designs for clinical trials. chapter 5 reading instructions 5.1: introduction 5.2: parallel group...

Designs for Clinical Trials

Chapter 5 Reading Instructions

• 5.1: Introduction• 5.2: Parallel Group Designs (read)• 5.3: Cluster Randomized Designs (less important)• 5.4: Crossover Designs (read+copies)• 5.5: Titration Designs (read)• 5.6: Enrichment Designs (less important)• 5.7: Group Sequential Designs (read include 10.6)• 5.8: Placebo-Challenging Designs (less important)• 5.9: Blinded Reader Designs (less important)• 5.10: Discussion

Design issues

?

Design issues

Objective

Research question

Design, Variables

Control

Ethics

FeasibilityCost

Statistics

Variability

Confounding

Statistical optimality not enough!Use simulation models!

Parallel Group Designs

R

Test

Control 1

Control 2

ijjijY

jni ,,1 kj ,,1

2,0~ Nij•Easy to implement•Accepted•Easy to analyse•Good for acute conditions

Where does the varation go?

8 week blood pressure

Placebo

Drug X

εXβY

Anything we can explain Unexplained

Between and within subject variation

Baseline 8 weeks

Placebo

Drug X DBP

mmHg

Female

Male

What can be done?

Stratify:

More observations per subject:

Run in period:

Randomize by baseline covariate and put the covariate in the model.

BaselineMore than 1 obsservation per treatment

Ensure complience, diagnosis

Parallell group design with baseline

R

Test

Control 1

Control 2

Baseline 8 weeks

Compare bloodpressure for three treatments, one test and two control.

Model: ijkkjiijkY 21 2,1i

3,2,1j

2,0 iid Nijk

2,0 iid sk N jnk ,,1

Observation

Treatment

SubjectjTreatment effect

Subject effect

Random error

Change from baselineThe variance of an 8 week value is

22 s

Change from baseline jkjjkjkjkjk YYZ 2121

The variance of change from baseline is

22

Usually 22222 2 ss

ijkkjijk VarYVar 22 1

ijkkijkk VarVarVar

jkjjkjkjkjk VarYYVarZVar 1212

jkjk VarVar 12

Baseline as covariate

R

Test

Control 1

Control 2

Baseline 8 weeks

ijijij xY

2,0 iid Nijk

Subject

TreatmentTreatment effect

jni ,,1

3,2,1jj

Random error

Baseline value ix

Model:

Baseline as covariate

x=baseline

Model: ijijij xY

111 iii xY

222 iii xY 1

2

Crossover studies

•All subject gets more that one treatment•Comparisons within subject

R

Wash

out

A

AB

B

Period 1 Period 2

Sequence 1

Sequence 2

A B

B A

•Within subject comparison•Reduced sample size•Good for cronic conditions•Good for pharmaceutical studies

Model for a cross over study

021

021 0 BA

2,1 sequence ofeffect ii 2

)( ,0 iid sequence within ,,1subject ofeffect siki Nink

2,1 period ofeffect jj BAtt , treatmentofeffect

20, iiderror random Nijk

ijkrjtjkiiijkY )(

Obs=Period+sequence+subject+treament+carryover+error

2 by 2 Crossover design

ijkYEA 11 AB 21

B 12 BA 12

11 122221

BABA

BBAABA

2

12

12

1

1221

21221211

Effect of treatment and carry over can not be separated!

