Designs for Clinical Trials. Chapter 5 Reading Instructions 5.1: Introduction 5.2: Parallel Group...
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Transcript of 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: