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

A brief introduction to randomisation

methods Peter T. DonnanPeter T. Donnan

Professor of Epidemiology and BiostatisticsProfessor of Epidemiology and Biostatistics

Treatment Allocation Treatment Allocation Methods OverviewMethods Overview

Fixed Methods:Simple

randomisationStratificationMinimisation

Adaptive Methods:Adaptive Methods:Urn randomisationUrn randomisationBiased Coin Biased Coin Play-the-winnerPlay-the-winner

Parallel-groupParallel-group

Randomised Controlled TrialRandomised Controlled Trial

RANDOMISED

Eligible subjects

Intervention

Control

RANDOMISED CONTROLLED RANDOMISED CONTROLLED TRIAL (RCT)TRIAL (RCT)

RandomRandom allocation to allocation to intervention or control so intervention or control so likely balance of all likely balance of all factors affecting outcomefactors affecting outcome

Hence any difference in Hence any difference in outcome ‘outcome ‘causedcaused’ by the ’ by the interventionintervention

Treatment Allocation Treatment Allocation MethodsMethods

Randomisation is main allocation method in scientific experimentsFirst proposed by Fisher (1935)‘‘The Design of Experiments’The Design of Experiments’

Two Properties :

1.Unbiased allocation2.Balances covariates, known and unknown

Treatment Allocation Treatment Allocation MethodsMethods

Properties required for unbiased and efficient treatment comparison:1. Equal distribution of known covariates2. Equal distribution of unknown, or unmeasured, covariates3. Balanced group size

Random allocation is the best means of ensuring equal distribution of unknown covariates

Random Allocation MethodsRandom 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

PROCESS OF PROCESS OF RANDOMISATIONRANDOMISATION

•Example - 5-digit Random numbers below

75792, 80169, 94071, 67970, 91577, 84334 03778, 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

RANDOMISATIONRANDOMISATIONPower 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

PROCESS OF PROCESS OF RANDOMISATIONRANDOMISATION

•Usually generate random numbers (statistical software or spreadsheet)

•Note that to be GCP–compliance requires:

1.Record of seed used to generate the random numbers so that list is replicable

2.Record of patient allocation

OUTCOME OF OUTCOME OF RANDOMISATIONRANDOMISATION

•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

Example of Parallel-group RCTExample of Parallel-group RCTSebag-Montefiore Sebag-Montefiore et al et al Lancet 2009; 373: 811-Lancet 2009; 373: 811-

820820•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

Random Allocation MethodsRandom Allocation Methods

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

Permuted BlocksPermuted Blocks

Guarantees balance in group size, at end of each block• Predictable, especially if block size known • Predictability depends on block size• Randomly vary block size• Start at random point in first block• Details in protocol? No!

AABABBBA BAABABBA BBAAABAB

n p

2 0.75

10 0.65

20 0.62

Stratified RandomisationStratified Randomisation

Randomise separately within each strata

• 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

Stratified Parallel-groupStratified Parallel-group

Randomised Controlled TrialRandomised Controlled Trial

Stratum

Eligible subjects

Active

Mild Moderate Severe

RANDOMISEDRANDOMISED

Control

ControlControl

Active Active

MinimisationMinimisationBalances a number of known prognostic factorsDeterministic case of Pocock-Simon (1975) methodStart 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 13 14

Total 26 30

MinimisationMinimisation

MinimisationMinimisationNext patient is female smoker thenGA = 1 x | 10-7 | + 1 x | 13-14 | = 4GB = 1 x | 9-8 | + 1 x |12-15 | = 4

ARM A ARM B

Smoker 9 7

Non-smoker 17 23

Male 14 16

Female 12 14

Total 26 30

Hence imbalance is equal so patient is allocated to treatment by chance pr=0.5

MinimisationMinimisationWhat happens if give more weight to smoking (2)?GA = 2 x | 10-7 | + 1 x | 13-14 | = 7GB = 2 x | 9-8 | + 1 x |12-15 | = 5

ARM A ARM B

Smoker 9 7

Non-smoker 17 23

Male 14 16

Female 12 14

Total 26 30

Hence patient is deterministically allocated to B

MinimisationMinimisation

• 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 will incorporate

minimisation• ICH-E9 recommends a random

element be added pr (0.7-0.8)

Treatment- or Response-Treatment- or Response-Adaptive RandomisationAdaptive Randomisation

Biased Coin RandomisationUrn randomisationPlay-The-WinnerPlay-The-Winner

Biased CoinBiased CoinAdaptive 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

Biased CoinBiased Coin

• Absolute difference generally usede.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 becomes more can become predictable

Urn RandomisationUrn Randomisation

More flexible Adaptive method is Urn RandomisationProbability 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

Urn RandomisationUrn Randomisation

Etc…..

Draw Allocation

Urn RandomisationUrn Randomisation

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

Other Adaptive Methods – Other Adaptive Methods –

Play-The-WinnerPlay-The-WinnerIf one treatment is clearly inferior over time, many patients getting the weaker drugZelen (1969) suggested classify each patient’s outcome as ‘success’ or ‘failure’Starts as simple randomisationIf patient ‘success’ then allocate same treatment to next patient.If patient ‘failure’ then allocate different treatment to next patient

Play-The-WinnerPlay-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 reachedBenefit to the patient is more patients get ‘successful’ treatment

Play-The-WinnerPlay-The-WinnerDrawbacks:Balance not an aim of method and imbalance can occurHigh susceptibility to selection biasRecent outcomes determine subsequent allocation and researcher can guess what next assignment will beRandomisation prob. changes over timeSo time trend in outcome confounds treatment effect and biases its estimateCan magnify early random differences

Optimal Biased CoinOptimal 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 computationAtkinson A.C, Statistics in Medicine, 1982

SummarySummary• 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

SummarySummary

• 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, 129-144 (1985)

RememberRemember

1.Primary goal of randomisation is to guarantee independence between treatment assignment and outcome

2.Any other goals are secondary (covariate balance, equal group sizes,…)

TCTU TCTU

• TCTU randomisation system provides simple, stratified and minimisation methods of randomisation