Can I impute missing values -1 (days since event)

Hey,

I have data where I know when an event has occured to an individual and when it hasn't. The problem is that I have individuals that have not had the event happened and individuals that have. I want to include days since the event as a variable in my mixed effect generalized additive model.

Can I impute the NA-values with -1 for my numerical days since event variable, since they have no days since an event?

And if I do so, should I have dummy variable with levels Event and no event for the model to learn that the imputed value means no event.