Introduction to Response Adaptive Randomization (RAR)

Author: Genpro Biostatistics Team

Randomization have proven to be an efficient way of reducing bias and thus is widely used in clinical trials. Randomization ensures that subject allocation is balanced across treatment group and is not influenced by external forces and thus provides equal chances for subjects to receive the treatment of interest as they are to receive the comparator treatment. But the balanced allocation across treatments may also mean exposing subjects to ineffective or less beneficial treatment. Especially in trials with large sample size or when study focuses on some rare condition or disease, this can lead to large proportion of the population of interests taking the ineffective (less effective) treatment.

Most often the patient participation itself is in the hope of getting treated by an evolving new treatment. In recent years Adaptive Designs, particularly Adaptive randomization techniques have gained popularity as it enables clinicians to assign more patients to treatment arms with superior outcomes by using outcome data from participants already in the trial. Adaptive Randomization techniques are promoted by regulatory authorities like FDA because of its flexibility that allows assigning fewer patients to treatment arms with inferior outcomes.

The research objective of the clinical trials can have a conflicting nature. Treatment allocation for discriminating the effects of various treatments and thus bringing an effective treatment to the market for the population of interest and number of patients exposed to ineffective treatment can both be of concern in a clinical trial. Response Adaptive Randomization is one way to help with this conflicting research aims.

In trials using RAR, treatment allocation is adjusted based on the accumulating data while the study is ongoing, using a predetermined defined set of rules. This allows more patients being assigned to the effective treatment once proven efficient based on the available data. There is little evidence to support this design in trials with restricted time frame and small samples.


Consider a trial with two treatments T1 and T2. Enrolment takes place sequentially with each enrolment including Ni {i = 1, 2, 3…} subjects into the trial. Since the effectiveness of the treatments are unknown at the beginning of the trial, the initial treatment allocation sets an equal probability (0.5) to both the treatments. The allocation probability continues to be equal until a significant response if observed and clinically proven for one among T1 and T2. Let P1 be the response rate of T1 and P2 be the response rate of T2.

Fix the maximum total number and number of subjects to each treatment group to be enrolled in the study.

The first N1 patients are equally allocated to the two treatments and observed for the response rate Yk (k=1, 2). With pk ~ beta(αk, βk ). if, among nk subjects treated in arm Tk, we observe yk responses, then

Yk ~binomial(nk,pk)

and the posterior distribution of pk  is,

pk|data  ~beta(αk+xk,βk+nk-xk)

During the trail, the Bayesian posterior distribution of pk is continuously updated, and the next Ni  patients are allocated to the kth treatment arm according to the posterior probability that treatment Tk is superior to all other treatment arms.

Πk =Pr(pk=max{pl,1≤l≤K}|data)

  • Futility: if Pr (pk < p. min | data) > θu, where p. min denotes the clinical minimum response rate, that is, there is strong evidence that treatment Tk is inferior to the clinical minimum response rate, we drop treatment arm Tk.
  • Superiority: if Pr(pk > p. target | data) > θl, where p. target denotes the target response rate, that is, there is strong evidence that treatment Tk is superior to prespecified response rate, we terminate the trial early and claim the treatment Tk is promising.

If Pr (pk > p.min | data) > θt, then treatment Tk is selected as the superior treatment. Otherwise, the trial is inconclusive. θu, θl , and θt are pre-specified cut-off points.

Once the superior treatment is identified over time in the trial, the treatment allocation can be adjusted in such a way that more patients benefit from the effective treatment.

RAR is the randomization procedure that uses patient responses from past treatment assignments to select the probability of future treatment assignments, with the objective to maximize power and minimize expected treatment failures. RAR is not applicable in trials with limited recruitment period and outcomes that occur after all patients have been randomized. Delayed responses can also limit the use of this technique. Covariate-adjusted response-adaptive randomization there can be a used in trials in which patient characteristics changes over time and has the potential to influence the outcomes.

Patient will be more interested in joining trials implementing RAR as the possibility of receiving effective treatment is higher compared to usual Randomized clinical trials.

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