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st: Variance of a ratio


From   Leonelo Bautista <lebautista@wisc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Variance of a ratio
Date   Fri, 17 Sep 2004 14:32:05 -0500

I have a variable R that represents the risk of disease in each subject. I
regress this variable against predictors of risk: 

	regress R sex age obese diabetic

In this model obese and diabetic are dichotomous variables. I want to
calculate the proportion of R that is attributable to obesity (P), after
adjustment by sex, age and diabetes. Therefore, I estimated the predicted R
in the whole population and in those without obesity using adjust:

	adjust, gen(adj1 seadj1) se
	adjust if obese==0, gen(adj2 seadj2) se

Then, I calculate P:	gen P=(adj1-adj2)/adj1

However, I need to calculate the variance of P. Since P is a ratio, there
seems to be no analytical way to estimate it. Therefore, I made 10000
simulations of P and got the variance from the simulated values, as follows:

	gen Ipop = adj1 +  seadj1 * invnorm(uniform()) 
	gen Inull = adj2 +  seadj2'* invnorm(uniform())
	gen P = (Ipop-Inull)/Ipop
	sum P
	gen Pmean=r(mean)   (Mean of P)
	gen Pvar=r(Var)	(Var of P)

Is this a reasonable approach? 

Thanks!

Leonelo E. Bautista

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