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Re: st: Method for confidence intervals in strate


From   Philip Ryan <philip.ryan@adelaide.edu.au>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Method for confidence intervals in strate
Date   Thu, 27 Feb 2003 00:28:45 +1030

Quoting Fred Wolfe <fwolfe@arthritis-research.org>:

> Does anyone know what method was used for the confidence intervals for the 
> SMR option in -strate-? There is no discussion in the manual.
> 


The following code fragment from strate.ado (*! version 6.3.8  17dec2002) is 
relevant here:

======
...
	gen double `rate' = `D'/`Y' if `touse'
	if "`jack'"!="" {
		replace `jm' = cond(`touse', `jm'/`jn', .)
		replace `jv' = cond(`touse', /*
		*/ sqrt((`jv' - `jn'*(`jm'^2))/(`jn'*(`jn' - 1))),.)
	}
	else {
		gen double `jm' = log(`D'/`Y') if `touse'
		gen double `jv' = sqrt(1/`D') if `touse'
	}
	local z = invnorm(0.5 + `level'/200)  
	gen double `cll' = cond(`D'==0, ., exp(`jm' - `z'*`jv')) 
	gen double `clh' = cond(`D'==0, ., exp(`jm' + `z'*`jv')) 

} // quielty
======

Note BTW the misspelt "quielty" !


Anyway, unless you specify the jacknife option, it looks like strate uses a 
normal approximation to the Poisson, based on the log(SMR), that is

Lower bound for the log(SMR) is:

 log(SMR) - z_alpha* sqrt(1/observed number of deaths)

Upper bound given analogously and then both limits are exponentiated.

This is given by Selvin in Practical Biostatistical Methods, page 463, who also 
refers to Breslow and Day Vol 2.  I don't have B&D to hand, but the derivation 
of the standard error of log(SMR) is probably by the delta method?

Phil
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