6.13 Meta-Analysis 91combination method. The other studies are labeled using the last name
of the fi rst author.
We note that the most convincing study is Suzuki, which other than
GRT had the largest sample size. Also, although, some of the studies
are small, most of the proportions run from 18 to 30%, making the
expected 25% very plausible. This meta - analysis is conclusive even
though the GRT result and the Molstad (because of small sample size)
paper are not convincing. One drawback of Fisher ’ s approach is that it
treats each study equally regardless of sample size. There are other
ways to combine the p - values where the studies are weighted according
to sample size.
Perhaps the simplest reasonable approach would be to just total the
number of restenosis events divided by the total sample size generating
two proportions that can be compared directly. In this case, the propor-
tions are 351/1214 and 379/1045 for cutting balloon and conventional
balloon, respectively. These sample proportions are 28.9 and 36.3%,
respectively, a difference of 7.4%.
Using a normal approximation for the two - sample two - sided test,
we get an approximate value of 3.56 for the test statistic, assuming the
common proportion under the null hypothesis p 0 = 0.40. The two - sided
p - value is less than 0.002, since for a standard normal distribution
P [ Z > 3.1] = 0.001 and hence P [| Z | > 3.1] = 0.002. Since 3.56 > 3.1,
we know the p - value is lower.
Although this analysis may seem compelling, it would not help to
get an approval. The FDA may accept results from meta - analysis, but
it would require a protocol and control and approval of the clinical
trials. Only GRT had a protocol and was a controlled clinical trial, with
its protocol accepted by the FDA. So they would not consider this as
clear and convincing statistical evidence.
Another example is based on fi ve published studies of blood loss
in pigs, comparing those with versus those without pretreatment with
the clotting agent NovoSeven ®. Table 6.5 shows the p - values for the
individual studies and the combined p - value using Fisher ’ s combina-
tion test. One advantage of Fisher ’ s method is that information about
the data in each study is not needed, and the tests applied in each study
need not be the same. For example, in one study, a nonparametric test
might be used, while in another, a parametric test is used. All that we
need to know is that the studies are comparable and valid, and have the
individual p - value in each case.