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

Readings

• Chapter 6 of Friedman, Furberg and DeMets

• Supplemental notes for week 3 on the class web site

• Other papers are cited in the notes

Key Points

• A random process should be used to generate treatment allocations or assignments

• Treatment allocations should be concealed until the time of randomization – “allocation concealment” is critical to prevent selection bias. Some refer to this as “blinded randomization”. (It should not be confused with blinding of treatments).

Randomization

Assignment of experimental units to

treatment by a random process such that

neither investigator nor patient knows the

treatment to be assigned at the time the

patient is registered.

Timing of Randomized Trials - Considerations

• 1st patient (Chalmers)

• Strong degree of equipoise (collective and individual uncertainty) exists

• Feasibility and timing

See Freedman B N Engl J Med 1987.

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)

Are the Groups Comparable (Table 1 in trial reports)ESPRIT Study: Baseline Characteristics

(N Engl J Med 2009; 361: 1548-59)

IL-2 Control TotalAge (median years) 40 40 40

Female (%) 19% 19% 19%

Non-white race (%) 25% 24% 25%

Median CD4+ cells/mm3 (IQR) 464 450 457 (372, 584)

Nadir CD4+ cells/mm3 (IQR) 200 194 197 (91, 306)

HIV-RNA < 500 copies (%) 79% 80% 80%

Prior clinical AIDS (%) 25% 27% 26%

Years prior ART (IQR)

No. Randomized

4.1

2071

4.3

2040

4.2 (2.2, 6.4)

Steps in Patient (Study Participant) Registration (Randomization)

1. Patient requires treatment (participants screened for risk factor eligibility)

2. Patient (participant) eligible for inclusion in trial

3. Clinician willing to randomize patient (participant)

4. Patient (participant) is willing to be randomized (consent is obtained)

5. Patient (participant) formally entered in the trial– Treatment assignment obtained from randomization list

(schedule)– Case-report and other records completed to document

randomization

6. Treatment commences as soon as possible

Usual Sequence of Events in a Randomized Clinical Trial

Determine eligibility+

Obtain informed consent

yes no

randomize

A B

Not eligible

follow-up

+ In many trials consent mustalso be obtained for screening.

Eligible

Key Elementsof Informed Consent

• A fair explanation of the procedures to be followed, and their purposes, including identification of any procedures which are experimental

• A description of any participant discomforts and risks reasonably to be expected

• A description of any benefits to the subject or to others which may be expected

• A disclosure of any appropriate alternative procedures that might be advantageous for the subject

Key Elementsof Informed Consent (cont.)

• An offer to answer any inquiries concerning the procedures• Instructions to a subject concerning the freedom to withdraw

his/her consent and to discontinue participation in the project or activity at any time without prejudice or explanation (this should be balanced by a statement that emphasizes participation until the end of the study to preserve integrity of research question)

• Reasons study may be stopped• An explanation as to whether compensation and medical

treatment are available if physical injury occurs and, if so, what it consists of or where further information may be obtained

• A statement describing the extent, if any, to which confidentiality of records identifying the subject will be maintained

• A commitment to share new findings that emerge.

See also Chapter 2 of Friedman, Furberg and DeMets

Informed Consent (cont.)

• Length of sample informed consents:– ESPRIT (8 pages) (experimental treatment: interleukin-2)– SMART (12 pages) (treatment strategy trial using approved drugs)– START (14 pages) (treatment strategy trial using approved drugs)– MRFIT (1 page)

• Comprehension (when assessed) by participants is low on key items suggesting simpler, not longer, forms may be better.

• Separate consent documents for stored specimens and substudies

• Multiple reviews of consent: Institutional Review Board (IRB), Ethics Committee and sponsor

Bad Allocation Schemes1. Ward 1 receives Drug A; ward 2, Drug B

2. M, T, W - Drug A

TH, F - Drug B

3. Every other patient receives A

4. Drug A on odd days

5. Drug A to patients born Jan. - Jun.; Drug B, Jul. - Dec.

AVOID SYSTEMATIC ALLOCATIONALLOCATION CONCEALMENT (BLINDED

RANDOMIZATION IS CRITICAL

The Unit of Randomization is Not Always the Individual Study Participant

• Right and left eye

• Kidneys from deceased donors

• Clusters of participants– Clinical sites (e.g., interventions aimed at

adherence, informed consent, counseling to avoid high risk behaviors)

– Households– Schools– Communities

Cluster RandomizationJ Acquir Immune Defic Syndr 2006; 43 (Suppl):S41-S47

38 clusters of clinical sites

Randomized

MedicationManager

+Electronicreminder(N = 9)

MedicationManager

Alone(N = 10)

Electronicreminder

Alone(N = 10)

Control(N = 9)

• 200-250 patients/cluster• Embedded in treatment trial

Cluster Randomized Study of Short Versus Standard (Long) Consent

Form

150+ clusters of clinical sites

Randomized

Short consent form(N = 2,000)

Long consent form( N=2,000)

Embedded in START study

A similar design is being used to study of on-site monitoring: research on research!

