**Observational data** can have several sources of bias, for example self selection into the study, treatment selection, or loss to follow up.

Can anybody point me to papers that discuss how one can adjust simultaneously for multiple sources of bias, in particular treatment selection and loss to follow up?

One “naive” idea would be to calculate weights based on multiplied probabilities from 2 selection models. For example, if one had one model for treatment selection and one for loss to follow up, one could be tempted to calculate weights from the multiplied estimated probabilities for treatment and loss to follow up.

However, this approach rests on the assumption that treatment selection and loss to follow up are independent. This seems like an important assumption that could often be false. For example, in the mental health area, pre-treatment symptom strength is associated with higher probabilities probability of both treatment and loss to follow up.

I am especially interested in pointers to structural models (DAGs) of such problems,

but I’ll appreciate any comment or pointer!

Thanks, Guido

PS: I found this discussion of multiplying probabilities from selection models: https://higherlogicdownload.s3.amazonaws.com/AMSTAT/fa4dd52c-8429-41d0-abdf-0011047bfa19/UploadedImages/Posters/2015%20Diqiong.pdf. But this does not discusss the assumptions of the approach, or provides further references.