# What's the interpretation of the ratio of the odds ratio between the experimental and the control arm?

Table 1 of this article show the associations between the outcome and variables, the authors presented the OR_ctr in control arm and OR_trt in the treatment arm and the ratio of these two measures.

I'm a little confused about the interpretation and the usefulness of the ratio of odds ratio between the experimental and the control arm: OR_trt / OR_ctr.

1. Does this ratio have the same interpretation of OR? Why do one calculate it?
2. How did they generate their data? Did they calculate OR_trt / OR_ctr to see the interaction between the variables and the treatment?
3. What is the relationship between treatment effect or risk difference, treatment benefit, and OR_trt / OR_ctr?

I would be grateful if someone could clarify these points for me.

Thank you for your help :) !

• Could you add more detail? It's not clear to me how you have 2 separate odds ratios: one for the control group and one for the experimental group. Could those just be odds for each group?
– TPM
Commented Jan 6, 2020 at 18:35
• @TPM They used OR_ctr for the control arm, I don't know how they calculated it? And how did they generate the outcomes for the control arm using OR_ctr? Commented Jan 7, 2020 at 13:39
• This doesn't make much sense to me. Normally you would have a binary variable indicating which group the subject is in, and a corresponding OR. I don't see how you get an OR for each group. Commented Jan 7, 2020 at 14:05

The table displayed in this question shows the choices of parameter values for a simulation study, not experimentally determined or calculated odds ratios. The simulation involved 12 binary covariates (the $$\mathsf {x_i}$$) each with a prevalence of 20% having the indicated associations with outcome without treatment ($$\mathsf {OR_C}$$). In one set of simulations ("Treatment arm, without interactions") these same odds ratios with respect to outcome were used for these covariates in the treatment group $$(\mathsf{OR_{TR}=OR_C})$$ so that the influence of treatment on outcome was independent of the covariate values. In the other set of simulations ("Treatment arm, with interactions") the effect of treatment was specified as shown in the table to depend on the covariate values as well.