Sub-population analysis

Question

I'm facing a statistical issue.

I'm analysing a medical dataset, in which I have a full population. I know if they have a certain disease or not. Let's say I have 100 000 people on this, 20% having the disease.

Now, I want to know if "Being older than 80" increases the risk of having the disease. I select all people in my full population that are over 80. Let's say, in this sub-population, I have 5 000 people, and 30% having the disease.

I'm stuck in this point : Even though the percentage of people having the disease is higher in my sub-population, since I have way less people, I think this could also be linked with incertitude and "uncluck". Does some metric exists to show if my sub-population rate change is due to incertitude, or is really due to the fact I selected the 80+, and they appear to be risky.

What I tried :

• Applying a confidence interval in my sub-population, and looking if my global population rate is in : The interval is like [29.5, 30.5] and is way far, but seems to be a nonsense, since it gives the possible value of my sub-population rate, and will never be linked with the global population one
• Comparison of 2 proportions : Seems not perfect to me since my 2 populations are not independant, and way unbalances

Answer 1

I myself found an answer through the book 100 Statistical tests, Kanji (1995)

The test to apply in such a situation is "Test 5 Z-test for the equality of two proportions (binomial distribution)", you can find it at the 27th page of the book ( = 36th slide of the pdf )