1. A brief introduction to randomisation methods
Peter T. Donnan
Professor of Epidemiology and Biostatistics

2. Treatment Allocation Methods Overview
Fixed Methods:
Simple randomisation
Stratification
Minimisation
Adaptive Methods:
Urn randomisation
Biased Coin
Play-the-winner

3. Randomised Controlled Trial
Parallel-group
Randomised Controlled Trial
Eligible subjects
RANDOMISED
Intervention
Control

4. RANDOMISED CONTROLLED TRIAL (RCT)
Random allocation to intervention or control so likely balance of all factors affecting outcome
Hence any difference in outcome ‘caused’ by the intervention

5. Treatment Allocation Methods
Randomisation is main allocation method in scientific experiments
First proposed by Fisher (1935)
‘The Design of Experiments’
Two Properties :
Unbiased allocation
Balances covariates, known and unknown

6. Treatment Allocation Methods
Properties required for unbiased and efficient treatment comparison:
1. Equal distribution of known covariates
2. Equal distribution of unknown, or unmeasured, covariates
3. Balanced group size
Random allocation is the best means of ensuring equal distribution of unknown covariates

7. Random Allocation Methods
Simple Randomisation – 0,1 computer generated list:
Coin toss pr (A) = 0.5
Least predictable method – can have long runs of same treatment
Risk of covariate imbalance especially with short sequences i.e. small trials

8. PROCESS OF RANDOMISATION
Example - 5-digit Random numbers below
75792, 80169, 94071, 67970, 91577, , 58563, 29068, 90047, 54870, 23327
With two treatments can be converted to:
A B B A B A
A B A B A B
Where last digit even = A and odd = B

9. RANDOMISATION Power of RCT is RANDOMISATION
Facilitates blind objective unbiased assessment of outcome – removes selection bias
But note not necessarily what the patient wants
Nor what the physician prefers
In a sense trial patients acting
altruistically

10. PROCESS OF RANDOMISATION
Usually generate random numbers (statistical software or spreadsheet)
Note that to be GCP–compliance requires:
Record of seed used to generate the random numbers so that list is replicable
Record of patient allocation

11. OUTCOME OF RANDOMISATION
Often just a randomised list ABBAAABB….
To ensure treatment balance use randomised blocks e.g. size 4 ABBA ABAB BAAB BABA
Electronic 24 hr telephone randomisation may be necessary or web-based
Usually provided by a trials unit

12. Example of Parallel-group RCT
Sebag-Montefiore et al Lancet 2009; 373:
Trial of short course preoperative radiotherapy vs. initial surgery with selective postoperative chemotherapy for operable rectal cancer (n=1350)
Reduction of 61% of risk of local recurrence with preoperative radiotherapy
HR = 0.39 (95% CI 0.27, 0.58)
Consistent evidence that short course preoperative radiotherapy is effective treatment for operable rectal cancer

13. Restricted Allocation Methods
Restricted methods improve balance but more predictable:
Permuted blocks – e.g BAAB ABAB ….
Stratification
Minimisation
Biased coin
Urn randomisation
Optimal biased coin

14. Permuted Blocks BAABABBA AABABBBA BBAAABAB
Guarantees balance in group size, at end of each block
• Predictable, especially if block size known
• Predictability depends on block size n
• Randomly vary block size
• Start at random point in first block
• Put details in protocol? No! n p 2
0.75 10
0.65 20
0.62

15. Stratified Randomisation
Randomise separately within each strata e.g. centre
• Each randomisation list should use restricted methods e.g. permuted blocks
• Ensures balance of known prognostic factors
• Limited to two or three factors, strata multiply
• ICH-E9 recommends stratification by centre
• Group small centres

16. Stratified Parallel-group Randomised Controlled Trial
Eligible subjects
Stratum
Mild
Moderate
Severe
RANDOMISED
Active
Control
Active
Control
Active
Control

17. Minimisation Balances a number of known prognostic factors
Deterministic case of Pocock-Simon (1975) method
Start with simple randomisation and after, say n=56 we end up with ……
ARM A
ARM B
Smoker 9 7
Non-smoker 17 23
Male 13 16
Female 14
Total 26 30

18. Minimisation

19. Minimisation Next patient is female smoker then
GA = 1 x | 10-7 | + 1 x | | = 4
GB = 1 x | | + 1 x | | = 4
ARM A
ARM B
Smoker 9 7
Non-smoker 17 23
Male 14 16
Female 12
Total 26 30
Hence imbalance is equal so patient is allocated to treatment by chance pr=0.5