Cluster Randomization Considerations

• It is important that the unit of randomization be taken into account both in the design and analysis (e.g., matched pairs).

• Like randomization of individual participants, allocation concealment (blinded randomization) is important.

• In some studies, individual consent is not required.• Observations/measurements on different participants

within clusters cannot be considered independent.• It is important to account for all members of the cluster in

the analysis (clusters are randomized but measurements are usually on individuals).

• The between-group (cluster) variability has to be accounted for in the analysis.

Example: Possible Biasin Treatment Assignment

Blinded randomization 57 14.0

Unblinded 45 26.7 randomization

Non-random assignment 43 58.1 or historical controls

Distribution of Prognostic Variables According to Treatment Assignment

No.Studies

At LeastOne Variable

Maldistributed* (%)

Source: Chalmers et al., NEJM, 1983.* p<.05

Treatment Resultsby Type of Assignment

Blinded randomization 8.8 0.003 ± 0.008

Unblinded 24.4 0.052 ± 0.016 randomization

Nonrandom assignment 58.1 0.105 ± 0.017 or historical controls

Percentp<0.05

Average TreatmentDifference

(Case-Fatality Rate)

Source: Chalmers et al., NEJM, 1983.

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

Categorization of Randomization Schemes

1. Fixed Allocationa. Simple randomizationb. Permuted block (restricted)c. Permuted blocks of different sizes randomly mixed (restricted)

2. Adaptive Allocation MethodsTreatments are assigned with probabilities which change during the course of the triala. Baseline adaptive procedureb. Response adaptive

Simple RandomizationThe number and order of patients receiving treatments A and B is determined by chance.

Example: Equal allocation

– Toss a coin: A = head, B = tails

– Random number table:A = odd, B = even(see next slide taken from Pocock, page 74)

– Uniform random number generator (equally probable numbers between 0.0 and 1.0):

A if < 0.5B if > 0.5

Produced by a process that gives results that can be viewed as a finite piece of a completely random series of numbers – roughly equal numbers of the digits 0-9..

Example: Non-uniform treatment allocation

British Aspirin Study2 treatments with allocation ratio 2:1 (Aspirin:no Aspirin)

Source: Br Med J, 296:313-16, 1988.

Treatment Random NumbersAspirin 1,2,3,4,5,6No Aspirin 7,8,9Don’t Use 0

Disadvantage of Simple Randomization

• Chance imbalance in numbers assigned to each treatment– At end of study– At periodic looks (e.g., interim analyses)

Could result in loss of power and logistical problems

Probability of Specified Treatment Allocations Using Simple Randomization

(10 Patients)

0 (10) 10 (0) 0.0021 (9) 9 (1) 0.022 (8) 8 (2) 0.093 (7) 7 (3) 0.234 (6) 6 (4) 0.41

5 5 0.25

Treatment A Treatment BBinomial

Probability

Binomial Probability

10 2: 8 1: 920 6: 14 4: 1650 18: 32 16: 34100 40: 60 37: 63200 86: 114 82: 118500 228: 272 221: 2791000469: 531 459: 541

Difference in Numbersor More Extreme

Prob. ≥ 0.05 Prob. ≥ 0.01Total Number

of Patients

To find N to obtain allocation ratio which results in a Prob ≥ 0.05

For large sample sizes can use normal approximation

Loss of Power Due to Chance Imbalance

Comparison of 2 Means

0.5 0.900.6 0.880.7 0.840.8 0.740.9 0.49

r Power

H0 : µA = µ B HA : µA ≠ µB ; µA - µB =

N = NA + NB and r = NA / N

Z 1- = - Z

Z 1- = - Z

1 1/2 Nr (1-r)

1 + 1 1/2 NA NB

1-/2

1-/2

1. Fixed Allocation Methods

Treatments are assigned with a pre-specified probability

A. Simple randomization

B. Permuted blocks

C. Permuted blocks randomly mixed

{Restricted

Permuted Block Randomization

1) Divide patients into blocks of equal size according to time they enter the study

2) Choose a block size

3) Write down all possible permutations

4) Randomly choose one

Advantages of Permuted Block Randomization

1. Forces balance at end of study and during patient accession

2. Reduces the likelihood of bias due to changing patient characteristics during course of study

3. Facilitates planning with regard to treatment administration (resource planning)

Disadvantages

1. If investigators become aware of block size (may be hard to mask in a non-blind study), some assignments are known within certainty,e.g., block size 4:

A A

The next assignments have to be B

2. From a theoretical point of view, analysis more cumbersome (more on this later)

Example: Permuted Block Randomization: Block Size = 4

Write down the 6 possible different sequences of 2As and 2Bs and randomly choose one for

the 1st 4 patients, next 4, etc.

