I am doing my head in over something very simple. Its more theoretical and I'm trying to work out a method. I am hoping someone can clarify something for me. It relates to working out how much an effect a confounder will have on an RR.

I understand how different confounders work in increasing or decreasing observed RRs and how this depends on the sizes of relationships between confounder and exposure and confounder and outcome, and also how it depends upon rarity of the confounder in the population.

I will illustrate with an example from a textbook which doesn't explain how they derived the answer.

Looking at the relationship between oral contraceptives(OC) and CHD

Suppose the true RR between OC and CHD is 3.0

One possible confound is age (say two groups <30 and >30)

Say the RR of age on CHD is 2.0

We also have a cohort of women where 60% of OC users are < 30 and 30% of non-OC users are < 30

The text says that this confounds the RR so that the observed RR is approx 2.5

Now I understand the direction and why the confound reduce the observed RR but is it possible to calculate/estimate that 2.5 from the figures given. I have been trying to derive a general formula but struggling. Hoping someone can clarify. Or is there some missing information that makes a general case impossible. I feel it should be so simple but can't derive a formula to get that answer. I don't expect its possible to derive exact effects but at least approximate effects.

Many thanks


PS This has nothing to do with an assignment. Its just something I would like to understand forgeneral interpretation of importance of confounds.