On 17 Jun 2001, Marc wrote (edited):
> I have to summarize the results of some clinical trials.
> The information given in the trials contain:
>
> Mean effects (days of hospitalization) in treatment & control groups;
> numbers of patients in the groups; p-values of a t-test (of the
> difference between treatment and control) .
> My question: How can I calculate the variance of the treatment
> difference, which I need to perform meta-analysis? Note that the
> numbers of patients in the groups are not equal.
> Is it possible to do it like this:
>
> s^2 = (difference between contr and treatm)^2/ ((1/n1+1/n2)*t^2)
Yes, if you know t. If all you know is that p < alpha for some alpha,
you then know only that t > the t corresponding to alpha (AND you need to
know whether the test had been one-sided or two-sided -- of course, you
need to know that in any case), you can substitute that corresponding t
to obtain an upper bound on s^2 -- ASSUMING that the t was calculated
using a pooled variance (your s^2), not using the expression for separate
variances in the denominator: (s1^2/n1 + s2^2/n2).
Note that this s^2 is NOT "the variance of the treatment difference",
which you said you wanted to know; it is the pooled variance estimate
of the variance within each group.
The variance of the difference in treatment means, which _may_ be what
you are interested in, would be
(difference)^2 / t^2
with the same caveats concerning what you know about t.
> How exact would such an approximation be?
Depends on the precision with which p was reported.
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