Compute an asymptotic interval with an approximation (Delta method)

[Dusan Petrovic]

Dear Statalisters,

I am performing an analysis where I need to calculate the percent attenuation between two CI (of OR or RR or HR)

Essentially, I have a CI for an unadjusted model and a CI for an adjusted model, and I want to compute the attenuation percentage between them, due to the covariable in the adjusted model. I'm doing this for a SR + Meta analysis, therefore, I do not have any data, I only the CIs from the articles.

The percentage attenuation is calculated as following:

percent_att=100*(Beta_unadj - Beta_adj)  /  Beta_unadj              //where Beta = log(HR) or log(OR) ...

Now, I also want to compute the 95%CI for percent_att (which would be my parameter of interest for the MA).

I was told by a statistician that I could do that with the following method: "Asymptotic Interval with an approximation (Method of the Delta, Wald IC)". I checked different methods (on the internet) but I don't have the background (Biology...) to understand this nor set up formulas for lower and upper limits.

Therefore, if someone would help me with proposing formulas for lower and upper limits, I would be extremely grateful.

As mentioned above, I have the 2 CI (unadjusted and adjusted) as well as the number of participants in each study.

Thank you very much for your kind help.

Best

Dusan

[Maarten Buis]

Attenuation is much more complicated in nonlinear models. See e.g. http://maartenbuis.nl/wp/oddsratio.html

[Maarten Buis]

Cross posted here: http://www.talkstats.com/showthread....elta-method%29

See http://www.statalist.org/forums/help#crossposting for why it is important to mention cross-posting

[Dusan Petrovic]

Thank you Maarten, sorry I forgot to mention the cross post, I was kinda desperate.

I figured out something: (See formula)
The issue that remains is the covariance, as it cannot be assessed based on two CI taken from the literature. One may assume that the two models are correlated because only one variable changes between them, but, what would be the amount of this covariance or correlation.

Best

Dusan

Best

Dusan

[Dusan Petrovic]

Erratum in equation