Calculating Standard Errors of Clustered data

[Joanne Delk]

Hello,

I have 8 timepoints of data from most of the hospitals in our state, 4 pre and 4 post intervention. At each timepoint hospitals provided the number of newborn admissions and the number of newborn admissions with hypothermia. From this we can calculate each hospital's newborn hypothermia rate.
To calculate the state hypothermia rate I take the mean hospital rate weighted by the newborn admissions.

I want to see if our intervention significantly decreased the state's hypothermia rate, but I don't know the appropriate way to calculate the standard errors. Our data has 120 hospitals and ~60,000 admissions.



As the hypothermia rate is right skewed I am using a negative binomial regression. Currently, I have been running the regressions with and without clustering hospitals.

nbreg hypothermia_rate i.pre_post [fweight=newborn_admissions]


nbreg hypothermia_rate i.pre_post [fweight=newborn_admissions] , cluster(hospital) irr


I would appreciate in any insight to the correct method.

thank you.

[Carlo Lazzaro]

Joanne:
welcome to this forum.
Previous posts on the debate between overdispersed poisson and negative binomial regression are in favour of the former, provided that you impose clustered standard errors tyat, given your notable number of hospitals, is the way to go.

[Carlo Lazzaro]

Joanne:
see for instance glm poisson vs nbinomial - Statalist.

[Jeff Wooldridge]

It appears that you no longer have a count variable but a fractional variable. So the unbounded exponential mean is not appropriate, and NegBin certainly isn’t. A fractional response model is better suited. I’d also just use a linear model.

Your description makes it seem like you aggregated data to the state level. Is it true you converted it to state-level panel data? I assume the intervention occurs at the state level. So whether you use state aggregates or the hospital-level data (and I’d lean toward the latter), you should cluster at the state level.

[Jeff Wooldridge]

You could use the count of hypothermia cases in Poisson regression with log(newborn-admissions) as an offset. This will give a proportionate effect.