1 2 3 4 5 6

A B A B A BA B B A B AB A A B B AB A B A A B

Unequal AllocationTo determine block size, consider the sum of the integers which define the allocation ratio:

Example: Mt. Sinai Hypertension Trial (MSHT); 3 treatment groups (K+, placebo, control) randomized 2:2:1

Use block size of 5 or multiples of 5

1. Generate all possible arrangements of numbers 1-5

2. Choose one at random

3. 1,2 = A; 3,4 = B; 5 = C

4. Repeat steps 2 and 3 as often as necessary

Randomly Mixed Permuted Blocks

A solution to the problem of easily guessing

future assignments (particularly important in

non-blind trials.

Example: The Multiple Risk Factor

Intervention Trial (MRFIT) used randomly

mixed block sizes of 2, 4 and 6.

Mixing Blocks of Sizes 2 and 4 Block Size 2 4

1 AB AABB2 BA BBAA3 – ABAB4 – BABA5 – ABBA6 – BAAB

Permutations

Two Step Procedure

1. Randomly choose block size

2. Randomly choose permutation within block size

Computer Program for Generating Random Permuted Blocks of Different

Size

1. Set number of treatments.

2. Set number of stratum.

3. Set block sizes to be used considering allocation ratio.

4. Randomly choose a block size (K).

5. Generate K uniform random numbers.

Computer Program for Generating Random Permuted Blocks of Different

Size (cont.)

6. Order the random numbers carrying along the original index (1-K).

7. Associate treatment codes with ordered index array.8. Print the K random assignments.9. Go to Step 4 and continue until desired number of

allocations have been generated.

Other Variations

• Mix block sizes with different probabilities. For example,

• Flip a coin for 1st assignment and mix block sizes afterwards

• Use a large block size initially (e.g., >8) and then smaller block sizes (e.g., mix 2, 4, and 6)

Block size Prob2 1/44 1/46 1/2

Baseline Adaptive Randomization Procedure

Def.: The probability of the next treatment assignment is altered on the basis of the previous assignments in order to achieve better balance (biased coin).

Considerations:1. Implementation (central)2. Multiple treatments3. Definition of lack of balance

Let D = No. of patients assigned to A - No. assigned to B

D = 0 Simple randomization (P = 1/2)

D > 0 Assign to B with prob. (P) > 1/2

D < 0 Assign to B with prob. (1 - P) < 1/2

What should P be set equal to?

Note P = 1 corresponds to permuted blocks of size 2.

Example Baseline Adaptive Randomization

• 20 patients are to be randomized, 1:1 allocation. After 10 patients, we have:– 5A and 5B (D=0): use schedule with 1:1

allocation (e.g., created with simple randomization)

– A is assigned– 6A and 5B (D=1): use schedule with Prob (B) =

2/3 (could also be created with simple randomization)

– B is assigned– 6A and 6B (D=0): continue as above

This could be implemented by preparing 3 schedules in advance: 1) 1:1 allocation; 2) 2:1 allocation favoring B; and 3) 1:2 allocation Favoring A. All could be prepared with simple randomization.

Suppose there are k treatments:

1) Rank treatments according to number of patients (fewest to largest);

2) Assign next patient with probability

k

1=i1ip wherekp...2p1p

Response AdaptiveRandomization

The probability of the next treatment assignment is altered on

the basis of the responses of previous patients enrolled.

Motivation: More patients receive the “best” treatment

Rosenberger, Cont Clinical Trials, 1999;20:328-342.

Play the Winner Rule

• Assign 1st patient to either treatment with probability ½.

• An observed success generates a future trial using the successful treatment on the next patient

• A failure generates a future trial on the alternative treatment

Zelen, 1969 JASA

1 A S

2 A S

3 A F

4 B S

5 B F

6 A S

7 A S

8 A S

Play the Winner RulePatient

Accession No. TreatmentSuccess/Failure

Some Problems Are Apparent

• Not a randomized design

• Selection bias - investigator knows next assignment

• Outcome may not be known when the next patient is enrolled

RandomizedPlay the Winner Rule

• Start MA and MB balls in urn (e.g., MA = MB for equal probability of A or B.

