On Fri, 5 Dec 2008 08:35:55 -0800 (PST), norky
Post by norky Post by Bruce Weaver Post by norky
I am calculating sensitivity and specificity as well as PPV and NPV of
a diagnotic tool. For the purposes of this study a sensitivity of
85%-100% will be considered a good predictor. I would also like to
calculate a 95% confidence interval. How do I determine the
appropriate sample size? I am getting conflicting answers from
others. Any help would be appreciated.
You say you are *calculating* sensitivity, specificity, PPV and NPV.
Presumably then, you have a 2x2 table. For sensitivity, the sample
size is the the first column sum; for specificity, it is the second
column sum; for PPV and NPV, it is the first and second row sums
respectively. Or am I missing something?
"When all else fails, RTFM."
Thank you both for your comments!
The issue that I think you are addressing, Bruce, is why I need a
sample size calculation. Yes, simple 2x2 table with new test on the
rows and gold standard on the top. I was told by some of my
collaborators that our estimates of sensitivity, specificity, etc.
should have a given precision, i.e., if I get a sensivity of 90%, I
would want a precise 95% confidence interval. I have a SAS macro that
will provide the CI for diagnositic test characterisitcs. However, I
would like the CI of these estimates to be narrow. I was told two
different ways in which to calculate the sample size necessary to
estimate the CI with the desired precision. One of which was using
the formula for a simple proportion, which was also suggested in one
of the responses here, and the other was much more complicated and
involved using the arcsin method. Thoughts?
When you say, "determine the appropriate sample size",
you seem to cast this into the paradigm of doing a power
analysis. For the sake of a power analysis, it is usually
advisable to have the whole proposed table -- that is,
for instance, specificity as well as sensitivity, and something
about the marginal Ns.
However, if you want to put a narrow CI on the effect size,
the way to do that is to extrapolate from hypothesized
effects, and escalate the Ns in order to achieve the narrowness
of the CI that you need. Is specificity a good measure of effect
for your problem?
I have a little difficulty arising from the fact that specificity,
by itself, is not at all assured to be a good measure of "effect"
for a 2x2 table, when compared to the Odds Ratio or even to
the phi coefficient.
Another thing that complicates this, for your example, is that
there are several ways to estimate the CI for extreme proportions.
The arcsine transformation is not very good outside of (10%, 90%),
but it is better than the additive formula (the one that gives
symmetric limits around the point estimate).
I'll suggest that you read up on Power analysis in Cohen, to
see if "sensitivity" is really what you want to look at. His
chapter on proportions does use the arcsine transformation,
if you want to go by that. Looking only for "significant" effects,
I've always adapted the 2x2 table from the chapter on rxk tables,
since the latter was more accurate for my purposes.