Why to Randomize a Randomized Controlled Trial?

(and how to do it)John Matthews

University of Newcastle upon Tyne

Schema of a simple trial

Eligible patients

Rx group 1

Rx group 2

Randomize

Outline of talk

• Many aspects to a trial: this talk focuses on just two

• Why you should randomize– benefits of doing so– dangers of failing to do so

• How to randomize– often glossed over & unspecified

Why Randomize?

• Compare groups at the end of the trial

• Difference is because of the Rx

• For this you need comparable groups

• Purpose of randomization is to make the treatment groups comparable

• Ensures that only difference in groups is due to trial treatments

How does it do it?

• Each group is a random sample of eligible patients, so both are representative of that same population

• In this sense they are comparable– same proportions of males, stage IV tumours,

ambulant cases, elderly patients etc.

• Anything which subsequently changes the groups will destroy this balance.

Why Randomize?

• Other benefits are– Randomization is largely unpredictable

• Why this is a good thing and why it might not obtain will emerge in the talk

– Randomization provides a valid basis for statistical inference

• This is important but is not addressed at all in this talk

What is wrong with non-randomized studies?

• Two main types of study, those with and those without concurrent control groups

Non-randomized studies II

• Without concurrent controls– Uncontrolled

• cannot really make much of such studies if there is any variation in outcomes.

– Historical controls • type of patient may change, due to eligibility criteria

• environment changes, due to trial

• data quality often quite different between groups

Non-randomized studies III

• Non-randomized concurrent controls– Alternation

– Odd/Even hospital no. or date of birth

– First letter of surname

• Difficult to argue that one group is different from another but allocation is predictable, so bias can arise from selection of patients: see Keirse (1988)– so randomization must be unpredictable

Features of a RCT

• Provide reliable evidence of Rx efficacy

• Essentially simple

• Much attendant methodology– ensure reliability of evidence– give credibility to results

• CONSORT statements www.consort-statement.org

indicate good practice in trial reporting

How to Randomize

• Toss a coin

• Essentially the right thing to do

• Try not to do it in front of the patient

• More sophisticated implementations possible

Is coin tossing OK?

• OK for big trials

• For small trials, such ‘simple randomization’ can lead to imbalance in group sizes

Example: trial with 30 patients

• If 30 patients are in a trial randomized using coin tossing there is a 14% chance of 15:15 split

• For 16:14 chance is 27%

• ‘Worse’ than 20:10 is 10%

• Why ‘worse’?

• Because imbalance leads to loss of power

Alternatives

• Could use a restricted randomization scheme– legitimate, intended to protect power– but often not mentioned in trial report: see Altman

& Doré, 1990; Schulz et al., 1994

• Needs to be done properly

• Only ensures similar numbers in groups

• Combine with stratification to ensure comparability for prognostic factors

Random Permuted Blocks

• An allocation sequence is, e.g.,A,B,A,A,A,A,B,B,B,Ai.e. 6 As, 4 Bs

• This sequence built up by using a computer to ‘toss a coin’

• Random Permuted Blocks (RPBs) is an alternative method which ensures imbalance can never be substantial

RPBs II

• All sequences of length 4 comprising 2 As and 2 Bs are1. AABB 2. ABAB 3. ABBA4. BBAA 5. BABA 6. BAAB

• Generate random sequence of numbers 1 to 6, say 6,5,2,6,… and substitute from above to give allocation sequence ofBAAB BABA ABAB BAAB

RPBs III

• Such sequences cannot be more than two out of balance

• Must be in exact balance after 4, 8, 12, etc. patients have been recruited

• So RPBs are, to some extent, predictable

• To avoid this, vary block length at random: use blocks of length six (3t) as well as 4 (2t)

Is it enough to equalise numbers?

• No, can still have imbalance in important prognostic factors– E.g. two groups of size 15: one comprises 14

young children and the other comprises 14 adolescents in a trial for diabetes

• Stratify recruitment with respect to age– i.e. use separate allocation sequence within

each stratum

Stratification

• RPBs can be used without stratification

• Stratification without using RPB (or an

equivalent device) is nonsensical

• Separate allocation sequence in each stratum can become cumbersome with many prognostic factors

• e.g. ambulant/not, over/under 55, M/F gives 8 allocation sequences

Minimisation

• More complicated, in principle• ensures balance on each factor separately, not for all

combinations

• keeps track of patients already in trial, computes an imbalance score and allocates to minimise this

• can include a random element

• Less cumbersome, in practice• largely because you need a computer

• Good if there are many prognostic factors

How to serve it all up

• Methods for delivering randomisation sequences to the clinic are important.

• They hold the key to ensuring adequate concealment of the allocation until the patient has been randomized.

Implementation methods

• Need to separate the person who generates allocation from those who assess eligibility

• Third party schemes• Telephone randomization service

• Pharmacy randomization

• Web-based service?

• Envelopes• Serially numbered, sealed and opaque

Then what?

• You will have two groups that are comparable and free from bias

• Well, sort of

• You have the best start, certainly

• Drop-outs, protocol violations etc. etc. disturb the comparability

• Might not have been comparable to start with!

• Need to allow for baseline imbalance and stratifying variables

Conclusion

• Randomization is needed in all clinical trials

• As with most aspects of trial design, the details of how you randomize are important

• The analysis needs to respect the design (esp. stratification) and make sensible adjustment for baselines

• All looking more awkward if there isn’t a statistician involved.

• Some details given at

www.mas.ncl.ac.uk/~njnsm/talks/titles.htm