Liu, PhD
24
Randomization

Stratification
By important prognostic factors: center, gender, age, baseline
characteristics.
Separate randomization within strata.
Too many stratified factors can be infeasible and impractical and
defeat the purpose of balanced effects
Restricted to at most two factors
Jen-pei Liu, PhD
25
Randomization

Multicenter Trials


Stratified randomization by center
Centralized randomization






Interactive Voice Randomization System (IVRS)
Allows verification of inclusion and exclusion criteria
Avoid attempts to protocol violation
Tedious
QA and QC to endure the correct assignment
Envelope system for timely verification
Jen-pei Liu, PhD
26
Randomization

Adaptive randomization

Treatment adaptive randomization


Response adaptive randomization


The chance of the next assignment depends upon the number of patients
currently assigned
The chance of the next assignment depends upon the response of the
current patient.
Covariate adaptive randomization (Minimization)

The next assignment depends upon the covariates of the current patient.
Jen-pei Liu, PhD
27
Randomization (Minimization)
Covariate
N
Age
<64
>=65
Peak flow rate (mL/s)
<9
>=10
AUC-7 symptom score
<=7
8-19
>=20
Placebo
Test Drug
106
107
57
56
49
51
45
61
44
63
25
52
29
Jen-pei Liu, PhD
26
51
30
28
Randomization (Minimization)




Selection of a measure of imbalance with respect to covariates
For each patient, compute the value of the measure for each
treatment
Assign the patient to the treatment with the smaller sum
The minimization can be also random with probability depends
upon the imbalance. e.g., 3/4 or 2/3 suggested by Pocock (1984)
Jen-pei Liu, PhD
29
Randomization (Minimization)






Criteria: Age > 64; flow rate < 9 mL/s and AUC-7 >=20.
The next patient is 68 years old with peak flow rate of 7.4 mL/s
and a AUA-7 score of 21 points.
Placebo: 50, 46, and 30 (total = 126)
Test drug: 52, 45, 31 (total = 128)
The sum of placebo is smaller
Assign this patient to the placebo group.
Jen-pei Liu, PhD
30
Correct Random Assignment
Patient No.
001
002
003
004
006
007
008
009
010
013
014
016
Random Code
13
14
15
16
17
18
19
20
21
22
23
24
Jen-pei Liu, PhD
Date
01022007
01032007
01042007
01062007
01102007
01152007
01202007
02012007
02022007
02152007
02172007
02202007
31
Incorrect Random Assignment
Patient No.
001
002
003
004
006
007
008
009
010
013
014
016
Random Code
20
16
24
14
19
17
15
23
13
22
18
21
Jen-pei Liu, PhD
Date
01022007
01032007
01042007
01062007
01102007
01152007
01202007
02012007
02022007
02152007
02172007
02202007
32
Randomization

The ratio of the subjects randomized to treatments
dose not have to be 1:1

The chance of assignment of the subjects to
treatment dose not have to be equal.
Jen-pei Liu, PhD
33
Unequal Allocation


Given a total sample size n and assignment probability of p to
the test drug and q=(1-p) to the control group
The variance of the treatment effect is


2/npq
The relative efficiency of equal to unequal allocation is

4pq
Jen-pei Liu, PhD
34
Unequal Allocation
Allocation Relative efficiency
1:1
1
6:4
0.96
2:1
0.89
7:3
0.84
8:2
0.64
Jen-pei Liu, PhD
35
Reading

Chow and Liu (2013)

Chapter 4 (randomization and blinding)
Jen-pei Liu, PhD
36
Design II
Early Phase Cancer Trials
Prepared by Jen-pei Liu, PhD
37
Early Phase Cancer Trials



Introduction
Phase 0 Trials
Phase I Trials




Phase II Trials



Traditional 3+3
Accelerated Titration Design
Continual Reassessment Method
Simon Two-stage Design
Randomized Phase II Design
Adaptation of Molecular Targeted Agents
Prepared by Jen-pei Liu, PhD
38
Cancer Phase 0 Trials
(Exploratory IND)





