Randomisation protocols

Minimisation, random permuted blocks, biased coin?

There seems to be a bewildering array of methods for simply determining which of two treatments a patient will receive. Why is this?

The reason is that an imbalance in patient numbers or characteristics can arise by chance if you simply toss a coin or throw dice to decide treatment allocation. Smaller trials are particularly prone to imbalance leading to the possibility that the treatment effect is partly due to one group being "healthier" than the other (for instance one group might be younger on average than the other).

Many methods have been developed to reduce the chance of imbalance between treatment groups. These work either by stratification combined with blocking or by making it more likely that a patient with a particular characteristic is allocated to the group in which this characteristic is under-represented at the time of randomisation. For instance a younger patient is more likely to be randomised to the group with the higher average age.

When deciding on a randomisation protocol for your trial, the first step is to identify a (preferably) small number of patient characteristics that you want to balance between treatment groups. These characteristics should be prognostic, i.e. should be known to be strongly related to the main outcome in your trial. There's (probably) no point balancing eye colour in a trial of ulcer healing. The characteristics that you wish to balance are often referred to as "stratification variables". It is common to include centre in the stratification for multi-centre trials.

Continuous stratification variables should be dichotomised, for instance you might split age into under 60 years vs. 60 years or older. The reason for this (and why you need to keep the number of stratifying factors to a minimum) is so that you have a reasonable number of patients in each group formed by all possible combinations of the stratifying variables. The treatments are balanced within these strata so if there's only one patient per group then the balancing cannot take place and you effectively go back to simple randomisation.

A summary of popular randomisation protocols

simple Simple

Equal chance of receiving each treatment.

  • Pros: simple to understand and implement.
  • Cons: imbalance likely for smaller trials (N<2000).
simple Blocked or random permuted blocks

Treatments are guaranteed to be balanced after a given block size. For instance, if the block size is 4 then after 4 randomisations 2 patients will be on treatment A and 2 on treatment B. The order in which treatments are allocated in this example could be any of AABB, BBAA, ABAB, BABA, ABBA, or BAAB. The order is chosen at random at the beginning of the block. Sometimes several block sizes are used (e.g. 4, 6 and 8) and a new block size is chosen at random when the current block ends - this is called random permuted blocks. The block size(s) chosen should not be revealed to trialists.

  • Pros: Balances the number of patients allocated to each treatment group.
  • Cons: Doesn't balance patient characteristics. Deterministic towards the end of the block.
simple Random permuted blocks within strata

One of the most widely used protocols. Random permuted blocks are used within stratification groups. This ensures that treatments are balanced at the end of every strata block.

  • Pros: Balances the number and characteristics of patients allocated to each treatment group.
  • Cons: Fairly complex to implement without computer software. Not suitable for very small trials.
simple Biased coin

This is a modification to simple randomisation where the chance of allocation is biased in favour of the under-represented treatment when the imbalance passes some threshold. For example, if after 10 randomisations 7 patients had been randomised to A and 3 to B, then the coin might be biased to give a 2/3 chance that the next patient is allocated to B and only 1/3 chance to A. Can be used within strata to balance patient characteristics.

  • Pros: Always maintains a random element, relatively simple.
  • Cons: Can still result in imbalance, especially in smaller trials.
Minimisation (dynamic determination)

This is a largely deterministic procedure that allocates patients to best maintain balance in stratifying factors. For instance suppose 5 patients age<60 (3 to A vs. 2 to B) and 7 female patients (2 to A vs. 5 to B) had been randomised so far. The next female patient age<60 would be allocated to A because in younger female patients treatment A is currently under-represented (3+2=5 on A vs. 2+5=7 on B). The procedure can be made less deterministic by using a biased coin approach for allocation to the under-represented treatment.

  • Pros: Guarantees balance, can be used in very small trials and with multiple stratification variables.
  • Cons: Complex to implement without software, sometimes criticised on methodological grounds due to lack of random element.