I have a dataset that consists of health insurance members. For each member, I have individual air pollution exposure measures for 2009, 2012, 2015 and 2018 and individual depression (outcome) measures for those same years. All the people in my dataset have moved to a new address between 2009 and 2018 and I wanted to analyze whether changes in air pollution exposure due to moving lead to changes in the outcome (depression). My plan was to calculate the difference in exposure before vs after moving and calculate the difference in outcome before vs after moving and see whether those two variables are correlated. So I would effectively check the correlation between the change in exposure and the change in outcome due to moving to a new address.

I am looking for publications with a similar design and I wonder if there is a specific name for this kind of design/analysis, can anyone help me out?

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