If I want to compare results from one study (measured in odds ratio) with another, is there formal statistical way to do it? Or do I just qualitatively assess the difference between the 2?
For example, I want to test if increase of risk of one disease by some environmental exposure (e.g. OR: 1.3 (95% confidence interval: 1.04-1.86) is really attributed to the environmental source or from occupational source. To test that, I chose to do another study looking at the same exposure and disease, but the source of exposure was occupational. I want to know if risk increase in the first study was really due to exposure from environmental source or occupational or both?
What I'm hearing is that you have odds ratios from two independent samples, and you wish to compare them. Is that right? If so, compute a z-test on the difference between the two ln(OR) values, as follows:
- Y1 = ln(OR) for sample 1
- SE1 = SE(Y1)
- Y2 = ln(OR) for sample 2
- SE2 = SE(Y2)
- SE(Y1-Y2) = SQRT(SE12 + SE22)
- Z = (Y1-Y2)/SE(Y1-Y2)
Your results from the two studies probably show you the SEs directly. If not, you can compute them easily enough from the 95% CIs.
HTH.
If you have enough information to transform the ORs to risk differences then that should be your way forward if all you have are ORs and CIs then frankly you will introduce large uncertanties. If the risk of the disease is very small 1% and below the OR will be very similar to the Relative risk ratio. if the disease is common then the OR will be quite different and if the disease occurence is different in the two studies then the ORs will not be comparable.
OK so let's assume the disease rate is rare in both studies, such that I can convert the OR into RR. How can I say the RR of a certain disease in the 1st study from exposure A is independent of the RR of the same disease in the 2nd study from exposure B?
My hypothesis is risk of breast cancer as measured by environmental exposure to diesel is largely attributed to occupational exposure to diesel. So there will be 2 studies. One looking at environmental exposure to diesel on breast cancer and the other one will look at occupational exposure to diesel on breast cancer. How can the OR/RR from these 2 studies be compared? In other words, how can I say the risk from the 1st study is actually contributed largely by exposure from occupational source?
That would be very though since you have two different populations in two different studies and probably different underlying sample strategies and regression models. so if your theory is that the environmental effect of diesel is mediated through the occupational effect then occupation really should have measured in a study together with whatever measure of environmental exposure. you can of course use a measure of the effect of occupational exposure (including the prevalence of being exposed or not) and run a simulation, but since your underlying populations are not the same you would introduce selection bias and uncertainty.
For a quick and dirty estimation which would only be hypothesis generating you could calculate the attributable risk from the exposures in the two different studies and simply subtract the risk attributed occupational exposure from the environmental exposure. BUT it would require the more than just the ORs
Thanks, the study population is the same. One previous study did the environmental measurement in relation to breast cancer before, my goal is to do the occupational part. I know there's Levene's formula to calculate population attributable risk from OR or RR. Should I just use that to compare?
What I'm hearing is that you have odds ratios from two independent samples, and you wish to compare them. Is that right? If so, compute a z-test on the difference between the two ln(OR) values, as follows:
- Y1 = ln(OR) for sample 1
- SE1 = SE(Y1)
- Y2 = ln(OR) for sample 2
- SE2 = SE(Y2)
- SE(Y1-Y2) = SQRT(SE12 + SE22)
- Z = (Y1-Y2)/SE(Y1-Y2)
Your results from the two studies probably show you the SEs directly. If not, you can compute them easily enough from the 95% CIs.
HTH.
Thanks, actually the sample is the same, but the two studies are independently done. So for example, imagine somebody did a case-control study looking at exposure to environmental diesel on breast cancer on a certain sample. I am planning to do occupational exposure to diesel exposure on breast cancer on the same sample. If you are wondering how can I get the same set of samples for the second study? That's because the both the studies have taken the samples from a national survey of breast cancer patients and non-diseased controls. If I want to disentangle the effect of environmental vs occupational exposure to diesel on breast cancer, what's the statistical approach for that?
If you do not have two independent odds ratios, then:
- SE(Y1-Y2) = SQRT[SE12 + SE22 - 2*COV(Y1,Y2)]
Short of estimating a single mutivariate model that generates estimates of both odds ratios, I'm not sure how you would obtain that covariance term.
For your reference, in addition to the risk differences and the attributable fractions, some other indices of exposure-disease associations may also prove useful, such as the 'causal-pie weights' and the 'completion potentials':
Liao SF, Lee WC. Weighing the causal pies in case-control studies. Ann Epidemiol 2010;20:568-573.
Lee WC. Completion potentials of sufficient component causes. Epidemiology 2012;23:446-453.
Liao SF, Lee WC. Sufficient cause modeling with matched data using SAS. Epidemiology 2013;24:936-937.
How would you separate the environmental exposure group from the occupational exposure group. Supposing an individual has both occupational end environmental exposure, how will you filter the two? I see some flaw in the research question just like Jennifer has noted above
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