Power analysis is about your ability to find statistical significance given
a particular sample size, effect size and alpha. Here you say you did power
analysis with an OR of 3 (which is a pretty big OR in the fields I work in,
but might be normal in your field). But your actual ORs in these two
examples were much higher. So, you found significance. But you get wide
CIs because of small cell sizes: This makes sense. You don't want to make a
precise statement based on 1 person (or even 3). The second CI is narrower
than the first because you have a smallest cell of 3 instead of 1.
Peter Flom Consulting
From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of Jan
Sent: Tuesday, November 01, 2011 10:16 PM
Subject: Wide CI but good power?
I am a doctoral student in epidemiology (SAS 9.1.3 on a PC)
I ran a logistic regression analysis with almost all categorical independent
variables. The 95% are very wide for many of the variables. For example
desperation OR 12.5 (CI 1.68, 92.9). I looked at a cross tabulation of my
outcome variable and desperation (dichotomous) and found cell sizes of
142,1,307, and 30. Small cell sizes I think could be causing my wide CI.
However I have similar cell sizes for the variable withdrawal (205,3,240,27)
and even though its OR is 11.3 (close to desperation) the 95%CI is 2.66,
48.4) Not narrow but not as wide as desperation.
I re-did my a priori power calculation using the actual prevalence in the
sample (70%), alpha 0.05, effect size 3 (OR), two sided and got 81% power
for my sample size of 460.
My question is can one have wide CI and good power at the same time or am I
confused? If this is possible could I get a narrower CI somehow given the
same prevalence in this population?
Thanks for any feedback!