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JUSTIFICATION OF SMALL SAMPLE NUMBERS IN EXPLORATORY STUDIES
What is an appropriate number of subjects per dose group to include in
an exploratory clinical study (e.g. first-in-man)? In such studies,
we have limited prior information and wish to collect information
generally on safety, tolerability, PK and possible potential PD
effects. There is not a specific primary endpoint on which we can
base a sample size calculation but data collected will be important
for the design of the next study.
We have a study proposed with n of 6 active + 2 placebo in each of 3
escalating dose groups. Is n of 6 sufficient? Alternatively, could
we drop down to n of 4, 3, or even 2?
Descriptive statistics will be used to summarise the data we collect
and for quantitative variables, we will calculate the 95 % confidence
interval (CI) for the mean using the standard formula:
Mean +/- t(n-1).SD//n
where t(n-1) is the value from the t-distribution on n-1 degrees of
freedom with 2.5% of the distribution lying above.
The value of t(n-1) increases dramatically as n decreases to 4 and
below. Thus the impact of increasing or decreasing the sample size
from 6 on the precision on any estimate can be calculated by
considering the ratio of t(n-1) values divided by the ratio of /n .
The following table shows the fold increase in the width of a 95 %
confidence interval compared to n of 6.
n fold increase in 95 % CI (compared to n of 6)
[t(n-1)/t(6-1)] / [sqrt(n)/sqrt(6)]
2 8.56
3 2.37
4 1.52
5 1.18
6 1.00
7 0.88
8 0.80
There is quite a marked deterioration in precision as n decreases from
n of 5. Thus n of 4 and below may not be a good idea and n of 5 is
risky once you allow for drop outs. Similarly, the improvement of
including 7 or 8 subjects does not increase precision to a great extent.
Could this consideration be used as a rationale to justify the choice
of the number of subjects to include, for example, in a first-in-man
study?
Does anyone know of any other justification of subject numbers in
early clinical trials where there is no specific primary endpoint with
associated estimate of variability?
Charlie Brindley (KinetAssist) and Sue McKendrick (AAIPharma, Edinburgh)
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