Group 1 Discussion Topic Thursday, 7 February. When should a clinical trial with prestratification be used?. Outline of Randomization Lectures. Background and definitions Generation of schedules 3. Implementation (to ensure allocation concealment, sometimes called blinded randomization)
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When should a clinical trial with prestratification be used?
3. Implementation (to ensure allocation concealment, sometimes called blinded randomization)
4. Theory behind randomization
A list showing the order in which subjects are to be assigned to the various treatment groups
Randomization Schedule1. Sealed envelopes
 Opaque
 Sequentially numbered
2. Telephone
 Answering service
 Coordinating center
 IVRS
3. Personal computers
 Local
 Through communication with coordinating center
1. Telephone answering service in New York City; 24hour coverage
2. Assignments obtained through hospital pharmacy
3. Sealed envelopes as backup
1. Assignments obtained by calling coordinating center after:
a. Three screening visits
b. Informed consent
c. Eligibility checklist
2. Sealed envelopes used as backup
Treatment of Mild assigned to the various treatment groupsHypertension Study (TOHMS)
1. Assignment (bottle no.) obtained using personal computer to call coordinating center computer after:
a. Three screening visits
b. Informed consent
c. Eligibility checklist
2. Call coordinating center for backup
3. Unique bottle no. for each participant
4. Bottle no. not assigned in sequence
Amer J Cardiol, 1987
Community Programs for Clinical Research on AIDS (CPCRA) assigned to the various treatment groups
1. Assignments obtained by calling Statistical Center:
– Minimal data collection
– Usually no data at Statistical Center prior to randomization
– Eligibility checklist reviewed on telephone call
2. Pharmacist telephones to confirm assignment
3. Unique study ID number (SID) for each patient
4. SID numbers not assigned in sequence
Components of CPCRA Randomization System assigned to the various treatment groups
1. Randomization schedule, based on randomly permuted blocks
2. SID numbers, sheets, and notebooks
3. Randomization logbooks
4. Eligibility checking program
5. Pharmacy checking program
6. Backup procedures
7. Training (local and for clinical sites)
C assigned to the various treatment groupsontrolled Onset Verapamil Investigation of Cardiovascular Endpoints (CONVINCE)
Preparation of Schedules
Permuted block* 13
Other 2
Computer 7
Random no. table 8
*Most common block size = 2 x no. treatments
Mechanics of Treatment Assignment
Telephone 12
Sealed envelopes 3
Source: Pocock et al., Br J Cancer, 1982
1. Verify eligibility, informed consent, and completeness of baseline data.
2. Complete patient accession log.
3. Obtain assignment.
4. Record assignment on log and data forms.
5. Initiate treatment as soon as possible after randomization.
Placebo
Alprenolol
No. randomized 193 200
2 weeks
No. given treatment 69 93
Excluded: 124 107
Disease history 84 74
Rx contraindication 11 10
Dead 17 18
Other 12 5
Ahlmark, Eur J Pharmac, Vol. 10, 1976
No Randomization
Response
No
Response
Response
Response
Chlorambucil
Chlorambucil
BCVP
BCVP
Induction and Maintenance Treatment for NonHodgkin’s LymphomaNonHodgkin’s Lymphoma Trial
CytoxanPrednisone
BCNUPrednisone
See Pocock, Clinical Trials: A Practical Approach, Page 72.
(A)
(B)
1 year of chemotherapy
OR
2 yearsof chemotherapy
Continue1 moreyear
1 yearof chemotherapy
Stop
Rivkin N, et al. J Clin Oncology, 11:17101716;1993.
“Eligible patients will be randomized in a 1:1 ratio to either the DC or VS group. Randomization will be stratified by clinical site. Randomization schedules will be constructed to ensure that approximately equal numbers of patients are assigned each treatment within clinical site.”
“Randomization was stratified by clinical site with the use of permuted blocks of random sizes.”
“Randomization was stratified by site, using randomly mixed permuted blocks of different sizes. Assignments were obtained by calling a central tollfree number”
3.Implementation (to ensure allocation concealment, sometimes called blinded randomization)
4. Theory behind randomization
Bradford Hill:
1. Eliminates bias from treatment assignment
2. Balances known and unknown differences between groups on average
3. More credible study
RA Fisher:
1. Assures validity of statistical tests (type 1 error)
Statistically Significant?
