Sample size estimation:
key points
i)
Why perform sample size estimations?
There
are several reasons for doing a sample size calculation. The two main ones are a) it gives a simple
stopping rule that allows the trial to be terminated in an unbiassed way and b)
it aims to ensure that trials are large enough to provide conclusive evidence
and small enough to be ethically acceptable.
ii)
Role of hypothesis tests
A trial ought to provide adequate evidence about the efficacy of the treatment
being investigated. To do this we need
to make sure the trial is sufficiently large.
A common criterion for determining this is to try to ensure that the
trial is large to have a good chance (the power)
to reject a null hypothesis of no treatment effect if the true treatment effect
is more than a minimal value (the minimum
clinically important difference).
iii)
Normal variables
The size of a trial with a Normally distributed outcomes requires the
investigator to specify the significance level, power, standard deviation of
the outcome and the minimum clinically important difference. In a two group trial, for a given total
sample size, the largest power is obtained by allocating equally to both
groups.
iv)
Binary variables
Similar to above, but dependence of variance on the true proportion means that
pre-specification of the two proportions, not just their difference is
needed. However, there is no standard
deviation to specify.