Matrix formulation

T22211211 ,,, TA 11

X

1111

1111

1111

1111

X

ijktjkiiijkY )(

021 021 021

Model:

Sum to zero:

Matrix formulation

Matrix formulation

25.0000

025.000

0025.00

00025.0

1XXT

2ˆˆ XXTCov

YTT XXX1ˆ

TYY TT X ˆˆ 2

Parameter estimate:

2ˆ25.0ˆ AVar

Estimates independent and

Alternatives to 2*2Compare A B

B A

A B

B A

B

Ato

Same model but with 3 periods and a carry over effect

2,1 sequence ofeffect ii 2

)( ,0 iid sequence within ,,1subject ofeffect siki Nink

3,2,1 period ofeffect jj BAtt , treatmentofeffect

20, iiderror random Nijk

021

021

0 BA

ijkrjtjkiiijkY )(

Parameters of the AAB, BBA design

11 122221

13

23

ijktjkiiijkY )( ijkijkYE

A 1111

AB 2112

BB 3113

B 1221

BA 2222

BA 3223

021 0321 021 0 BA

Matrix again

A

A

2

1

1

111111

111011

010111

111111

111011

010111

X

25.000000

019.00006.00

0033.017.000

0017.033.000

006.00019.00

0000017.0

1XXT

Effect of treatment and carry over can be estimated independently!

Other 2 sequence 3 period designs

A B

B A

B

A

A A

B B

B

A

A B

B A

A

B

A A

B B

A

B

1

2

3

4

AVar ̂

AVar ̂

AACorr ˆ,ˆ

1 2 3 4

0.19 0.75 0.25 N/A

0.25 1.00 1.00 N/A

0.0 0.87 0.50 N/A

Comparing the AB, BA and the ABB, BBA designs

A B

B A

B

A

A B

B A

2ˆ25.0ˆ AVar 2ˆ19.0ˆ AVar

Can’t include carry overCarry over estimable

2 treatments per subject3 treatments per subject

Shorter duration Longer duration

Excercise: Find the best 2 treatment 4 period design

More than 2 treatments

Tools of the trade: 1XXT

A B

B C

C

A

C A

A C

B

B

B A

C B

C

A

A B

B D

C

A

D

C

C A

D C

D

B

B

A

•Investigate•Define the model

A B

B C

C A

A C

B C

C B Watch out for drop outs!

Titration Designs

Increasing dose panels (Phase I):

•SAD (Single Ascending Dose)•MAD (Multiple Ascending Dose)

Primary Objective:

•Establish Safety and Tolerability•Estimate Pharmaco Kinetic (PK) profile

Increasing dose panelse (Phase II):

Dose - response

Titration Designs (SAD, MAD)

•X on drug•Y on Placebo

Dose: Z1 mg

•X on drug•Y on Placebo

Dose: Z2 mg

•X on drug•Y on Placebo

Dose: Zk mg

Stop if any signs of safety issues

VERY careful with first group!

Titration DesignsWhich dose levels?

•Start dose based on exposure in animal models.•Stop dose based on toxdata from animal models.•Doses often equidistant on log scale.

Which subject?

•Healty volunteers•Young•Male

How many subjects?

•Rarely any formal power calculation.•Often 2 on placebo and 6-8 on drug.

Titration Designs

Not mandatory to have new subject for each group.

Gr. 1 Gr. 2 Gr. 3Gr. 1 Gr. 2 Gr. 4

X1 mg

X2 mg

X3 mg

X4 mg

X5 mg

XY mg

12+2 12+212+212+212+2 12+2

•Slighty larger groups to have sufficiently many exposed.•Dose in fourth group depends on results so far.•Possible to estimate within subject variation.

Factorial designEvaluation of a fixed combination of drug A and drug B

A placeboB placebo

A activeB placebo

A placeboB active

A activeB active

The U.S. FDA’s policy (21 CFR 300.50) regarding the use of a fixed-dose combination

The agency requires:

Each component must make a contribution to the claimed effect of the combination.

Implication: At specific component doses, the combination must be superior to its components at the same respective doses

P

B AB

A

Factorial designUsually the fixed-dose of either drug under study has been approved for an indication for treating a disease.

Nonetheless, it is desirable to include placebo (P) to examine the sensitivity of either drug give alone at that fixed-dose (comparison of AB with P may be necessary in some situations).

Assume that the same efficacy variable is used for studying both drugs (using different endpoints can be considered and needs more thoughts).