Conduct before phase I trials
To confirm endpoints of mechanism of action, bioavailability,
pharmacodynamics, metabolic, and microdose assessments based on human,
not extrapolated from animal studies
More of a discovery, rather than development
Number of patients: 10-15
Dose: subtherapeutic
Prepared by Jen-pei Liu, PhD
39
Cancer Phase I Studies

Objectives of cancer phase I trials for cytotoxic agents





Determine the maximum dose and schedule of an investigational agent that
patients can tolerate
Provide the adverse events associated with agent administration in a dosedependent fashion
Use a variety of dose-escalation strategies for a target of a toxicity rate of
33% (?) or less
Dose-limiting toxicity (DLT): unacceptable or unmanageable safety profile
using some criteria such as grade 3 or greater according to US NCI
Common Toxicity Criteria (CTC)
DLT is usually evaluated at the first cycle of chemotherapy – acute toxicity
(not chronic or cumulative effects)
Prepared by Jen-pei Liu, PhD
40
Issues of Phase I Designs for MTD

Complete the trials with







Minimum amount of patients, and
Minimum amount of time
Recognize differential dosing-limiting clinical toxicity
Ineffective at lower doses but fatal at higher doses
Heterogeneous patients with different tumor types
Include a stopping rule to allow flexibility to extend to higher or lower dose
levels
Investigators and regulatory agencies dictate the dose level for the first
patient
Prepared by Jen-pei Liu, PhD
41
Cancer Phase I Studies


Designs for determination of maximum tolerable dose
 For PhaseⅠcancer chemotherapy (cytotoxic)
 Pre-selected fixed dose levels
Maximum Tolerable Dose (MTD)
 Quantitative Definition
Some percentile of a tolerance distribution w.r. to some definitive dose-limiting
clinical toxicity, Storer (1989), Korn, et al (1994)
logit[P(x, θ)] = α + βx,
MTD =X m = (k p -α)/β,
where θ = (α,β)
where k p = logit(p)
Prepared by Jen-pei Liu, PhD
42
Drawbacks of the Current Practice
for Standard Design




No room for de-escalation
No further analysis of data
No objective estimation of MTD with statistical models
No sampling error and no confidence interval.
Prepared by Jen-pei Liu, PhD
43
Accelerated Titration Designs
Richard Simon (1997)

Rationale



Address the flaws of traditional designs
Attempt to obtain information about interpatient variability and
cumulative toxicity
stay for 3 courses to allow for intra-patient dose
modifications
Distinguish between moderate and dose-limiting toxicities
Prepared by Jen-pei Liu, PhD
44
Accelerated Titration Designs
Richard Simon (1997)
Scheme

The first stage
1 patient per level until 1 DLT or 2 moderate toxicities

The second stage
Traditional design, i.e. add 2 patients to the current dose that
triggered the switch.
Prepared by Jen-pei Liu, PhD
45
Accelerated Titration Designs
Richard Simon (1997)

MTD
Estimated as the highest dose where at most 1/6 patients developed DLT
Compared to traditional designs




Go through the lower doses quickly, and thus reduces under-treated
patients in absolute sense and speed up the completion
Obtain similar estimate of MTD
Provide more information. Upon completion, a model can be fitted to
estimate inter- and intra-patient variability
Require careful patient management to track the toxicity over multiple
course
Prepared by Jen-pei Liu, PhD
46
Bayesian Sequential Design
The Continual Reassessment Method (CRM)
O’Quigley, Pepe, Fisher (1990), O’Quigley (1992), Moller (1995)


Step 1

Determine the dose-toxicity relationship

Select fixed dose levels

Determine the prior probability of slope

Choose a fixed sample size
Step 2
Determine the dose for the first patient as the dose level which produces the prior probability of
dose-limiting clinical toxicity closest to p.
Prepared by Jen-pei Liu, PhD
47
Bayesian Sequential Design

Step 3
Update the posterior distribution of slope after each patient’s toxicity result becomes available. The
dose level for the next patient is the one which gives the posterior probability of dose-limiting
clinical toxicity closest to p.

Step 4
Repeat Step 3 until the results of the last patient are available.

