I have a binary variable indicating whether a c-section was carried out or not. C-section is more than 10% prevalent in the population. I want to model predictors of c-section. Initially I had used an
xtlogit model in Stata to model this. The xtlogit command runs a multilevel model. I need a multilevel model because the outcome may be clustered at the hospital level, so I use a random intercept to allow for this. However, the odds ratios that are returned seem problematic. In some instances, an OR of >500 is given back for some explanatory variables. This is probably because the OR is overestimating the true underlying risk. This happens when a violation of the "rare outcome" assumption occurs (because c-section is >10% in the population - the assumptionis violated here). http://www.bmj.com/content/348/bmj.f7450.full?ijkey=NHT1YVsoX1RCm8r&keytype=ref
Instead, I ran an
xtpoisson model which gives risk estimates that are much more plausible. I used a poisson model because I read on this post that it is appropriate model binary outcomes in this manner when a RR is required. Poisson regression to estimate relative risk for binary outcomes
However, the estimates of variance are now completely different to what was estimated with the
xtlogit. For example in the
xtlogit model I calculated a VPC of 30%. This is now 2% from the
xtpoisson. Should the VPC have changed this much? Which is the more reliable estimate to use?