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My outcomes is binary variable. I would like to perform logistic regression model to estimate the treatment effect of Xs. However, the follow up time was longer for outcomes=1 and shorter when outcomes=0. The probability of the outcome can be affected by the follow up time, the longer a subject was followed up, the more chance we observe a outcome=1. I considered including the follow up time as an offset, like poisson regression model. Is it reasonable? Otherwise, how can I control the difference in follow up between the two groups.

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