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Suppose I have a dataset, and I want to use it to analyse the association between BMI and stroke. The dataset has some missingness for BMI(independent variable) and some missingness for covariates such as blood pressure. There are many complete covariates and suppose the dataset could be imputed.

My question is whether I could impute the BMI (independent variable) and missed covariates using other complete covariates? A coauthor said that what I could impute is only covariates, not independent variable. Is it right?

If the outcome (dependent variable) is also missed, could I impute that? (impute independent and dependent variables and covariates using other complete variables?)

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There are many opinions on the matter. Naysayers seem to get nervous, especially, about imputing outcomes. But the validity of imputation is a theoretical result, and the theory supports imputing anything you want: independent variable, outcome, and covariates. The known contraindication for imputation is missing not at random (MNAR) data, that is missingness depends on the missing value itself. I find it especially odd that, when the discussion of imputation is presented, there is an assumption that imputation of the outcome should be particularly scrutinized for this bias. Wrongly imputing any covariate can lead to arbitrarily bad/wrong inference! Unfortunately, there's no real way to verify the assumption, and the requirement of no MNAR is common to all missing data methods: even complete case analysis. As my professor told me: the best solution for missing data is not to have it. When I refer to "imputation" I specifically mean multiple imputation.

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  • $\begingroup$ I like the opinion that your professor told you. Unfortunately, it is difficult to avoid missing data in practice. I have to deal with these missing data as correctly as possible. My professor is not familar with multiple imputation and told me I could not impute the exposure variable (only impute the covariates). $\endgroup$
    – li jiaqi
    Jan 12 at 8:17
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    $\begingroup$ What would he do if the exposure is missing? Excluding records from analysis makes even stronger assumptions than any imputation. E.g. MI is valid under some assumptions (e.g. MAR + certain distributional assumptions, also some MNAR scenarios), & is somewhat wrong if assumptions aren't met. Excluding records ("complete case analysis") makes an incredibly strong missing completely at random assumption that is usually guaranteed to be wrong & is known to often lead to huge bias (you can of course hope that for you it's not so bad/that so little data are missing that it has little effect). $\endgroup$
    – Björn
    Jan 12 at 9:12
  • $\begingroup$ @lijiaqi tagging for transparency. Bjorn's point is well made and consistent with this answer: not imputing is also a decision that requires assumptions tantamount to those for imputation. $\endgroup$
    – AdamO
    Jan 12 at 17:06
  • $\begingroup$ @Björn (My english is not good so I want to confirm your opinion. You think complete case analysis leads to huge bias, and imputation is necessary, right?) Most of our previous studies were based on complete case analysis and used dummy varibales for missed covariates. I read many journal`s statistical recommendations and started to use multiple imputation. I agree with your opinion and am reading more related paper. $\endgroup$
    – li jiaqi
    Jan 13 at 0:49
  • $\begingroup$ Thank you AdamO. And could you tell me how to tag for transparency? I do not understand that. $\endgroup$
    – li jiaqi
    Jan 13 at 0:52

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