Table 2. - Sample sizes for all alternatives in scenarios with equal
sensitivity and specificity
Although the most dramatic effects of misclassification were observed
when p 0 was near 0 or 1 (more than fourfold
increase in sample size for p 0=0.01 with
left-sided alternative and Se = Sp = 99%), even in the
best case, that is when p 0=0.5, the increase in
necessary sample size was 22% with Se =Sp =95%, and 9%
with Se =Sp =98%.
For the two-sided alternatives, results differ depending on whether the
assumed true proportion pa is smaller or greater
than p 0. Increase of necessary sample size is
greater than that for the respective one-sided alternative illustrated
by the extreme sample size increase of more than 6400 individuals (from
an initial 433) in case of the two-sided alternative withp a<p0 whenp 0=0.01 with Se =Sp =95%.
Our results showed that ignoring even small misclassification
probabilities may result in considerable power loss. Here we studied the
exact binomial test in detail, but results are similar for other tests
for the binomial proportion. Our R function enables sample size
calculation for any test given an R function for the test is available.
Presumably similar tendencies could be observed in the comparison of two
or more binomial samples, which will be investigated later.
Although not presented in the article, we performed the same
calculations for several asymptotic methods as well (Agresti-Coull, Wald
and Wilson) resulting in similar amount of sample size increase.