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Replacing missing values with random observations from the dataset

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I have a large dataset (around 16,000) with missing values for a little less than 1,000 of them. Rather than using a regression to replace the missing values, I would like to replace them randomly with existing observations in the data set(conditional on matching key variables like a stratified age variable, gender, and diagnosis).

I know that I could create a random sample that fits these requirements, but I'm not sure how to them use that sample to replace the missing values.

Thanks for your help!
Heather

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