Yes
No
Reject
null hypothesis (HO)
Do not reject
HO
Sampling variationis an unlikelyexplanation for thediscrepancy
Sampling variationis a likelyexplanation for thediscrepancy
Population at Large
Definition ofCondition
Population withoutCondition
Population with Condition
Entry Criteria
With Conditionbut Ineligible
Study Population
Eligible butnot Enrolled
Enrollment
Study Sample
Source: Chapter 4, Friedman, Furberg and DeMets.
Population A
y ~ G(y  A)
Random Sample
nA patients
yAj ~ G(y  A)
Population B
y ~ G(y  B)
Random Sample
nB patients
yBj ~ G(y  B)
G is normal, i ~ N(i , 2)
Student’s ttest is most powerful test for testing Ho : A = B
N Population at LargeA patients
NB patients
Invoked Population Model – Randomization Model
Nonrandom Selection of Clinics in a Nonrandom Selection of Communities
Undefined Sampling Procedure for Patients(a variety of sources are used)
N = NA + NB patients
Randomization
Source: Lachin J. Cont Clin Trials, 1988.
1. Calculate test statistic for sample data, e.g., A  B difference, tstatistic
2. Determine the number of possible randomization sequences
3. Enumerate all of these permutations; calculate the test statistic for each and their cumulative distribution
4. Determine where the teststatistic for sample lies on distribution of all possible values
Treatment Group
A B
18 9
13 16
3 17
17 17
n 4 4
mean 12.75 14.75
(sd)2 46.92 14.92
pooled (sd)2 30.92
1 Population at Large
4
1
4
+
tstatistic with 6 degrees of freedom12.75  14.75
t(6) =
= 0.51, p = 0.628
30.92
The number of permutations using simple random allocation (1:1) of NA and NB assignments is given by:
(
)
NA + NB
NA
= (NA + NB)!/ NA ! NB!
NA = NB = 4 and number of permutations =70
Cumulative Distribution
t
Randomization
Students’ t(6)
2.48 1/70 .014 .024
2.15 4/70 .057 .038
1.88 5/70 .071 .055
1.45 8/70 .114 .097
1.26 12/70 .171 .127
1.09 15/70 .214 .159
.78 18/70 .257 .233
.64 22/70 .314 .273
.51* 25/70 .357* .314*
.25 28/70 .400 .405
.125 32/70 .457 .452
0.0 38/70 .543 .500
.125 42/70 .600 .548
.25 45/70 .643 .595
.51 48/70 .686 .686
.64 52/70 .743 .727
.78 55/70 .786 .767
1.09 58/70 .828 .841
1.26 62/70 .886 .873
1.45 65/70 .928 .901
1.88 66/70 .943 .945
2.15 69/70 .986 .962
2.48 70/70 1.000 .976
*
* sample value, 2sided pvalue 50/70 = 0.71 versus 0.63
Simple Randomization of 20 Patients
Outcome (Alive/Dead)
Treatment
Accession No.
1 A A
2 B D
3 A D
4 B D
5 B D
6 B D
7 A D
8 A A
9 B D
10 B D
11 A A
12 A A
13 B D
14 A A
15 A A
16 B D
17 A A
18 B A
19 B A
20 A A
Dead
Alive
A
B
Fisher’s exact test pvalue = 0.0115 (1tailed)
Dead Randomization and Students’ Distribution
Alive
A
8
2
B
2
8
Alive
Dead
A
9
1
B
1
9
Dead
Alive
A
10
0
B
0
10
Pvalue = Probability 2 or fewer of the 10 deaths were randomly allocated to A
or
or
P Randomization and Students’ Distribution

value
=
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9
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10
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Fisher’s Exact TestOutcome
(Alive/Dead)
Accession No.
Treatment
1 A A
2 B D
3 A D
4 B D
5 B D
6 B D
7 A D
8 A A
9 B D
10 B D
11 A A
12 A A
13 B D
14 A A
15 A A
16 B D
17 A A
18 B A
19 B A
20 A A
Randomization and Students’ Distribution
pvalue =
= 0.0069
1
2
1
2
1
6
1
6
1
Probability
Alive
Dead
A
1
1
Block 1
1
2
B
0
2
Dead
Alive
A
1
1
Block 2
1
2
B
0
2
Dead
Alive
A
2
0
Block 3
1
6
B
0
2
Alive
Dead
A
2
0
Block 4
1
6
B
0
2
Alive
Dead
A
2
0
Block 5
1
B
2
0
 Randomization and Students’ Distribution
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r
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Prob (r
alive
on
A)
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N
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General SetupAlive
Dead
A
n
r
n  r
(N  R) –
(n  r)
B
R  r
N  n
R
N  R
N
Based on hypergeometric distribution.