Additive interaction with conditional logistic regression

[Sayaka Horiuchi]

Dear Statalist,

I am analyzing data from a case-control study using conditional logistic regression.
Could anyone teach me how to fit the additive interaction with the conditional logistic regression?
I understand that the additive risk model can be applicable to case-control studies as well.
Your help is really appreciated.

[Roman Mostazir]

Hi, welcome to the forum. Please follow the forum rules outlined in FAQ section . You could have explained a bit better to help others to understand your problem. However, I am not sure what do you mean by additive interaction. But any term in the right hand side of the equation is an additive term for the regression equation. For example,

 y = a + x + z + error

An interaction term between 'x' and 'z' will be a multiplicative term (x*z) but additive to the equation itself i.e.,

 y = a + x + z + x*z + error

Since you have not explained clearly, I can only imagine that an additive interaction may mean taking the log of x and z i.e.,

y = a + log(x) + log(z) + error

which is equivalent to

y = a + log(x*z) + error

[Paul Dickman]

The following paper provides a definition (in equation 1) of what epidemiologists sometimes call interaction on the additive scale (or "additive interactions"). The same paper also provides Stata code illustrating how to estimate such interactions. The code is for logit, but the same approach applies for clogit.

Tyler J. VanderWeele and Mirjam J. Knol, A Tutorial on Interaction, Journal Epidemiologic Methods
https://doi.org/10.1515/em-2013-0005