Re: st: svy adjustment for rates

[Steven Samuels <sjsamuels@gmail.com>]

Sujit-

 -svy: ratio- and -svy: poisson- give different CIs because one works on ratio scale (ratio ± k*SE) and the other works on the log scale and then transforms to the ratio scale.  In the sampling texts, the -svy: ratio- approach is presented. In statistics, different consistent estimators of the same quantity are frequently encountered.  Contrary to your belief, both the -svy: ratio- and -svy: poisson- standard errors are "correctly" survey-adjusted.  I happen to like the CI based on the log ratio, because the CI for X/Y can be found by inverting the endpoints of the CI for Y/X; thus the two CIs give the same conclusions.  Also I suspect the log-based CIs are more accurate. With large enough samples there is little difference. 


Steve

Steven J. Samuels
Consulting Statistician
18 Cantine's Island
Saugerties, NY 12477 USA
Voice: 845-246-0774
Fax:   206-202-4783 
sjsamuels@gmail.com



On Feb 23, 2011, at 7:40 AM, Sujit Rathod wrote:

Hi Steve - many, many thanks for this code.  It's exactly what I've been
looking for.

What I meant by the Poisson CIs was that I don't believe I can get this
from -ratio: deaths/survival_time-, and so survey-adjusting it with
-svy: ratio: deaths/survival_time- wouldn't be correct either.

This appears to be the case in the auto dataset, where -ratio- gives
different CIs than -Poisson-.

With the combination of xi, noomit and svy, I get Poisson CIs that are
survey-adjusted.

I'm looking for a good surveying book, so will try to order Lohr.  I had
Heeringa on my to-order list already.

Thanks again!  --sujit
------------------------------

Date: Tue, 22 Feb 2011 08:57:17 -0500
From: Steven Samuels <sjsamuels@gmail.com>
Subject: Re: st: svy adjustment for rates


Sujit Rathod -


Sujit-

"And while I can run something like -svy: ratio deaths/survival_time-
these do not give me the correct (Poisson?) CIs."

Absolutely incorrect.  Survey-adjusted standard errors are based not on
the Poisson assumption, but on the repetitions of the sampling
procedure. To see why, I recommend a good sampling text such as Sharon
Lohr, Sampling: Design and Analysis, Duxbury, 1999 and 2009.

Below is code. The point estimates are the same, but I would prefer the
result from -svy: poisson-, because it gives asymmetric CIs based on the
log of the ratio.

*******************
sysuse auto, clear
svyset _n

svy: ratio rep78/turn, over(foreign) 

xi, noomit: svy: poisson rep78 i.foreign, nocons exposure(turn) irr
xi, noomit: svy: nbreg   rep78 i.foreign, nocons exposure(turn) irr
*********************** 

Steve

Steven J. Samuels
Consultant in Statistics
18 Cantine's Island
Saugerties, NY 12477 USA
Voice: 845-246-0774
Fax:   206-202-4783 
sjsamuels@gmail.com




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