1. Re-randomising patients within clinical trials
Tim Morris
MRC Clinical Trials Unit at UCL
14 May 2018 | International Clinical Trials Day

2. Re-randomisation design
Definition: Patients who have previously participated may be re-entered into a trial. Number of periods in the trial is determined by patient.

4. Re-randomisation design
Three requirements:
Can re-randomise only when follow-up for a previous period is complete
Randomisation within patient as well as across patients (no requirement to stick or switch from previous period)
Treatment effect is ~constant across periods

5. R1. Complete follow-up before re-randomisation
Outcomes need to be measurable within a relatively short time frame. Implications for time-to-event outcomes. Time to death precludes re-randomisation (unless you are happy to randomise the deceased and follow up for death).

6. R1. Randomise within patient
In cluster randomised trials we have to account for cluster in the analysis to get a valid estimate of variance. Failure to do so → problems with coverage / type I error. In crossover trials we have to account for patient in the analysis to get a valid estimate of variance.

7. R1. Randomise within patient
Cluster randomised → Not cluster randomised – ignoring clusters in the analysis would not lead to problems with coverage, but ↑ standard error. Crossover → Not crossover – ignoring patient effect in the analysis does not lead to coverage / type I error problems, but ↑ standard error. Moral: Randomisation structure introduces problems with coverage / type I error rates; it is not the clustering of outcomes itself.

8. R1. Randomise within patient
Trials tend to involve patients participating once or perhaps a predefined number of times (crossover trial). Why not randomise once, twice, thrice… according to patients’ needs, but don’t force patients to stick with their original treatment or switch from it at second period? Randomise within patient as well as across patients. The analysis can treat observations as independent and (effectively) we have a parallel group trial. If enough are re-randomised we may account for patient effects e.g. via a mixed model.

9. R3. Treatment effect constant across periods
Requirement 3 assumes the effect of treatment is common over randomisations. This is untestable until the analysis.
Should only be considered for interventions where the assumption is reasonable.
Bad idea for educational interventions (unless the condition involves memory loss).
Would results of a trial be generalised to offering treatment repeatedly in practice?

10. Re-randomisation design (recap)
Allow patients who have previously participated to be re-entered into trials, with three requirements:
Cannot re-randomise until follow-up for a previous period is complete
Randomisation within patient as well as across patients (no requirement to stick or switch from previous period)
Treatment effect is constant across periods
Have maths and simulation results show statistical properties are good even when patients behave inconveniently (e.g. more likely to return when they have certain outcomes).

11. Re-randomisation in practice
Several trials have reasons to do this:
Reason
Trial
Unethical not to when we are in equipoise
Attire trial
Many of our eligible patients are returners and we need numbers
N-alive
Can’t identify whether someone has already participated at enrolment
Empire trial

12. Issues / questions
Generalisability – loss or gain? Becomes important in presence of ‘informative cluster size’?
No Bayesian justification (could there be for original design?)
Can we exploit clustering within patients to ↓ standard error, instead of saying, ‘it’s perfectly safe to ignore it in the analysis’? (more Bayesianly justifiable)
How do patients feel about the design compared to a single randomisation? Would they feel cheated if randomised to control two or three times? What is the best model of consent?

13. References
Kahan BC, Forbes AB, Doré CJ, Morris TP. A re-randomisation design for clinical trials. BMC Medical Research Methodology. 2015; 15(1):96+
Parzen M, Lipsitz SR, Dear KBG. Does clustering affect the usual test statistics of no treatment effect in a randomized clinical trial? Biometrical Journal. 1998; 40(4):385–402.
Kahan BC, Morris TP. Assessing potential sources of clustering in individually randomised trials. BMC Medical Research Methodology. 2013; 13(1):58+.
Kahan BC, Morris TP, Harris E, Pearse R, Hooper R, Eldridge S. Re-randomization increased recruitment and provided similar treatment estimates as parallel designs in trials of febrile neutropenia. Journal of Clinical Epidemiology. 2018; 97:14–19