Comparing three groups, one dependent variable (binary)

Question

I have a sample consisting of patients from 3 different nationalities (A, B and C). One of my variables is dichotomous, and I want to compare proportions for this variable between nationalities. The hypothesis is that nationality is associated with (and could (partially) explain) this outcome. Based on recent research I would expect there to be a difference in outcome between nationalities A and B. However, I also would like to know whether this difference exists between B and C (and possibly A and C, although hypothetically less likely).

My (made-up) data:

             Nationality            
             A    B     C   Total
Outcome Yes 50    20    17  87
        No  18    23    7   48
    Total   68    43    24  135

Just looking at the data I would expect there to be a significant difference in outcome between groups A and B (and possibly B and C). Based on what I have found from different sources I could use a Chi square / Likelihood Ratio, but this wouldn't help me to determine which groups are significantly different from each other (or would it?).

Alternatively, would it be correct to use a logistic regression? I did a logistic regression with dummies for nationalities B and C (nationality A as baseline group (0) as it is the biggest group and as there seems to be a difference between A and B). Does it make sense to do another regression (dummies for nationalities A and B) to see whether there is also a difference between B and C? Or just make dummies for A and C so I can do the comparisons I am most interested in (B vs. A, B vs. C) in one analysis? I understand that regression and Chi square tests essentially work in different ways, and I am wondering which one would be most appropriate.

Answer 1

You can use a logistic regression. Since you have only one factor variable Nationality it might be practical to omit the intercept. With R notation something like:

mod0 <- glm(Outcome ~ 0 + Nationality, family=binomial, data=your_df)
summary(mod0)

and then, after fitting, you can test the specific contrasts you have expressed interest in.