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Group 1 Discussion Topic Thursday, 7 February. When should a clinical trial with pre-stratification 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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Group 1 discussion topic thursday 7 february

Group 1 Discussion TopicThursday, 7 February

When should a clinical trial with pre-stratification be used?


Outline of randomization lectures
Outline ofRandomization Lectures

  • Background and definitions

  • Generation of schedules

    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

A list showing the order in which subjects are to be assigned to the various treatment groups

Randomization Schedule


Implementation schemes
Implementation Schemes assigned to the various treatment groups

1. Sealed envelopes

- Opaque

- Sequentially numbered

2. Telephone

- Answering service

- Coordinating center

- IVRS

3. Personal computers

- Local

- Through communication with coordinating center

  • International coordinating centers in HIV treatment trials use web-based system


Urokinase pulmonary embolism trial upet circulation 1973
Urokinase-Pulmonary Embolism Trial (UPET) assigned to the various treatment groupsCirculation, 1973

1. Telephone answering service in New York City; 24-hour coverage

2. Assignments obtained through hospital pharmacy

3. Sealed envelopes as back-up


Multiple risk factor intervention trial mrfit jama 1982
Multiple Risk Factor Intervention Trial (MRFIT) assigned to the various treatment groupsJAMA, 1982

1. Assignments obtained by calling coordinating center after:

a. Three screening visits

b. Informed consent

c. Eligibility checklist

2. Sealed envelopes used as back-up


Group 1 discussion topic thursday 7 february

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 back-up

3. Unique bottle no. for each participant

4. Bottle no. not assigned in sequence

Amer J Cardiol, 1987


Group 1 discussion topic thursday 7 february

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


Group 1 discussion topic thursday 7 february

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)


Group 1 discussion topic thursday 7 february

C assigned to the various treatment groupsontrolled Onset Verapamil Investigation of Cardiovascular Endpoints (CONVINCE)

  • Interactive Voice Response System (IVRS)

    • Touch-tone keypad used for data entry of key eligibility data

    • System verifies eligibility and assigns medication code (bottle number)

    • Caller re-enters medication code as a double-check

    • System also used for medication refills


Survey of 15 major cancer centers for methods of randomization
Survey of 15 Major Cancer Centers for Methods of Randomization

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


Timing of randomization usual sequence of events
Timing of Randomization RandomizationUsual Sequence of Events

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.


Alprenolol vs placebo in post mi
Alprenolol vs. Placebo in Post-MI 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


Induction and maintenance treatment for non hodgkin s lymphoma

No Randomization

Response

No

Response

Response

Response

Chlorambucil

Chlorambucil

BCVP

BCVP

Induction and Maintenance Treatment for Non-Hodgkin’s Lymphoma

Non-Hodgkin’s Lymphoma Trial

Cytoxan-Prednisone

BCNU-Prednisone

See Pocock, Clinical Trials: A Practical Approach, Page 72.


Adjuvant chemotherapy for breast cancer
Adjuvant Chemotherapy for Breast Cancer Randomization

(A)

(B)

1 year of chemotherapy

OR

2 yearsof chemotherapy

Continue1 moreyear

1 yearof chemotherapy

Stop

Rivkin N, et al. J Clin Oncology, 11:1710-1716;1993.


Recommendations
Recommendations Randomization

  • Make assignments close to the onset of treatment from a central source after checking eligibility

  • Implement the randomization with a method that ensures allocation concealment

  • Never deviate from the schedule

  • Verify assignments


Examples of problems with allocations concealment
Examples of Problems with Allocations Concealment Randomization

  • Hypertension Detection and Follow-up Program (HDFP) – a single site (envelopes that were opened in advance)

  • Heparin for acute MI (N Engl J Med 1960) – (envelopes not opaque or consecutively numbered)

  • Captopril for hypertension (Lancet 1999) (large baseline differences indicating envelopes opened in advance)


Documentation and reporting of randomization methods
Documentation and Reporting of Randomization Methods Randomization

  • Document methods for generating schedules, but do not share details with the investigators

  • Describe allocation ratio and stratification variables in the protocol

  • Report how randomization was done in the trial report


Example s trategies for m anagement of a nti r etroviral t herapy smart study
Example: RandomizationStrategies for Management of AntiRetroviral Therapy (SMART) Study

  • Protocol:

    “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.”

  • Trial Report (N Engl J Med 2006; 355:2283-96):

    “Randomization was stratified by clinical site with the use of permuted blocks of random sizes.”


