Immortal time bias

In a retrospective cohort study using an electronic database the exposure is the administration of drug A, the outcome will be mortality. If we select subjects at time zero but subjects that did not receive treatment A do receive it later for various reasons how do we handle that? These subjects will ultimately be considered as having received treatment A yet they will have a potentially significant head start. I read that a time-varying Cox regression model is a potential solution but know very little about its methodology. Are there other options?

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Landmark analysis, see here


Thank you Jochen, this is just what I was looking for.