Re: st: Calculating confidence intervals for the ratio of stratified standardised mortality rates

[Steve Samuels <sjsamuels@gmail.com>]

The proper term for your rates are "directly standardized rates"
"Stratified" is implied and also applies to indirect standardization.

Your question isn't quite clear, but I assume that you mean that you
want a comparison of the two time periods for each category of
"all_data". Here is code for a single category of all_data. You can
get results for all categories with a -foreach- or -forvalues- loop.

******************************************
dstdize ... if all_data==1, by(time) using...

matrix a = r(adj)
matrix s  = r(se)
scalar ratio = a[1,1]/a[1,2]
scalar  slr = 
   sqrt((s[1,1]/a[1,1])^2 + (s[1,2]/a[1,2])^2)
scalar bound = 
   -slr*invnorm((1 -c(level)/100)/2)
scalar upper = exp(log(ratio) + bound)
scalar lower = exp(log(ratio) -bound)
scalar list ratio lower upper
******************************************

The formula for the log scale SE (slr) is based on the large sample
result that for an estimate R the delta method estimate of variance is:

var (log W)≈ var(W)/W   

The formula applies to each component of the log ratio, since they are
independent.

log ratio = log(adj rate 1) - log(adj rate 2)

I also have a Mata-based solution that is likely faster if you have a
lot of all_data categories and that puts the results into a data set.
It's a bit too long to list here. If you'd like to see it, join
stackoverflow.com and ask your question in the Stata area
http://stackoverflow.com/questions/tagged/stata.

Steve

On Nov 7, 2013, at 9:08 AM, Paul Mee wrote:
> 
> All
> 
> Apologies if this is a rather naive question but I hope someone can help me. 
> 
> I have been calculating age/sex standardised mortality rates stratified by geographical areas I used dstdize for this in stata and it worked fine and gave me the standardised rates and importantly confidence intervals which I extracted from the relevant macros/matrices . For reference this is the command I used 
> 
> dstdize total_hiv_tb_death population adj_cat, by(all_data) ///
> using("C:\work\Research\Analysis\Paper1_mortality\stata\rates\std_pop_09_10.dta") level(90)
> 
> No I need to calculate the ratio between the standardised mortality rates in two time periods (i.e. from different separate dstdize commands ) and calculate confidence intervals for these mortality rate ratios . 
> 
> Any help with how to do this in stata would be very much appreciated.
> 
> Paul 
> 
> paul.mee@wits.ac.za 
> 
> 


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