topic Re: Odds Ratio Interpretation in Statistical Procedures

Odds Ratio Interpretation

steph_ — Mon, 24 Feb 2025 21:02:08 GMT

Hello!

I need some help interpretating an odds ratio SAS output.

Below is the code. The hot_spot variable is coded as 1= yes, its a hypertension hotspot, 0 = no, it is not a hypertension hotspot. The rural variable is coded as 0= not rural and 1=rural.

proc logistic data=work.research_lr;
class rural / PARAM = REF;
model hot_spot (event='1') = rural;
run;

And this is the output:

What would be the correct interpretation?

Thanks in advance!

Re: Odds Ratio Interpretation

quickbluefish — Mon, 24 Feb 2025 21:44:25 GMT

I think your life will be easier if you use the DESCENDING option in the proc logistic statement -- that will make 0 the referent ("no") category for all binary variables. Right now, you've currently got 0 as the referent group for your dependent (left hand side) variable (because of the event= syntax) and *1* as the referent group for the rural variable. So interpretation is pretty non-intuitive at the moment. Instead, do this:

proc logistic data=work.research_lr DESCENDING;
model hot_spot = rural;
run;

Doing the above should result in an odds ratio that's the reciprocal of what you currently have -- 1/0.627 = 1.595
An OR of 1.595 (assuming a confidence interval that does not include 1) would mean that rurality is predictive of hot spot hypertension. More specifically, the interpretation is that the odds of hypertension are 1.6X higher for rural people than for non-rural people.

Re: Odds Ratio Interpretation

quickbluefish — Mon, 24 Feb 2025 21:45:37 GMT

By 'predictive', I just means it's positively associated with hypertension, not that rurality causes hypertension.

Re: Odds Ratio Interpretation

Ksharp — Tue, 25 Feb 2025 02:34:00 GMT

That stands for
ODDS1= P( hot_spot ='1')/P( hot_spot ='0') when rual=0
ODDS2= P( hot_spot ='1')/P( hot_spot ='0') when rual=1
ODDS1/ODDS2=0.627

rural=0 has lower 0.373(=1-0.627) probability of getting P( hot_spot ='1') than rual=1 .

https://support.sas.com/kb/42/728.html