20. Minimisation What happens if give more weight to smoking (2)?
GA = 2 x | 10-7 | + 1 x | | = 7
GB = 2 x | | + 1 x | | = 5
ARM A
ARM B
Smoker 9 7
Non-smoker 17 23
Male 14 16
Female 12
Total 26 30
Hence patient is deterministically allocated to B

21. Minimisation Dynamic – uses allocations and patient characteristics
Deterministic – predictability high in theory, low in practice?
Uses categorical covariates
Does require more complex programming
But ensures balance on known factors
TCTU system incorporates minimisation
ICH-E9 recommends a random element be added pr ( )

22. Treatment- or Response-Adaptive Randomisation
Biased Coin Randomisation
Urn randomisation
Play-The-Winner

23. Biased Coin
Adaptive technique, which is a modified version of flipping a coin
Start as simple randomisation, with an unbiased (fair) randomisation process (pr = 0.5)
If group size becomes unequal then the probability of treatment allocation changes to
FAVOUR THE SMALLER GROUP
Alter prob. so if arm A has nA < nB
Then pr(A) > 0.5
If arms are balanced then use equal
Prob i.e. 0.5

24. Biased Coin • Absolute difference generally used
e.g. if group size differs by >3, use ratio of 2:1 to favour smaller group
• `Big stick’ randomisation, force next patient into smaller group
• Improves balance but can become predictable

25. Urn Randomisation More flexible Adaptive method is Urn Randomisation
Probability of treatment assignment depends on the magnitude of imbalance
Start with two coloured balls in an urn
• Sample with replacement
• Add extra ball of opposite colour to the one selected each time

26. Urn Randomisation
Draw
Allocation
0 1
1 1
2 1
Etc…..

27. Urn Randomisation Improves balance at start of trial
• simple randomisation as trial progresses
• Effect depends on no. balls at start and no. balls added
e.g. start with 10 red, 10 blue for less effect, add more balls each time for greater effect
• Useful for smaller trials
In larger trials urn randomisation eventually behaves like complete simple randomisaton

28. Other Adaptive Methods –
Play-The-Winner
If one treatment is clearly inferior over time, many patients getting the weaker drug
Zelen (1969) suggested classify each patient’s outcome as ‘success’ or ‘failure’
Starts as simple randomisation
If patient ‘success’ then allocate same treatment to next patient.
If patient ‘failure’ then allocate different treatment to next patient

29. Play-The-Winner
Prob of patient’s allocation is unknown at start and depends on prob of ‘success’
Trial stops when fixed pre-specified number of ‘failures’ observed or predetermined sample size is reached
Benefit to the patient is more patients get ‘successful’ treatment

30. Play-The-Winner Drawbacks:
Balance not an aim of method and imbalance can occur
High susceptibility to selection bias
Recent outcomes determine subsequent allocation and researcher can guess what next assignment will be
Randomisation prob. changes over time
So time trend in outcome confounds treatment effect and biases its estimate
Can magnify early random differences

31. Optimal Biased Coin
Dynamic, uses allocations and patient characteristics
• Coin is biased so that next allocation minimises treatment effect variance , based on OLS regression model
• Continuous covariates
• Continuous outcome
• Non-deterministic
• Complex, matrix computation
Atkinson A.C, Statistics in Medicine, 1982

32. Summary
For large trials differences in methods have little effect so stick to simple randomisation
Methods described mainly for smaller trials
Permuted –block randomisation prone to selection bias – keeping these unknown reduces this potential
How much detail in protocol?
Omit size of blocks in protocol
Urn randomisation – use instead of blocks?
Urn randomisation reduces selection bias,
and protects against high imbalance better
than simple randomisation with small samples

33. Summary
Optimal biased coin – an alternative to minimisation but difficult to program – rarely used
Adaptive methods more complex to program and difficult to implement
Stratification factors – No evidence base for stratifying by many factors
Always stratify by centre? Probably
So fixed randomisation methods
generally preferable
Treatment allocation methods in clinical trials: a review.
Leslie A. Kalish and Colin B. Begg. Stats in Med, Vol.4, (1985)

34. Remember
Primary goal of randomisation is to guarantee independence between treatment assignment and outcome
Any other goals are secondary (covariate balance, equal group sizes,…)

35. TCTU randomisation system (TRuST) provides simple, stratified and minimisation methods of randomisation