Outline ofRandomization Lectures

1. Background and definitions

2. Generation of schedules

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

4. Theory behind randomization

Randomization Schedule

A list showing the order in which

subjects are to be assigned to the

various treatment groups

Implementation Schemes1. Sealed envelopes

- Opaque- Sequentially numbered

2. Telephone- Answering service- Coordinating center- IVRS

3. Personal computers- Local- Through communication with coordinating center

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

5. Through electronic medical record for “point-of-care” or “clinically integrated” randomized trials.

Urokinase-Pulmonary Embolism Trial (UPET)

Circulation, 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

1. Assignments obtained by calling coordinating center after:a. Three screening visitsb. Informed consentc. Eligibility checklist

2. Sealed envelopes used as back-up

Treatment of MildHypertension 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

Community Programs for Clinical Research on AIDS (CPCRA)

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

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)

Controlled 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

IVIG Trial Randomization

Procedure summarizes data entered & asks you to re-enter weight

If randomization is successful, 3 documents are available

to save and print

Treatment Prescription

Double-check dose against your calculation on the Baseline CRF, and complete bottom portion

Timing of Randomization

Usual Sequence of Events

1. Verify eligibility, informed consent, and completeness of baseline data.

2. Obtain assignment.

3. Record assignment on log and case report forms.

4. Initiate treatment as soon as possible after randomization.

No. randomized 193 200

2 weeks

No. given treatment 69 93

Excluded: 124 107Disease history 84 74Rx contraindication 11 10Dead 17 18Other12 5

Alprenolol vs. Placebo in Post-MI

Alprenolol Placebo

Ahlmark, Eur J Pharmac, Vol. 10, 1976

Non-Hodgkin’s Lymphoma Trial

Induction and Maintenance Treatment for Non-Hodgkin’s Lymphoma

Cytoxan-Prednisone BCNU-Prednisone

BCVP Chlorambucil

ResponseNo

Response

BCVP Chlorambucil

ResponseNo

Response

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

Adjuvant Chemotherapy for Breast Cancer

1 yearof

chemotherapy

2 yearsof

chemotherapy

(A)

Stop Continue1 more

year

(B)

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

OR 1 year of chemotherapy

Recommendations

• 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

• 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

• 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: Strategies 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)

• 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 ofRandomization Lectures

1. Background and definitions

2. Generation of schedules

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

4. Theory behind randomization

Advantages of 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)

Fisher and the Validity of Statistical Tests (1)

• 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)

• 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

Statistically Significant?

Yes No

Rejectnull hypothesis (HO)

Do not rejectHO

Sampling variationis an unlikely

explanation for thediscrepancy

Sampling variationis a likely

explanation for thediscrepancy

Relationship of Study Sample to Study Population and Population at

LargePopulation at Large

Population withoutCondition

Population with Condition

With Conditionbut Ineligible

Study Population

Eligible butnot Enrolled

Study Sample

Source: Chapter 4, Friedman, Furberg and DeMets.

Definition ofCondition

Entry Criteria

Enrollment

Population Model as aBasis 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

G is normal, i ~ N(i , 2)

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

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

NA patients NB patients

Source: Lachin J. Cont Clin Trials, 1988.

Randomization Model Assumptions

• 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

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

Treatment GroupA 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

30.92

12.75 - 14.75 = -0.51, p = 0.628t(6) =

14

14

+

t-statistic with 6 degrees of freedom

The number of permutations using simple random allocation (1:1) of NA and NB

assignments is given by:

NA + NB

NA( )

NA = NB = 4 and number of permutations =70

= (NA + NB)!/ NA ! NB!

Cumulative Distribution of t-statistic Obtained from Randomization and Students’ Distribution

-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 .4520.0 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 .7671.09 58/70 .828 .8411.26 62/70 .886 .8731.45 65/70 .928 .9011.88 66/70 .943 .9452.15 69/70 .986 .9622.48 70/70 1.000 .976

Cumulative Distribution Randomization Students’ t(6) t

*

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

Impact on P-value of Ignoring Blocking in the Analysis

1 A A2 B D3 A D4 B D5 B D6 B D7 A D8 A A9 B D10 B D11 A A12 A A13 B D14 A A15 A A16 B D17 A A18 B A19 B A20 A A

Simple Randomization of 20 Patients

TreatmentOutcome

(Alive/Dead)Accession No.

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

8 2

2 8

A

B

Alive Dead

8 22 8

AB

Alive Dead

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

9 11 9

AB

Alive Dead

10 00 10

AB

Alive Dead

or

or

Fisher’s Exact Test P -value =

10

2

æ

è ç

ö

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8

æ

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20

10

æ

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+

10

1

æ

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9

æ

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20

10

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=.01096 +.00054125 +.00000541

=0.0115

Restricted Randomization (block size = 4)

1 A A2 B D3 A D4 B D

5 B D6 B D7 A D8 A A

9 B D10 B D11 A A12 A A

13 B D14 A A15 A A16 B D

17 A A18 B A19 B A20 A A

TreatmentOutcome

(Alive/Dead)Accession No.

1 1

0 2

A

B

Alive Dead Probability

Block 1

1 1

0 2

A

B

Alive Dead

Block 2

2 0

0 2

A

B

Alive Dead

Block 3

2 0

0 2

A

B

Alive Dead

Block 4

2 0

2 0

A

B

Alive Dead

Block 5

12

12

16

16

1

p-value = = 0.006912 1

2 16 1

6 1

General Setup

Based on hypergeometric distribution.

A

B

r

R - r

Alive

R

n - r

(N - R) –(n - r)

Dead

N - R

n

N - n

N

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öçè

æ

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n

Nrn

RN

r

R

A)on alive Prob (r

Randomization Theory Summary

• 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.