Marginal vs conditional odds ratios in matched binary outcome studies

[Timothy Reason]

Dear all,

I've been reading up on matched-case control studies lately and have posted two examples along with my interpretation below. I'd be really grateful if anyone could tell me whether I'm interpreting the marginal/conditional odds ratios correctly based on these study designs, and also help me understand when it might be useful to consider marginal versus conditional odds ratios in this context as I'm struggling to understand what the actual usefulness of the marginal odds ratio is. I've been told it's potentially more useful to policy makers while subject specific/conditional odds ratios are more useful to clinicians, but when I break it down I just can't see the added utility of using a marginal odds ratio? 

Diabetic retinopathy example

In this example, patients are given either a new or standard treatment in each eye and then assessed for blindness, so we can summarise the study by saying they:

- Matched on individuals

- Stratified by treatment

- Assessed for blindness

My understanding is that the conditional odds ratio should be interpreted as the the relative odds of an eye going blind on the new treatment versus an eye going blind on the standard treatment in a person. The marginal odds ratio should be interpreted as the relative odds of eyes in general going blind on the new treatment versus the standard treatment in the whole population, i.e. based on the total number of eyes on the new treatment versus the old treatment and not specific to an individual person. 

The conditional odds ratio seems to be the more useful measure here as it accounts for the fact that certain individuals in the population may be at high risk of going blind. It also preserves the randomised nature of the comparison. The marginal odds ratio seems less useful, as you may just have an imbalance of high risk people on the new or standard treatments and thus may over/underestimate the true treatment effect. I can't see how, in this context the marginal odds ratio would ever be useful but maybe I'm just missing something?

Lung cancer example

In this example, patients with or without lung cancer were classed either as cases or controls, matched on age/sex and asked whether they had ever smoked, so they:

- Matched on age/sex

- Stratified by whether or not they had lung cancer

- Assessed smoking status

My understanding here is that the conditional odds ratio should be interpreted as the relative odds of being a smoker given that you were a lung cancer case versus if you were a control of the same sex and age. Using the fact that the odds ratio is reversible, this can then be thought of as the relative odds of developing lung cancer if you're a smoker, compared to someone of the same age and sex. Is that correct? The marginal odds ratio should be interpreted as the relative odds of developing lung cancer if you're a smoker, compared to being a non-smoker, but averaged out across the population. This means the interpretation is now not specific to two people of the same age and sex, but instead applies at a general population level, is this the correct way to think about it? If so, again I don't see the added utility of considering the marginal odds ratio here, even if you are a policy maker. In what context would the marginal odds ratio be useful here and why?

Hope that makes sense, any help would be gratefully received!

Tim

[Frank Harrell]

My quick reading of what you wrote gave me the impression that you understand the issues very well.  I think that a marginal odds ratio is useful only to a decision maker who wishes to make a mass decision for heterogeneous groups of persons.  Making the same decisions for all members of a group will not necessarily make the best decisions for individuals.

Frank

[SteveDrD]

It (marginal odds ratio) also seems to be useful to journal editors, although for the life of me I cannot figure out why.

 

Steve Denham