# How do I calculate whether something is an independent risk factor?

I do not know what calculation/formula to use to show that something is an independent risk factor.

E.g., in a cohort study:

Group A (n=1000) - exposure to X - outcome exposed 70/1000 demonstrate Z

Group B (n = 1000) - no exposure -- outcome control 23/1000 demonstrate Z

However, of Group A 750 also exposed to Y -- 60 demonstrate Z

Group B 300 also exposed to Y -- 16 demonstrate Z

How do I show that Y is an 'independent risk factor' for Z.

(I know that I can calculate the Risk Ratio to compare Exposure X to control, but do not know what formula I use to show that Y is an independent risk factor for Z).

UPDATE -

I realised that my question was related to whether the second criteria (Y) may be confounding the outcome... I.e. To establish whether the second variable may be confounding the results need to show:

1) that Y is an independent risk factor; 2) that Y is not an intervening variable and 3) that Y is associated with the study factor.

I couldn't work out how to show (1).. But then realised that what I had to do was look only at the non-exposed people. I calculated the RR for them in relation to Y. (16/300 -exposed)/(7/700-) = 5.3... So in the control group people exposed to Y have a 5.3 greater risk than those not exposed to Y of developing Z. I would argue that this shows that Y is an independent risk factor (as there is no exposure to X; exposure to Y; and an increased risk of developing Z).

(2) and (3) are satisfied.

I then used the stratification approach to demonstrate that the results were actually confounded... (which they were).

If Z is a binary variable all its own, the easiest way to do this would be to stratify your results by Z.

So calculate the risk ratio for subjects with Z = 0 and for subjects with Z = 1. The two risk ratios should be the same if the relationship between the exposure and outcome is independent of Z.

For more complex versions of Z, there are other, correspondingly more sophisticated methods, such as including Z in a regression model estimating the relationship between X and Y.

• Thank you... You got me well on the road to thinking this through! I am very grateful. I will add comment to show what I ended up with. Commented Apr 3, 2013 at 5:38
• Sorry - did not add comment -- just updated my question... Commented Apr 3, 2013 at 6:11

Mantel-Haenszel...look here for a very clear explanation:

https://wiki.ecdc.europa.eu/fem/w/fem/the-mantel-haenszel-method.aspx