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Some of the outcome data in my data set are missing. I believe that the missing data mechanism is missing at random (MAR) as the observed characteristics significantly differ between the missing and non-missing data but there is no theoretical background supporting that there are unobserved factors that can determine if the data is missing or not.

I want to drop the missing observations instead of using an imputation method. However, I am not sure how to prevent bias. I can control for the factors that explain if the data is missing or not simply by adding them into regression but I am not sure if this would be enough.

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One option is to run the regression analysis both ways (imputation vs dropping) and see which results are more useful. For your problem, find the best empirical estimate of bias and see if that estimate changes because on the feature engineering choice.

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