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

[Steve Samuels <sjsamuels@gmail.com>]

You are welcome, Paul.  A couple of inessential improvements:

1. For:

slr = sqrt((s1:/a1):*(s1:/a1) +(s2:/a2):*(s2:/a2))

substitute:

slr = sqrt((s1:/a1):^2 +(s2:/a2):^2)

s1, s2, a1, and a2 are matrices, and
the ":" before an arithmetic operation tells
Mata to apply the operation to every element
of the matrices.

2. For:
z = -invnormal((100 - st_numscalar("c(level)"))/200)

Substitute:

z = invnormal(.5 + st_numscalar("c(level)")/200)


Steve

On Nov 11, 2013, at 1:41 AM, Paul Mee wrote:

Steve

Thanks for the detailed answer , much appreciated

Paul 

Paul Mee
Senior Data Scientist
MRC/Wits Rural Public Health and Health Transitions Research Unit (Agincourt) School of Public Health University of Witwatersrand 
SA Office Number +27 (0) 13 795 5076 (tel/fax) 
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e-mail: paul.mee@wits.ac.za 
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-----Original Message-----
From: Steve Samuels [mailto:sjsamuels@gmail.com] 
Sent: 09 November 2013 19:24
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Calculating confidence intervals for the ratio of stratified standardised mortality rates


I see some code specific to my test data set got into the last part.
I've revised to be specific to Paul's problem.

Steve


Here's the Mata version after all. It requires only two
-dstdize- calls and will produce the rate ratio and CI for any number of categories.

************************************
forvalues i = 1/2 {
dstdize ... by(all_data) using(), ///
if time==`i'
mata: a`i' = st_matrix("r(adj)")
mata: s`i' = st_matrix("r(se)")
}

mata:
ratio = a1:/a2
lr = log(ratio)
slr = ///
sqrt((s1:/a1):*(s1:/a1) +(s2:/a2):*(s2:/a2)) z =  ///
-invnormal((100 -st_numscalar("c(level)"))/200) lower = exp(lr - z:*slr) upper = exp(lr + z:*slr) d=(ratio \ lower \ upper)'
end

clear
getmata (ratio lower upper) = d
gen all_data=_n
format ratio lower upper %8.3f
list all_data ratio lower upper
save results, replace
*********************************. 

> 
> 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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