variance from xtpoisson in comparison to variance from xtlogit

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?

• If this is not a Stata question, then you should explain to the majority of non-Stata users here what the commands you used do and not presume that it's evident from their names. Even more crucially, what is the response (outcome) variable such that a Poisson model appears an alternative to a logit model? Is that the binary variable mentioned in the first sentence? It doesn't seem surprising that models with very different structure don't give similar results. Oct 12, 2015 at 11:25
• Hi @NickCox. Thank you for suggestions, I have now amended question. Am happy to edit further if required. Apologies for not explaining xt commands and hope the above is clearer. Oct 12, 2015 at 11:43
• Thanks; that should improve the question for those who know more about this. Oct 12, 2015 at 11:55
• You might find Bill's comment in a related question interesting. Oct 12, 2015 at 17:13
• thanks @DimitriyV.Masterov. what did you do in the end? Did you use the poisson for your binary outcome? Oct 12, 2015 at 17:28