Step 5
The estimated MTD is determined as the dose which minimizes some pre-selected criterion such as
some quadratic error loss function with respect to the probability of dose-limiting clinical toxicity.
Prepared by Jen-pei Liu, PhD
48
Advantages of Continual
Reassessment Method



Try to accommodate the situations
 Patients at high risk of death
 Fatal toxicity of new drug at high doses
 No efficacy at lower doses
 No information about dose range
A well-defined goal of estimating a percentile of the dose-toxicity relationship
It should converge to percentile with increasing sample size.
Prepared by Jen-pei Liu, PhD
49
Issues of Continual Reassessment
Method





Assumption of a homogeneous patient population for the prior
distribution of parameters
It treats patients in cohorts of 1
It takes too long to complete the trial
It is less conservative so that it may treat patients at very high
dose levels
Difficulty in choice of a criterion metric
Prepared by Jen-pei Liu, PhD
50
Modifications of CRM

Goodman, Zahurak & Piantadosi (1995)
> 1 patient per cohort, dose increase is limited to 1 level, start at the lowest level

Moller (1995)
Combined with a preliminary up-and-down design, limit escalation to 1 level.

Piantadosi & Liu (1996)
Incorporate pharmacokinetics parameters
Some of other simulation studies for comparing CRM’s with nonparametric
approach: O’Quigley & Chevret (1991), Chevret (1993), Ahn (1996)
A special issue of CRM in Statistics in Medicine was published in 2011
Prepared by Jen-pei Liu, PhD
51
Cancer Phase II Trials

Endpoints:

Response/tumor shrinkage measurements




Most commonly used in phase II cancer trials
Changes in radiographic measurements
4 categories: complete response, partial response, stable,
and progression
Progression-free survival

Time to progression or death whichever occurs early
Prepared by Jen-pei Liu, PhD
52
Cancer Phase II Trials


A screening trial to allow early termination for inactivity or high
activity.
Define


P0: undesirable response (CR+PR) rate (5-10%)
P1: target response rate (> 25%)
The rationale is based on the hypothesis testing
H 0 : p  p0 against H1 : p  p1
and the error limits : Type Ⅰ  , Type Ⅱ  
Prepared by Jen-pei Liu, PhD
53
Simon’s design



Procedure
 Stage 1: If X1 > r1
go to stage 2
≦ r1
stop and reject the drug
 Stage 2: If X1+X2 is ≦ r
reject the drug
>r
accept the drug
Given p0, p1, α, β, then (n1, n2, r1, r) are optimized to minimize either
 The expected sample size under p0, or
 The maximal sample size n1 + n2
Not readily evaluable, but tables of designs under different values of parameter are
available from the paper.
Prepared by Jen-pei Liu, PhD
54
Randomized Phase II Cancer
Designs

Reasons:

Simon 2-stage design is a single arm trial




Biased
No control
Estimated response rates treated as population rates
Traditional phase II trials required large sample sizes
Prepared by Jen-pei Liu, PhD
55
Randomized Phase II Cancer
Designs






Pick-the-winner selection designs
Apply statistical methods for ranking and selection to choose a
promising new agent for phase III confirmatory trials
Not designed and no power to detect statistical significant differences in
responses between treatments
Randomization to eliminate bias
To select the treatment with the greatest responses rate regardless of
how small the differences
Extension to survival and PFS
Prepared by Jen-pei Liu, PhD
56
Adaptation of Molecular Targeted
Agents

Issues:




Failure to translate the tumor shrinkage into patient benefit such as survival
Different mechanisms from cytotoxic agents
Quality of assays for biomarkers
References:


Chapter 6 of Chow and Liu (2013)
Clinical Cancer Research:


