Question: Estimating/translating odds ratio for different percentile intervals
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Lb40 wrote:

Hi,

I have a question regarding a translation in odds ratio curve OR(x). More specifically, let's say we have an OR(x) which we get using logistic regression. We look at the interval bounded with 25% and 75% percentiles of the variable X and denote the value of interval with X25-75. For further interpretation of the odds ratio we want to have OR(X25-75) = 1, however in our case we get X50 = 1.02. So my question is: how do we translate the odds ratio curve to get the OR(X25-75) = 1? In other words: How do we get the OR estimates for different percentile intervals?

See for example table 4 from this paper or table 2 from this paper.

Thanks!

written 3 months ago by Lb40

I think in the table 2 of the 2nd paper they SET their risk as baseline, so it is artificially 1. And you calculate OR for other percentile relatively to your value in X25-75 interval. Of course X50 may be different from 1 - since X50 is not X25-75.

Yes, I also think they SET it. But I don't understand what is the correct way to estimate the OR for an interval, because the OR curve gives you values for each point (percentile). So do you think it would be correct if you take an average of 1000 (or more) values from 25 to 75 percentile to get an estimate for the interval 25-75? Let's say you do that and you get 1.05. Then you SET the OR for this interval to 1 (by dividing it with 1.05). So according to this SET baseline you need to translate the other intervals too. I would divide all of the intervals that I am interested in (for ex. 0-1, 1-10, 10-25, 25-75, 75-99, 99-100) with 1.05. Do you think this is the case or I am missing the point here? Thanks! :)

I guess you can not simply divide with 1.05. Look, you have 2 cohort of individuals (Control - Test). And you have percentiles. For e.g. percentile 0-1 and 25-75 you may create this table https://en.wikipedia.org/wiki/Odds_ratio , first table. Exposed is 0-1, non exposed is 25-75. I think that's how it is done, even if I am not an expert in such studies (so if smb thinks I wrote bullshit please tell me why)

Hmm.. I don't think that is a solution, but I could be wrong... I already have an Odds ratio curve which I got using logistic regression so the only question here is the interpretation/translation of OR values for specific percentiles to the OR values for intervals between percentiles (with additional baseline setting)..

I am afraid that the division will break your confidence intervals =) you can also do this, https://en.wikipedia.org/wiki/Ordered_logit , treating quantiles as ordered groups

My 'train' set has two classes: 'case' vs 'control' so I don't know how would I do that with my data, but thanks for the idea. :)

Ordering is performed according to the percentiles, not according to the binary category

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I talked with the author of one of the papers and the idea you suggested was actually the correct method to do that! Just wanted to let you know that you were right ;) thanks again!