Time-dependent variables questions

I've been asked to comment on a retrospective cohort study and I have a bit of a dilemma.

Participants in the cohort had the option of receiving up to 3 treatments (0-3 exposures) over a series of months. Each contributed person-time until they caught the disease, died, etc. The disease outcome was fairly rare (about 500 per 100,000 person-years). A Poisson model was used.

The majority of person-time among those who received any treatment came from those who received all 3. Relatively few received only 1 (but more people). The vast majority received no treatments. In other words, it would appear as though those who opted for treatment, did it early, received all 3 treatments, and contributed more person-time.

The researchers defined treatment as a time-dependent variable arguing that this allowed each participant to contribute person-time to each treatment level (0 treatments, 1 treatment, etc).

However, my colleagues think that this approach may bias towards a single treatment, and that a better approach would be to categorize each participant based on the number of treatments they ended up with at study end (e.g., no treatments, 1 treatment, etc).

Both approaches make sense to me, so I'm unsure about which one is best.

Secondarily, I'm not so sure about the Poisson model. Given the relative rarity of the event, maybe a zero-inflated Poisson would be better, or perhaps a Cox proportional hazards model.
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