Factorial design

Sample mean Yi ∼ N( μi , σ2/n ), i = A, B, AB n = sample size per treatment group (balanced design is assumed for simplicity).

H0: μAB ≤ μA or μAB ≤ μB

H1: μAB > μA and μAB > μB j=A, B

Min test and critical region:

BAjYYn

T jABjAB , ;

ˆ2:

CTT BABAAB :: ,min

Group sequential designs

A large study is a a huge investment, $, ethics

•What if the drug doesn’t work or is much better than expected? •Could we take an early look at data and stop the study is it look good (or too bad)?

Repeated significance test

Let: 2,~ jij NY Test: 210 : H

Test statistic:mk

Zmk 2

21

2

ˆˆ

mk

iijj Y

mk 1

1̂

0HFor 1,1 Kk If CZk Stop, reject

otherwise Continue to group 1k

If CZk Stop, reject 0H

otherwise stop accept 0H

True type I error rate

Tests Critical value P(type I error) 1 1.96 0.05 2 1.96 0.08 3 1.96 0.11 4 1.96 0.13 5 1.96 0.24

Repeat testing until H0 rejected

Pocock’s testSuppose we want to test the null hypothesis 5 times using the same critical value each time and keep the overall significance level at 5%

For 1,1 Kk If KCZ pk , Stop, reject

otherwise Continue to group 1k

If KCZ pk , Stop, reject 0H

otherwise stop accept 0H

Choose KC p , Such that

)1 analysisany at Reject ( 0 KkHP

After group K

0H

Pocock’s test#Tests Critical value P(type I error) 1 1.960 0.05 2 2.178 0.05 3 2.289 0.05 4 2.361 0.05 5 2.413 0.05

All tests has the same nominal significance level

A group sequential test with 5 interrim tests has level

0158.0413.212'

Pocock’s test

2.413

-2.413

kZ

k stage

0Reject H

0Reject H

0Accept H

O’Brian & Flemmings test

For 1,1 Kk If kKKCZ pk /, Stop, reject

otherwise Continue to group 1k

If KCZ pk , Stop, reject 0H

otherwise stop accept 0H

Choose KC p , Such that

)1 analysisany at Reject ( 0 KkHP

After group K :

:

Increasing nominal significance levels

0H

O’Brian & Flemmings test

Test (k) CB(K,) CB(K,)*Sqrt(K/k) ’ 1 2.04 4.56 0.000005 2 2.04 3.23 0.0013 3 2.04 2.63 0.0084 4 2.04 2.28 0.0225 5 2.04 2.04 0.0413

Critical values and nominal significance levels for a O’Brian Flemming test with 5 interrim tests.

Rather close to 5%

O’Brian & Flemmings test

-6

-4

-2

0

2

4

6

0 1 2 3 4 5 6 Stage K

Zk

0.000005

0.0013

0.0084 0.0225 0.0413

Comparing Pocock and O’Brian Flemming

O’Brian Flemming Pocock Test (k) CB(K,a)*Sqrt(K/k) ’ CP(K,a) ’ 1 4.56 0.00001 2.413 0.0158 2 3.23 0.0013 2.413 0.0158 3 2.63 0.0084 2.413 0.0158 4 2.28 0.0225 2.413 0.0158 5 2.04 0.0413 2.413 0.0158

Comparing Pocock and O’Brian Flemming

-6

-4

-2

0

2

4

6

0 1 2 3 4 5

Stage k

Zk

Group Sequential Designs

•Efficiency Gain (Decreasing marginal benefit)•Establish efficacy earlier•Detect safety problems earlier

•Smaller safety data base•Complex to run•Need to live up to stopping rules!

Pros:

Cons:

Selection of a design

The design of a clinical study is influenced by:

•Number of treatments to be compared•Characteristics of the treatment•Characteristics of the disease/condition•Study objectives•Inter and intra subject variability•Duration of the study•Drop out rates

Backup

22212221 YVarYVarYYVar

2222

2221

11 ss nnBack up: