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I have been reading about how to deal with missing values in predictive modeling and majority of the suggested solutions deal with either imputation or deletion. But what to do with missing values where imputing or deleting them removes valuable information?

For example: Lets assume one of my variables is blood pressure, where in most cases patients have had their blood pressure measured and recorded in their health records, when they have gone for any medical appointment in the past. Some cases however, where a patient has not had a reason for a medical appointment and has thus never had their blood pressure recorded, the value is missing. If we assume that not having had a reason to go to a medical appointment is a predictor of health as well, imputing the missing values would cause us to lose valuable information. In a case like that, how do you deal with missing values ?

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