Designs for Clinical Trials - Chalmers · 2008-02-05 · Titration Designs Not mandatory to have...
Transcript of Designs for Clinical Trials - Chalmers · 2008-02-05 · Titration Designs Not mandatory to have...
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
ijiijY εµ +=
jni ,,1 K=kj ,,1 K=
( )2,0~ σε 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 XDBPmmHg
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 εξτµ +++= =21 2,1=i3,2,1=j
( )2,0 iid σε Nijk
( )2,0 iid sk N σξjnk ,,1K=
Observation
Treatment
SubjectjτTreatment effect
Subject effectRandom error
Change from baseline
The variance of an 8 week value is
22 σσ +s
Change from baseline ( )jkjjkjkjkjk YYZ 2121 ετε +−=−=
The variance of change from baseline is 22σ
Usually 22222 2 ss σσσσσ +<⇒<
( ) { }( )ijkkjijk VarYVar εξτµ +++= =22 1
( ) ( ) ( )=+=+= ijkkijkk VarVarVar εξεξ
Baseline as covariate
R
Test
Control 1
Control 2
Baseline 8 weeks
ijijij xY εβτµ +++=
( )2,0 iid σε Nijk
Subject
TreatmentTreatment effect
jni ,,1K=
3,2,1=jjτ
Random error
Baseline value ix
Model:
Crossover studies
�All subject gets more that one treatment�Comparisons within subject
R
Was
h ou
t
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 =+γγ
021 =+ππ0=+ BA ττ
2,1 sequence ofeffect == iiγ( )2
)( ,0 iid sequence within ,,1subject ofeffect siki Nink σξ K==
2,1 period ofeffect == jjπ{ }BAtt , treatmentofeffect ∈=τ
( )20, iiderror random σε Nijk =
ijkrjtjkiiijkY ελδτπξγµ ++++++= )(
Obs=Period+sequence+subject+treament+carryover+error
2 by 2 Crossover design
[ ] =ijkYEAτπγ ++ 11 AB λτπγ +++ 21
Bτπγ ++ 12 BA γτπγ +++ 12
11µ 12µ22µ21µ
( ) ( )( )
( ) ( )( )
( )BABA
BBAABA
λλττ
λττππλττππ
µµµµ
+−−
=−−+−+−−+−
=−+−
21
2121
1221
21221211
Effect of treatment and carry over can not be separated!
Matrix formulation
( )T22211211 ,,, µµµµµ =( )TAτπγµβ 11=
βµ X=
−−−−−−
=
111111111111
1111
X
ijktjkiiijkY ετπξγµ +++++= )(
021 =+λλ021 =+ππ021 =+ττ
Model:
Sum to zero:
Matrix formulation
Matrix formulation
( )
=−
25.0000025.0000025.0000025.0
1XXT
( ) ( ) 2ˆˆ σβ XXTCov =
( ) YTT XXX 1ˆ −=β
( ) TYY TT Xβσ ˆˆ 2 −=
Parameter estimate:
( ) 2ˆ25.0ˆ στ =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 == iiγ( )2
)( ,0 iid sequence within ,,1subject ofeffect siki Nink σξ K==
3,2,1 period ofeffect == jjπ{ }BAtt , treatmentofeffect ∈=τ
( )20, iiderror random σε Nijk =
021 =+γγ021 =+ππ
0=+ BA ττ
ijkrjtjkiiijkY ελδτπξγµ ++++++= )(
Parameters of the AAB, BBA design
11µ 12µ22µ21µ
13µ
23µ
ijktjkiiijkY ετπξγµ +++++= )( [ ] ijkijkYE µ=
Aτπγµµ +++= 1111
AB λτπγµµ ++++= 2112
BB λτπγµµ ++++= 3113
Bτπγµµ +++= 1221
BA λτπγµµ ++++= 2222
BA λτπγµµ ++++= 3223
021 =+λλ 0321 =++ πππ 021 =+ττ 0=+ BA λλ
Matrix again
−−−−−
−−−−−−
−
=
A
A
λτππγµ
β2
1
1
111111111011
010111111111
111011010111
X
( )
−−
=−
25.000000019.00006.000033.017.0000017.033.000006.00019.000000017.0
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 τ̂
( )AVar λ̂
( )AACorr λτ 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 στ =AVar ( ) 2ˆ19.0ˆ στ =AVarCan�t include carry over Carry over estimable2 treatments per subject 3 treatments per subject
Shorter duration Longer duration
Excercise: Find the best 2 treatment 4 period design
More than 2 treatments
Tool of the trade: Define the model
( ) 1−XXT
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
A B
B C
C A
A C
B C
C B Watch out for drop outs!
Titration DesignsIncreasing 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 ofthe 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:
BAjYYnT jAB
jAB , ; ˆ2: =
−=
σ
( ) 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,~ σµ jij NY Test: 210 : µµ =H
Test statistic:mk
Zmk 221
2
ˆˆ
σµµ −= ∑
=
=mk
iijj Y
mk 1
1µ̂
0HFor 1,1 −= Kk K If αCZk ≥ Stop, reject
otherwise Continue to group 1+k
If αCZk ≥ 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 K If ( )KCZ pk ,α≥ Stop, reject
otherwise Continue to group 1+k
If ( )KCZ pk ,α≥ Stop, reject 0H
otherwise stop accept 0H
Choose ( )KCp ,α Such that
α== )1 analysisany at Reject ( 0 KkHP K
After group K
0H
Pocock�s testTests 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' =−= φα
Pocock�s test
2.413
-2.413
kZ
k stage
0Reject H
0Reject H
0Accept H
O�Brian & Flemmings test
For 1,1 −= Kk K If ( ) kKKCZ pk /,α≥ Stop, reject
otherwise Continue to group 1+k
If ( )KCZ pk ,α≥ Stop, reject 0Hotherwise stop accept 0H
Choose ( )KCp ,α Such that
α== )1 analysisany at Reject ( 0 KkHP K
After group K :
:
Increasing nominal significance levels
0H
O�Brian & Flemmings test
Test (k) CB(K,αααα) CB(K,αααα)*Sqrt(K/k) αααα’ 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
0.00130.0084 0.0225 0.0413
Comparing Pocock and O�Brian Flemming
O’Brian Flemming Pocock Test (k) CB(K,a)*Sqrt(K/k) αααα’ CP(K,a) αααα’ 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( ) ( )22
22
2221
11 σσσσ +++= ss nnBack up: