Charles Huber discusses the interpretation of models with log-transformed outcomes in Stata News 34-2 at https://www.stata.com/stata-news/news34-2/spotlight/

In a randomised trial of a new treatment (treat 0,1), the primary outcome is the number of hours of illness (hours); hours is log-normal (lnhours). Rather than 'regress lnhours', Charles Huber suggests using 'gsem' so that the SE of the variance of the errors is calculated (and he then discusses the use of 'poisson'). Using Stata 16.1 in Windows 10:
Code:
gsem lnhours <- i.treat i.x2 i.x3
'treat' has coefficient -.4217, with 95% CI -.6604 to -.1829 (to 4 places).
Code:
display exp(_b[1.treat])
Returns 0.65596214. I want to calculate the 95% CI for 0.65596214.
Code:
margins, expression(exp(predict(eta))*(exp((_b[/var(e.lhours)])/2)))at(treat=(0 1))
calculates the margins (95% CI) for both treat=0 (control) and treat=1 (intervention) separately.

But how do I calculate the correct 95% CI for the ratio of 0.65596214 (treat=1/treat=0)?

I'd be grateful for advice..

Frank Shann