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Sin-Ho Jung INNOVATIVE CLINICAL TRIAL DESIGNS 1

Innovative Clinical Trial Designs

Sin-Ho Jung

Stephen L George

Department of Biostatistics and Bioinformatics

Duke University

Sin-Ho Jung INNOVATIVE CLINICAL TRIAL DESIGNS 2

Project 1: Innovative Clinical Design and Analysis

• Develop methods for design and sample size calculation for longitudinal and joint

models for longitudinal and survival data

• Develop statistical methodology for the design and analysis of group randomized

cancer prevention trials with survival and recurrent event outcomes

• Develop statistical methodology for cancer drug development

– Develop methods for the design and analysis of clinical trials of targeted therapy

– Develop designs for Phase II trials that are predictive of Phase III trial success

– Develop methods for the design and analysis of partially randomized clinical trials

Sin-Ho Jung RANDOMIZED PHASE II TRIALS 3

Randomized Phase II Cancer Clinical Trials


Traditional Phase II Cancer Clinical Trials

• To investigate if an experimental therapy has promising efficacy and is worth further

investigation

• Small sample sizes⇒ exact method

• Single-arm design: usually recruit a small number of patients only to the experimental

therapy arm to be compared to a historical control

• Appropriate only when reliable and valid data for an existing standard therapy are

available for the same patient population

• The response assessment method in the historical control data should be identical to

the one that will be used for a new study

• Often no historical control data exist satisfying these properties


Two-Stage Randomized Phase II Trials

Notations

• Arm x = experimental arm; Arm y = control

• Response probabilities: px, py

• H0 : px = py vs H1 : px > py

• At stage k(= 1, 2),

- randomize nk patients to each arm

- observe # of responders Xk and Yk from arms x and y, respectively

• X = X1 + X2, Y = Y1 + Y2


Two-stage design by Jung (2008)

• Stage 1: Proceed to stage 2 if X1 − Y1 ≥ a1

Stage 2: Accept the exp. Rx if X − Y ≥ a

• Xk ∼ B(nk, px), Yk ∼ B(nk, py)

• For (n1, n2, a1, a)

α = P (X1 − Y1 ≥ a1, X − Y ≥ a|px = py)

1− β = P (X1 − Y1 ≥ a1, X − Y ≥ a|px, py)

• PET = P (X1 − Y1 < a1) ⇒ minimax and optimal designs

• α depends on py ⇒ conservative α-control

α = P (X1 − Y1 ≥ a1, X − Y ≥ a|px = py = 0.5)


Randomized Phase II Trials

based on Fisher Exact Test


Single-Stage Trial (Fisher Exact Test)

Arm x Arm y Total

Response Yes x (px) y (py) z

No n− x (qx) n− y (qy) 2n− z

Total n n


Single-Stage Design (continued)

• Accept arm x (or, reject H0 : px = py) if X − Y ≥ a

• Given n and X + Y = z,

α(z) = P (X − Y ≥ a|z, θ = 1) =m+∑

x=(z+a)/2

f(x|z, θ = 1)

1− β(z) = P (X − Y ≥ a|z, θ = θ1) =m+∑

x=(z+a)/2

f(x|z, θ1)

where θ = pxqy/(pyqx)

f(x|z, θ) =

(nx

)(n

z−x

)θx

∑m+i=m−

(ni

)(n

z−i

)θi

for m− ≤ x ≤ m+, m− = max(0, z − n), m+ = min(z, n)

• Given (n, z, α∗), choose the smallest a satisfying α(z) ≤ α∗


Single-Stage Design (continued)

How to choose n?

• Specify (α∗, 1− β∗, px, py)

• Given n,

- given z, choose the smallest a = a(z) such that α(z) ≤ α∗

- marginal power

E{1− β(z)} =2n∑

z=0

{1− β(z)}g(z)

where g(z) is PMF of Z = X + Y under H1 : px > py, i.e.

g(z) =m+∑

x=m−

(n

x

)px

xqn−xx

(n

z − x

)pz−x

y qn−z+xy

for z = 0, 1, ..., 2n

• Choose n such that 1− β = E{1− β(z)} ≥ 1− β∗


Two-Stage Randomized Phase II Trial

• Stage 1: Randomize n1 patients to each arm & observe x1 and y1

- Given z1(= x1 + y1), find a stopping value a1 = a1(z1)- If x1 − y1 ≥ a1, proceed to stage 2; Otherwise, stop trial

• Stage 2: Randomize n2 patients to each arm & observe x2 and y2 (z2 = x2 + y2)- Given (z1, z2), find a rejection value a = a(z1, z2)- Accept the experimental arm y, if x− y ≥ a

X1 and X2 are independent, and given Xk + Yk = zk, Xk has conditional PMF

fk(xk|zk, θ) =

(nk

xk

)(nk

zk−xk

)θxk

∑mk+i=mk−

(nk

i

)(nk

zk−i

)θi

for mk− ≤ xk ≤ mk+, where mk− = max(0, zk − nk) and mk+ = min(zk, nk)


Two-Stage Design (continued)

How to choose (a1, a) given (n1, n2, z1, z2)

• Choice of a1

- a1 = 0- PET: PET(H0, z1) ≥ γ0

- β-use: P (X1 −X2 < a1|H1, z1) = β1(< β)

• For a1 = 0 and (z1, z2), choose the smallest a such that

α(z1, z2) ≡ P (X1 − Y1 ≥ a1, X − Y ≥ a|z1, z2, θ = 1) ≤ α∗



How to choose (n1, n2)

• For stage k(= 1, 2), Zk = Xk + Yk are independent with PMF

gk(zk) =mk+∑

xk=mk−

(nk

xk

)pxk

x qnk−xkx

(nk

zk − xk

)pzk−xk

y qnk−zk+xky

for zk = 0, ..., 2nk

• Choose (n1, n2) so that

1− β ≡2n1∑

z1=0

2n2∑z2=0

{1− β(z1, z2)}g1(z1)g2(z2) ≥ 1− β∗



Among (n1, n2) satisfying (α∗, 1− β∗)-condition,

Minimax design has the smallest maximal sample size n(= n1 + n2).

Optimal design has the smallest marginal expected sample size EN under H0, where

EN = n1 × PET0 + n× (1− PET0)

PET0 ≡ E{PET0(Z1)|H0} =2n1∑

z1=0

PET0(z1)g01(z1)



Fisher Test vs. Binomial Test (Jung, 2008)

• Designs

- (n1, n2) = (30, 30)- α∗ = 0.1, 0.15, 0.2

- ∆ = px − py = 0.15, 0.2 under H1

• Compare marginal power


0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

1.0

∆= 0.15, α= 0.1

P2

α or

1−

β

0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

1.0

∆= 0.15, α= 0.15

P2

α or

1−

β

0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

1.0

∆= 0.15, α= 0.2

P2

α or

1−

β0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

1.0

∆= 0.2, α= 0.1

P2

α or

1−

β

0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

1.0

∆= 0.2, α= 0.15

P2

α or

1−

β

0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

1.0

∆= 0.2, α= 0.2

P2

α or

1−

β


Example: CALGB 50502

GVD chemo Rx combined with SGN-30 in relapsed/refractory HL

• Arm x: GVD + SGN-30

Arm y: GVD + placebo

• Based on H1 : (px, py) = (0.85, 0.7), θ1 = 2.43

• (α∗, 1− β∗) = (0.15, 0.8)

• Minimax design:

Stage 1: Randomize n1 = 36 patients to each arm

- If X1 − Y1 ≥ 0, proceed to stage 2

- O.w, reject arm x and stop the trial

Stage 2: Randomize n2 = 29 patients to each arm

- Accept Arm x if X − Y ≥ a

• Critical value a depends on z1 = X1 + Y1 and z = X + Y


For (θ1, α∗) = (2.43, 0.15)

Conditional

(z1, z) a α 1− β

(51,108) 5 .1046 .6983

(51,109) 4 .1499 .7543

(52,91) 6 .1235 .8758

(52,92) 7 .0881 .8285

For (px, py) = (0.7, 0.85), marginal (α, 1− β) = (.1083, .8004)


Conclusions

The proposed method

• is using multi-stage Fisher exact test

• does not require specification of px = py = p0

• conservatively controls the marginal type I error at the wide range of p0 values

• is powerful

• can be easily extended to unbalanced allocation design


Core B: Data Compilation core

• To develop and maintain well annotated and documented analysis-ready data sets

• from cancer clinical trials and related studies

• for use by program investigators

• to illustrate the effect of new methodology applied to actual data


Sources of Data (Core B)

• Clinical Trials

– Cancer and Leukemia Group B (CALGB)

– Duke Comprehensive Cancer Center

– Lineberger Comprehensive Cancer Center (UNC)

– Others (e.g., colorectal trials)

• Observational Data Sets

– CanCORS

– SEER-MEDICARE

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