Hello,
I am undertaking a meta-analysis of risk estimates between exposure to air pollution and asthma diagnosis in childhood. The studies I collected in my review calculated the risk estimates based on different increase intervals in air pollution exposure and I want to standardize that so as to be able to tell what air pollution interval the pooled estimate relates to.
For example, in one study an increase of 10.3 µg/m3 nitrogen dioxide was associated with an OR of 1.18 (0.93, 1.50) for asthma diagnosis - I want to find out what OR is associated with a 10.0 µg/m3 nitrogen dioxide instead? Can you please advise on how to do that?
Many thanks,
Haneen.
Chapter17 on Urban air Pollution by Cohen et al in the WHO Comparative Quantification of Health Risks Study WHO.Geneva 2004 vol 2 p 1353-1433 deals comprehensively with this problem..
If you have a study where the effect is modelled with a continuous exposure variable it is easy. Just substitute exposure value in regression equation.. If only categories are used you would need some exposures distribution data from the original study to create a pseudo-continuous variable for comparisons.
Ross' answer is correct, as far as I can see.
Here is the derivation:
The odds ratio comes from the logistic model
odds = exp(b0+b1*x) = exp(b0)*exp(b1*x)
or, on the log scale (this makes the math simpler because products and ratios turn into sums and differences:
log odds = b0+b1*x
The odds ratio OR for x1 is the relative change in the odds when x changes from x0 to x0+x1. So the log odds at x0 and x0+x1 are
log odds(x0) = b0 + b1*x0
log odds(x0+x1) = b0 + b1*(x0+x1) = b0 + b1*x0 + b1*x1
The ratio of the odds, i.e. the difference of the log odds, is the (log) odds ratio:
log OR(x1) = log odds(x0+x1) - log odds(x0) = b1*x1
This OR value is given. In your case: log OR(x1=10.3) = log(1.18) = b1*10.3
From this one can calculate the value of b1:
b1 = logOR(x1)/x1
From above we can give the OR for any other value x=x2:
log OR(x2) = log odds(x0+x2) - log odds(x0) = b1*x2
An from the given x1 (10.3) and the given OR (1.18) we already know b1, so we can substitute b1 and get
log OR(x2) = b1*x2 = logOR(x1) * x2/x1
end thus
OR(x2) = exp(logOR(x1) * x2/x1) = OR(x1)^(x2/x1)
In your case:
log OR(10.0) = 1.18 ^ (10.0/10.3) = 1.174
And the CI:
lower: 0.93 ^ (10.0/10.3) = 0.932
upper: 1.5 ^ (10.0/10.3) = 1.482
[edit: typo]
I am just curious to know whether this study is a retrospective or prospective? Because calculating OR will be straightforward and easy to be interpreted in prospective study. I am doing a something similar using a retrospective study. But I don`t know how to calculate OR and probability of disease given the exposure out of that. Here is the link to my question https://www.researchgate.net/post/How_can_I_use_case-control_study_to_calculate_the_probability_of_the_disease. Your opinion is appreciated. Thanks.
Hi again! Just a follow-up on the same question - is it possible to convert hazard ratios/ risk ratios using the same method? I am assuming not since it is calculated differently? If not, is there another way to standardize HR/ RR for similar pollution intervals?
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