How do I show something is an 'independent variable'?

#1
Please help. I am totally confused about how to show that something is an independent risk factor.

I.e. 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

I know that I can calculate the Risk Ratio to compare Exposure X to control, to see how much more likely the risk is for Group A given exposure X.

However, to complicate matters there is an exposure (Y) that moves across both groups. I.e.:

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.e. is there a formula I use to show that Y is an independent risk factor for Z?

Thanks!
 

noetsi

Fortran must die
#2
Something is an independent variable because you believe it is driving change not being driven by some other factor. I am not sure that is what you mean by an independent risk factor however.

Independence and dependence is driven by theory not a formula you can run (although you can test if there is a statistical relationship between X and Y you can't show empirically X-> Y rather than Y-> X or X and Y effect each other at the same time. This is normally done through theory not data analysis).
 
#3
Re: How do I show something is an 'independent risk factor'.

Something is an independent variable because you believe it is driving change not being driven by some other factor. I am not sure that is what you mean by an independent risk factor however.
Thank you! Yes - you are right, was not looking for 'independent variable' -- I was looking for how to work out whether something was an 'independent risk factor'. I realised that my question was related to whether the second criteria (Y) may be confounding the outcome... I.e. To establish whether Y 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 8.8 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 too.
 
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