1. Why to Randomize a Randomized Controlled Trial? (and how to do it) John Matthews University of Newcastle upon Tyne

2. Schema of a simple trial Eligible patients Rx group 1 Rx group 2 Randomize

3. 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

4. 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

5. 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.

6. 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

7. What is wrong with non- randomized studies? Two main types of study, those with and those without concurrent control groups

8. 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

9. 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

10. 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

11. 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

12. Is coin tossing OK? OK for big trials For small trials, such ‘simple randomization’ can lead to imbalance in group sizes

13. 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

14. 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

15. Random Permuted Blocks An allocation sequence is, e.g., A,B,A,A,A,A,B,B,B,A i.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

16. RPBs II All sequences of length 4 comprising 2 As and 2 Bs are 1. AABB 2. ABAB 3. ABBA 4. 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 of BAAB BABA ABAB BAAB

17. 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)

18. 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

19. 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

20. 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

21. 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.

22. 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

23. 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

24. 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