Odds ratio for no. of hypertensives in different age groups

Question

I have 6 age groups 18-20, 20-30, …, >60. I want to see the significant association between age and no. of hypertensives. I used Chi-square test for this and I found significant. Now can I compute odds ratio to each group so that to get in which age group risk is more? If I can use OR how to do it ?

Answer 1

You could use odds ratios for that purpose, but it is probably more informative to use either odds or probabilities. Consider the example below (using Stata):

. clear

. input str20 agegroup hyp nonhyp

                 agegroup        hyp     nonhyp
  1. "18-20"  10 100
  2. "21-30" 200 2000
  3. "31-40" 300 2500
  4. "41-50" 300 2500
  5. "51-60" 350 2000
  6. ">60"   500 2000
  7. end

. 
. gen odds = hyp / nonhyp

. gen odds_ratio = odds / odds[1]

. gen pr = hyp / (nonhyp + hyp)

. 
. list, clean ab(10)

       agegroup   hyp   nonhyp   odds   odds_ratio         pr  
  1.      18-20    10      100     .1            1   .0909091  
  2.      21-30   200     2000     .1            1   .0909091  
  3.      31-40   300     2500    .12          1.2   .1071429  
  4.      41-50   300     2500    .12          1.2   .1071429  
  5.      51-60   350     2000   .175         1.75   .1489362  
  6.        >60   500     2000    .25          2.5         .2  

the odds is the expected number of "successes" (hypertensive) per "failure" (non-hypertensive), so for the age group 18-20 we expect to find .1 hypertensive for every non-hypertensive. So the age group with the largest odds is most likey to suffer from from hypertensia.

An alternative way of quantifying how likely it is that someone suffers from hypertensia is to look at the expected proportion of "successes" (hypertenisive) within each age group. This is an estimate of the probability. Again the age group with the largest number is most at risk.

In principle the odds and the probability contain exactly the same information, so the choice between them is really just a matter of what your intended audience is most comfortable with. Most of the time (but not always) that will be the probability.

The odds ratio can also be used to find the age-group most at risk but it does not directly tell you how high that risk is. It is the ratio of odds comparing an age group with a reference age group. In this exampel I chose the first age group as the reference. So the first odds ratio is necesarily 1, the second odds is also the same as the first odds, so the odds ratio is also 1, The third odd is 1.2 times larger than the first odds, etc. So the age group with the largest odds ratio will be the age group with the largest odds of suffering from hypertensia, but it does not directly tell you how high that risk is, just how high it is relative to some baseline.