# Methods for randomly allocating people between active and placebo in clinical trials

I'm looking for a way to allocate people to either group A or B. Data for the study group has 3 main variables:

1. Age 65-90
2. Male or Female
3. APOE + or APOE – (this is a blood test)

I then need to allocate them to either A (active tablet) or B (placebo).

Ideally, I need both groups A and B to be comparative, so fairly even. Total number of participants will be 120. Can anyone suggest a random allocation method for doing this? Or is it perhaps better to just randomly assign and completely ignore the above variables?

## 2 Answers

If you have good reasons to think that these three factors influence the outcome, you may want to block them. Otherwise, you could still use blocking (e.g., Imai, King, & Stuart, 2008), but it's probably not that important in that case.
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Imai, K., King, G., & Stuart, E. A. (2008). Misunderstandings between experimentalists and observationalists about causal inference. Journal of the Royal Statistical Society, 171, 481–502. doi: 10.1111/j.1467-985X.2007.00527.x

Assuming all three factors are prognostic (i.e. strongly related to the primary outcome) the most common methods of balancing them within the treatment groups are:

1. Random permuted blocks within strata
2. Minimisation

In both cases you must categorise your age variable - it's usual to create 2 categories based on median age in your patient population unless you have other pre-defined cut-points. Let's assume you categorise into 65-75 and 76-90 years.

The potential problem with using blocks within strata is that you have 8 strata (2 age-groups x 2 sexes x 2 APOE states) and only 120 patients. In the best case assuming you recruit 50% females and 50% APOE+, you would have 15 patients per strata. In reality you're likely to have some strata with fewer patients and others with more. If, for instance, being APOE+ is rare (5%) then the APOE+ strata (65-75/Male/APOE+, 76-90/Male/APOE+, 65-75/Female/APOE+, 76-90/Female/APOE+) are likely to have only 1 or 2 patients each. This would mean you don't have enough patients within these strata to complete any blocks, so the blocking doesn't get a chance to work and balance the treatments. You can choose very small blocks (size 2) to combat this, but it makes the allocation sequence more predictable which is undesirable.

Minimisation doesn't suffer from this problem with sparse strata, but is complicated to implement. You would need to use some specialist software or an online randomisation service if you choose minimisation.