How to correctly combine two binary variables into one dependent variable?

I want to create a combined death or stroke rate binary variable.
For each row (patient data), I have data for death and stroke (yes/no) separately.

How should I create the two variables into one dependent variable to use in multivariate logistic models?
I worry that simply using the OR function (e.g. >alldata$DeathStroke <- ifelse(alldata$Death=="Yes"| alldata$Stroke=="Yes", c("Yes"), c("No")) will involve unwanted interaction.. Or, would that be okay?

I'm using R.

Thank you in advance for your help!