I've read some RCT articles recently in which the sample size is not equally assigned into the placebo and intervention groups.e.g. 40 VS 20.is it a defect or is there a scientific reason behind it?
You can defined an attribution ratio (e.g. 2:1, it means that 2 individuals will be recruted in the first group for one individual in the second group).
There is no problem in doing so, but you have to take it into account when estimating the number of subjects you will need in your trial. The different formula used to estimate the number of subjects needed include this parameter, see for example the book "sample size tables for clinical studies" by Machin et al.
The reason for such a design is that sometimes, recruiting patients in one of the group is easier (or cheaper ), but for simplicity most designs choose a 1:1 ratio.
Book Sample Size Tables for Clinical Studies, Third Edition
Stéphane is absolutely correct on both the rationale and method. In Hulley and Cummings, Designing Clinical Research, the authors provides the following formula for a 1:k randomization: n’ = n (k+1)/(2k) (where n is the sample size from the equal group design). The only thing I would add is that even though the 1:k randomization allows you to deal with recruitment for rare or costly cases, the 1:1 design is the most statistically efficient (i.e. yields the smallest standard errors)
Not necessary but it's the most 'powerful' design, caeteris paribus, where power is defined as needing the fewest subjects to get to a significance test
Stephane and Atul have done justice to the question. Just to summarise it is not compulsory to have equal number but for statistical efficiency and simplicity a 1:1 ratio is most favourable.
Well, to be precise, a 1:1 allocation ratio doesn't always give the best power.
For example, when comparing binary data in two groups with proportion of respectively pi1 and pi2, the optimal ratio is sqrt( (pi2*(1-pi2)) / (pi1*(1-pi1))).
But in practice, tuning this ratio generally doesn't change a lot, and can add a lot of complexity in the design. So we stay with 1:1 ratio in the majority of trials!
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