st: delta method for unobserved confounding coefficient

[Adam Olszewski <adam.olszewski@gmail.com>]

Dear listers,
I was wondering if someone could enlighten me with regards to my
understanding of the delta method application in Stata.
I am trying to obtain sensitivity measures for unmeasured confounding
after Cox regression in IPT-weighted data. I would like to implement
the method from
Lin DY, Psaty BM, Kronmal RA. Assessing the sensitivity of regression
results to unmeasured confounders in observational studies. (1998)
Biometrics. 54(3):948-63. PubMed PMID: 9750244.
According to the article, assuming certain parameters (p0, p1, gamma),
one can calculate the corrected coefficient of the Cox regression
using a fairly simple formula :

beta_corr = _b[x] - log((exp(gamma)*p1 + 1 -p1)/(exp(gamma)*p0 +1-p0))

The authors recommend calculating the confidence interval of the
b_corr with the delta method.
If I run the -nlcom- command written like this:

nlcom (beta_corr:
_b[xrt]-log((exp(`gamma')*`p1'+1-`p1')/(exp(`gamma')*`p0'+1-`p0'))),
post

I do indeed get a nice-looking beta_corr and a 95%CI. However, I admit
to doing this without a thorough understanding of the -nlcom- method.
Can I assume that this is indeed the proper 95%CI by delta method? In
particular, should I be worried about the fact that the data is
pweighted? The sample is large enough to accomodate the "large number"
assumption.

I would appreciate any input or suggestion!
Best regards,
Adam Olszewski
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