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I was wondering how does one study the average treatment affect in scenarios suchs as mortality rates.

For example: suppose we want to study the effect that a certain medicine has on the mortality rates os the patients. How can we do a study such as Difference-In-Differences or Propensity Scores if the differences before the treatment are zero? (for a patient to receive or not the treatment he/she has to not have died before being given the treatment, so the mortality rates of the control and treatment group are zero)

Can someone help me understand causal inference in this situations where there's no difference before the treatment is implemented?

Thank you!

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Patients will likely differ in terms of measurable pre-treatment attributes. If you have access to these covariates, they should be an input to you adjusting method of choice (i.e. inverse propensity weighting). What do you mean by "differences before the treatment are zero?" If by that you mean that the propensity of each treatment assignment is independent conditioned on all attributes (treatment is random), then correlation is causation and the causal effect is easily calculated. But that is not likely to be the case.

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