Dear Chandrasekhar:

You have to covert the probabilities in rates in the control group:

p=1-e^(-rt)

Once the rates are calculated, you can multiply the rates by relative risk. After that,

you have to convert the rates in probabilities.

r=(-ln(1-p))/t

Sincerely,

Vicente Gimeno Ballester

Dear Vicente Gimeno Ballester,

Thank you so much for your  response and valuable information.

I will follow your method and i will get back to you if further assistance  needed.

It would be more beneficial for me if you could provide the source (reference) for detailed explanation of above mentioned formula.

Thanks,

Boya chandrasekhar

contact mail ID: [email protected]

Hi. I am almost certain that the first answer you received is incorrect.

First off, the answer is different for OR versus RR because the two are defined differently. Here is a link to an excellent ResearchGate description of the difference by Rafik Karaman that shows both formulas.

https://www.researchgate.net/post/What_is_the_meaning_of_Odds_ratio_and_Risk_ratio_and_how_can_use_them_in_epidemiological_studies

I’d add that by the method of Zhang & Yu, If P is the probability of the outcome in the unexposed group, RR = OR /((1-P) + (P*OR))

Zhang J, Yu KF. What’s the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes. JAMA. 1998; 280:1690–1.

Second, the first response assumed you have log odds (the logit coefficient) rather than the OR or RR. Most statistical packages let you choose your outputs and offer OR output that has already been exponentiated. Don’t do that twice.

Third, if you look at the definitions, you will realize that both RR and OR are ratios. You cannot compute the probabilities from the OR or the RR without supplying some of the probabilities from another source. Since RR is the ratio of the probabilities of a positive outcome, treatment/control, if you know the probability absent intervention, simply multiply by the RR to get the probability with intervention. So the (presumably good) outcome in your case would be 1.67 times as likely in the treatment group as it is in the control group.

I am a bit surprised that your meta-analysis gives you a RR rather than an effect size differential. If indeed, you have an effect size there, the answer is entirely different. BESD gives a quick approximation. But BESD can be way off. For a better method, see my article:

Exact Method for Computing Absolute Percentage Change in a Dichotomous Outcome from Meta-Analytic Effect Size: Improving Impact and Cost-Outcome Estimates, T Miller, J Derzon, D Hendrie, Value in Health, 14:1, 144-151, 2011.

Dear Dr. Miller,

I appreciate your response and I find it really helpful. I am conducting a CEA about renal transplant patients comparing between sirolimus and Belatacept as prophylaxis post transplant. I am trying to redo the analysis in this study

https://www.dovepress.com/cost-utility-analysis-of-immunosuppressive-regimens-in-adult-renal-tra-peer-reviewed-article-PPA

using my own cost data but I didn't understand how did the authors use OR, RR to calculate probabilities (not mentioned clearly in the full text)?

I appreciate your help and support

Thanks