Vol. 15(6) March 15, 2009
Vol. 16(6) March 15, 2010
Prepared by Jen-pei Liu, PhD
57
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本作品轉載自Microsoft Office 2010 PowerPoint 設計主題範本-Blends，依據
Microsoft 服務合約及著作權法第46、52、65條合理使用。
4
Simons FE. A comparison of beclomethasone, salmeterol, and placebo in children
with asthma. Canadian Beclomethasone Dipropionate-Salmeterol Xinafoate Study
Group. N Engl J Med. 1997 Dec 4;337(23):1659-65.
本作品依據著作權法第 46、52、65 條合理使用。
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Barst RJ, Rubin LJ, Long WA, et al. A comparison of continuous intravenous
epoprostenol (prostacyclin) with conventional therapy for primary pulmonary
hypertension. N Engl J Med. 1996 Feb 1;334(5):296-301.
本作品依據著作權法第 46、52、65 條合理使用。
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Wernicke JF, Dunlop SR, Dornseif BE, et al. Fixed-dose fluoxetine therapy for
depression. Psychopharmacol Bull. 1987;23(1):164-8.
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《Design and analysis of clinical trials: concepts and methodologies》， 作者: Chow,
SC, Liu, JP，出版社: Wiley(second edition )，p128。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
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《Design and analysis of clinical trials: concepts and methodologies》， 者: Chow, SC,
Liu, JP ，出版社: Wiley(third edition )，p156。本作品依據著作權法第 46、52、65
條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
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《Design and analysis of clinical trials: concepts and methodologies》， 作者: Chow,
SC, Liu, JP ，出版社: Wiley(third edition )，p160。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
15
22
The bias of an
estimate of the
treatment …
《Forcing a sequential experiment to be balanced》， 作者: BRADLEY EFRON，出版：
Biometrika (1971) 58 (3): 403-417. 本作品依據著作權法第 46、52、65 條合理使用。
Method for
unrestricted
randomization
《Design and analysis of clinical trials: concepts and methodologies》， 作者: Chow,
SC, Liu, JP，出版社: Wiley(third edition )，p.130 。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd0470887656.html
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作品
Method for
Permuted-block
randomization
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《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP，出版社: Wiley(third edition )，p.133。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
24
《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP，出版社: Wiley(third edition )，p.134 。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
25
《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP ，出版社: Wiley(third edition )，p123。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
26
《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP，出版社: Wiley(third edition )，p238 。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
27
《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP ，出版社: Wiley(third edition )，p137。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
60
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《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP，出版社: Wiley(third edition )，p139 。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
28
29-30
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Selection of a
measure of
imbalance …
《Design and analysis of clinical trials: concepts and methodologies》， 作
者:Chow, SC, Liu, JP ，出版社: Wiley(third edition )，p139-140。本作品依據著作
權法第 46、52、65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd0470887656.html
34
Given a total
sample size n and
assignment
probability of p …
《Design and analysis of clinical trials: concepts and methodologies》， 作
者:Chow, SC, Liu, JP，出版社: Wiley(third edition )，p161 。本作品依據著作權法
第 46、52、65 條合理使用。
http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
40
Objectives of
cancer phase I
trials for cytotoxic
agents…
《Design and analysis of clinical trials: concepts and methodologies》， 作
者:Chow, SC, Liu, JP ，出版社: Wiley(third edition )，p212-213。本作品依據著作
權法第 46、52、65 條合理使用。
http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
61
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41
Recognize
differential dosinglimiting clinical
toxicity
《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP ，出版社: Wiley(third edition )，p213。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd0470887656.html
42
Designs for
determination of
maximum tolerable
dose
《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP ，出版社: Wiley(third edition )，p213。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd0470887656.html
《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP ，出版社: Wiley(third edition )，p217-291。本作品依據著作權法第 46、
52、65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd0470887656.html
44-46
47-48
The Continual
Reassessment
Method (CRM)
《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP ，出版社: Wiley(third edition )，p221。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd0470887656.html
62
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51
《Design and analysis of clinical trials: concepts and methodologies》， 作
者:Chow, SC, Liu, JP，出版社: Wiley(third edition )，p221。本作品依據著作權法
第 46、52、65 條合理使用。
http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
52
《Design and analysis of clinical trials: concepts and methodologies》， 作
者:Chow, SC, Liu, JP ，出版社: Wiley(third edition )，p229。本作品依據著作權法
第 46、52、65 條合理使用。
http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
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《Design and analysis of clinical trials: concepts and methodologies》， 作
者:Chow, SC, Liu, JP ，出版社: Wiley(third edition )，p232。本作品依據著作權法
第 46、52、65 條合理使用。
http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470887656.html
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《Design and analysis of clinical trials: concepts and methodologies》， 作者:Chow,
SC, Liu, JP ，出版社: Wiley(third edition )，p229。本作品依據著作權法第 46、52、
65 條合理使用。http://as.wiley.com/WileyCDA/WileyTitle/productCd0470887656.html
63