Reporting example that includes method of implementation hiv trial in south africa phidisa ii
Reporting Example That Includes Method of Implementation: HIV Trial in South Africa (Phidisa II)

  • Trial Report (JID 2010; 202:1529-1537):

    “Randomization was stratified by site, using randomly mixed permuted blocks of different sizes. Assignments were obtained by calling a central toll-free number”


Outline of randomization lectures1
Outline of HIV Trial in South Africa (Phidisa II)Randomization Lectures

  • Background and definitions

  • Generation of schedules

    3.Implementation (to ensure allocation concealment, sometimes called blinded randomization)

    4. Theory behind randomization


Advantages of randomization
Advantages of Randomization HIV Trial in South Africa (Phidisa II)

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)


Fisher and the validity of statistical tests 1
Fisher and the Validity of Statistical Tests (1) HIV Trial in South Africa (Phidisa II)

  • Randomization guarantees that statistical tests will have the valid significance levels.

  • Even though groups may not be exactly balanced with respect to covariates, randomization permits a probability distribution to be determined for comparing treatments for outcomes of interest


Fisher and the validity of statistical tests 2
Fisher and the Validity of Statistical Tests (2) HIV Trial in South Africa (Phidisa II)

  • Randomization provides a basis for an assumption free statistical test of the equality of treatments – need to analyze your data taking into account the way the randomization schedule was prepared.

  • Such tests are referred to as randomization tests or permutation tests


Test of significance at the end of a trial
Test of Significance HIV Trial in South Africa (Phidisa II)at the End of a Trial

Statistically Significant?

Yes

No

Reject

null hypothesis (HO)

Do not reject

HO

Sampling variationis an unlikelyexplanation for thediscrepancy

Sampling variationis a likelyexplanation for thediscrepancy


Relationship of study sample to study population and population at large
Relationship of Study Sample to Study Population and Population at Large

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 model as a basis for statistical testing
Population Model as a Population at LargeBasis for Statistical Testing

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)


Example
Example Population at Large

G is normal, i ~ N(i , 2)

Student’s t-test is most powerful test for testing Ho : A = B


Group 1 discussion topic thursday 7 february

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.


Randomization model assumptions
Randomization Model Assumptions Population at Large

  • Under HO responses are assumed to be fixed (non-random) values – each patient’s response is what it would have been regardless of treatment A or B

  • The observed difference between A and B only depends on the way treatments were assigned (independent of other patient characteristics)

  • To assess whether observed difference is “unusual”, consider all possible ways patients could have been assigned A or B (permutation test)

  • Under simple randomization, permutation test is asymptotically equal to homogenous population model.


Randomization or permutation test
Randomization or Permutation Test Population at Large

1. Calculate test statistic for sample data, e.g., A - B difference, t-statistic

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 test-statistic for sample lies on distribution of all possible values


Example 3 eight experimental units are randomly allocated to receive treatment a or b
Example 3 Population at Large: Eight experimental units are randomly allocated to receive treatment A or B

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


T statistic with 6 degrees of freedom

1 Population at Large

4

1

4

+

t-statistic with 6 degrees of freedom

12.75 - 14.75

t(6) =

= -0.51, p = 0.628

30.92


Group 1 discussion topic thursday 7 february

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 of t statistic obtained from randomization and students distribution
Cumulative Distribution of t-statistic Obtained from Randomization and Students’ Distribution

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, 2-sided p-value 50/70 = 0.71 versus 0.63


Impact on p value of ignoring blocking in the analysis
Impact on P-value of Ignoring Blocking in the Analysis Randomization and Students’ Distribution

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

  • 2

  • 2 8

B

Fisher’s exact test p-value = 0.0115 (1-tailed)


Group 1 discussion topic thursday 7 february

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

P-value = Probability 2 or fewer of the 10 deaths were randomly allocated to A

or

or


Fisher s exact test

P Randomization and Students’ Distribution

-

value

=

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=

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Fisher’s Exact Test


Restricted randomization block size 4
Restricted Randomization (block size = 4) Randomization and Students’ Distribution

Outcome

(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


Group 1 discussion topic thursday 7 february

Randomization and Students’ Distribution

p-value =

= 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


General setup

- Randomization and Students’ Distribution

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N

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Prob (r

alive

on

A)

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N

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General Setup

Alive

Dead

A

n

r

n - r

(N - R) –

(n - r)

B

R - r

N - n

R

N - R

N

Based on hypergeometric distribution.


Randomization theory summary
Randomization Theory Summary Randomization and Students’ Distribution

  • Guarantees control of type I error in hypothesis tests

  • Permutation or randomization tests are motivated by the random assignment of patients

  • The more restrictions imposed on the randomization, the harder it is to determine the permutation distribution.

  • Permutation tests are not routinely used in the analysis of trials (conservative). Can be useful to consider blocking if population is heterogeneous over time.