• Draw a ball for each assignment and replace it• Success on A: Add balls of Type A and balls of Type B• Success on B: Add balls of Type B and balls of Type A• Failure on A: Add balls of Type A and balls of Type B• Failure on B: Add balls of Type B and balls of Type A• > less randomization (e.g., = 1 and 0) • = simple randomization

Wei and Durham, 1978 JASA

Conditions Under Which the RPW Rule is Reasonable

• The therapies have been evaluated previously for toxicity• Response is binary• Delay in response is moderate, allowing adapting to take place• Sample sizes are moderate (at least 50 subjects)• Duration of the trial is limited and recruitment can take place during

the entire trial• The trial is carefully planned with extensive computations done

under different models and initial urn compositions• The experimental therapy is expected to have significant benefits

to public health if it proves effective

See Rosenberger, Cont Clinical Trials, 1999;20:328-342.

Extracorporeal Membrane Oxygenation(ECMO Trials)

• Used RPW with MA = MB = 1; = 1; and 0.

• Total 12 patients – 11 given ECMO (A balls) and all survived; 1 given control (B balls) and died (1st patient received ECMO and survived; the 2nd control and died; all subsequent patients received ECMO) (Pediatrics 1985; 76:479-87)

• Two other trials followed:– A trial done in Boston that used 1:1 randomization until 4 deaths on

an arm (phase 1); in phase 2, all patients assigned successful treatment until 4 deaths or significant result. Combined phase 1 and 2 results were 1/29 deaths on ECMO and 4/10 deaths on control (Pediatrics 1989; 84:957-63).

– A conventional trial in the UK done (30/93 deaths on ECMO and 54/92 on control after one year) (Pediatrics 1998; 101:1-10).

Other Considerations in Using a Response Adaptive Randomization

Scheme1. Multiple endpoints

2. Changing patient characteristics

3. Implementation, timing of response

4. Ethical concerns of investigators, e.g., suppose allocation probability for treatment decreases from 1/2 to 1/10

5. More difficult to describe; less acceptable (credible) to others

6. Most useful for large differences

Adaptive Designs in Clinical Trials

• Currently, research on adaptive designs, defined as modifications to trials procedures and/or statistical methods during the conduct of a study, is a hot area.

• Play-the-winner is probably the earliest type of adaptive design

• The term “adaptive design” is used very broadly and includes:– Covariate adaptive randomization (e.g., minimization)– Sample size re-estimation– Group sequential designs– Drop-the-loser designs– Adaptive dose-finding– “Switchover designs” or dynamic treatment regimes– Phase II/III seamless designs

Requirements for Sound Treatment Allocation Scheme According to Meinert

1. Assignment remains masked to the patient, physician and all other clinic personnel until it is needed for initiation of treatment.

2. Future assignments cannot be predicted from past assignments.

3. Order of allocation is reproducible.

4. Methods for generation and administration of schedules are documented.

5. Process used for generation has known mathematical properties.

6. Process provides a clear audit trail.

7. Departures from the established sequence of assignments can be detected.

Reference: Meinert, Chapter 8

Key Requirements of a Randomization Schedule

1. Unpredictability (allocation concealment)

2. Approximate balance (desired allocation ratio) within strata

3. Extendability …

4. Well documented; reproducible

Why Paranoid – Mistakes Are Embarrassing!

• Herpes simplex vaccine trial (N Engl J Med 2012): “…owing to a programming error, the initial subjects were randomized at a 3:1 ratio in favor of the HSV-vaccine group.” (Instead of 1:1; N’s 4,577 vs 3,746)

• HIV trial (Arch Int Med 1995): “…an error occurred in the randomization program. This error resulted in a nonrandom excess of patients assigned to the zidovudine arm…” (Analysis restricted to 617 instead of 830 patients)

• Anemia trial (AJKD 2002): no mention of error in trial report. In FDA Medical Officer review, it is noted that sponsor reported to FDA in 1999 that allocation ratio of 2:1 darbepoetin alpha vs epoetin had been reversed.

•

Preparation of Randomization Schedules: Typical Situation

• Schedules are prepared in advance and kept in a safe place (e.g., secured computer files)

• Block randomization used to ensure desired allocation ratio

• Procedure should not permit investigators to determine treatment assignments in advance (randomly mixed permuted blocks) (less of an issue in double-blind studies)

• Separate schedules prepared for different treatment sites (clinics) and strata (more on this later)

• Entire procedure should be documented in writing and audited