For a meta-analysis sometimes studies will report odds ratio or risk ratio only, without reporting number of events.
To incorporate these studies in a meta-analysis using Review Manager (RevMan), one can include these studies under generic inverse variance. However, they must all be the same type (all odds ratio, or all risk ratio).
Odds ratios can be converted into risk ratios using this tool - https://clincalc.com/Stats/ConvertOR.aspx
However, for RevMan you need the lower confidence limit as well. My question is - is the above method of converting odds ratio into risk ratio valid for also converting the odds ratio's lower confidence limit into the odd's ratio lower confidence limit.
Note: this is for teaching purposes, so simple solutions are preferred.
It depends on the source of the odds ratio. It should work for any 2x2 table because the OR is base rate independent and so you can plug the base rate back in. It will break down if you try and use an odds ratio computed in some other way (e.g., for a continuous predictor; for an ordinal model etc.).
I actually think in this case meta-analysis of odds ratios is superior unless all the studies have the same base rate. It seems that you'd be confounding base rate differences in the studies with risk differences if you model the RR. I had a quick look at the literature and it seems as though the answer is "it depends" and one should model the impact of baseline risk regardless of using RR or OR to assess this.
Joseph Whittaker Based on the Zhang and Yu (1998) study, who are the developers of the online tools you have used:
"It can also be used to correct the lower and upper limits of the confidence interval by applying this formula to the lower and upper confidence limits of the adjusted odds ratio."
But there are some concerns about the type of your outcomes [directions of events] and interpretation of results:
In case of exposures that decrease the event rate OR would be lower than RR and vice versa.
Naser Hatami Yes, you are correct (I did not read the paper carefully enough). I have double-checked Zhang and Yu's example calculations, and they do indeed use their formula to convert odds ratio confidence intervals.
Odds ratios (OR) and risk ratios (RR) are measures of the effect size in a statistical analysis, and they are often used to estimate the relationship between an intervention or exposure and an outcome. ORs and RRs can be converted to each other using the following formula:
RR = OR / (1 - p0) + OR * p0
where p0 is the baseline probability of the outcome in the control group.
For example, suppose a study found that the OR for the risk of developing a certain disease among people who were exposed to a certain risk factor was 2.0, and the baseline probability of the disease in the control group was 0.1. To convert the OR to an RR, we can plug these values into the formula:
RR = 2.0 / (1 - 0.1) + 2.0 * 0.1 = 2.2
This means that the risk of developing the disease is 2.2 times higher among people who were exposed to the risk factor compared to those who were not exposed.
It is important to note that ORs and RRs are not interchangeable and have different interpretations. ORs are used to estimate the odds of an event occurring, whereas RRs are used to estimate the relative risk of an event occurring. ORs are generally preferred in case-control studies, whereas RRs are generally preferred in cohort studies.
Osinachi Ekeagwu could you please, explain what baseline probability is?
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