For my research I have 2 measurements on pathway activation: STAT1 and STAT3. Both measurements can either be active or inactive. So in total i have 4 groups: STAT1 (active/inactive) and STAT3 (active/inactive).
I want to calculate the risk of having cardiac involvement (yes/no) for these four groups. So, I would want to know the chance of having carciac involvement when STAT1 is active and STAT3 is active but also when STAT1 is active but STAT3 is inactive etc. (for all situations)
What sort of analysis would I have to use to get p-values for all different situations of activation of STAT1 and STAT3.
I'd suggest a binomial model (aka "logistic regression"). You response variable (cardiac involvement) is binary. You have two predictors: STAT1 and STAT3, each of them being catagorical. I'd include the interaction of STAT1 and 3 in the model to see if the combined effect differs from the sum of the individual effects.
The binomial model will estimate the log odds of cardiac involvement depending on the values of the predictors. An "effect" thus is a difference of log odds, what is a log odds ratio. The effect estimates will come with standard errors, and their ratio is approximately z-distributed, so you can use Wald z-Tests to assess the statistical significance of the estimates.
https://data.princeton.edu/r/glms
http://r.qcbs.ca/workshop06/book-en/binomial-glm.html
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