# Odds ratio and prevalence of an outcome

If someone could help me out, I'm confused with a finding in a paper:

In a group of rural children with obesity there was a greater rise in prevalence in obese children from 1 year to the next one when compared to the urban group, but the OR for obesity in the former group was lower than in the latter group.

I don't understand how can you get a greater prevalence of a condition and at the same time a lower risk for developing it.

• For context you should provide a link to the paper. I think it might be like when an epidemic reaches a peak the number of people with the disease is high but because it stops spresding the risk goes down. – Michael R. Chernick Apr 11 '17 at 2:25
• It´s not published, it is a kind of "case study" that we are reviewing in class. Thanks for your viewpoint, I haven´t considered before. – barbie22 Apr 11 '17 at 18:43

I think that the answer is this: there was a greater rise in prevalence in the rural group, which means that the proportion of people with obesity went up more in the rural group than in the urban group, but the OR was less in the rural group, which means that the proportion of people with obesity in the rural group was still less then in the urban group.

Example:

Suppose there are $3$ people in the rural group and $6$ people in the urban group and the numbers with obesity are:

rural     urban
year 1   1         4
year 2   2         5

The rise in prevalence in rural is $2/3 - 1/3 = 1/3$. The rise in prevalence in urban is $5/6 - 4/6 = 1/6$, which is less. But the prevlance (and therefore the OR) is still higher in the urban group ($5/6 > 2/3$).

• Thank you for the example, it clarifies the concept for me. But in terms of clinical significance (not statistical), I would think that this "low" OR in the rural group is a little misleading because the rise is greater than in the urban group, so I could deduce this group needs more interventions for prevention of obesity. Is that a valid assumption? – barbie22 Apr 11 '17 at 19:03