Does multiple imputation (MI) introduce bias in estimates? I am trying to use MI to deal with missing values in my data set. If I understand correctly, MI is about simulating multiple data sets from a given initial data set and imputing possible values derived from them. But if I am to run statistical analysis with data set completed by MI, am I essentially not using the same initial data set twice, and thereby introducing bias into the analysis?
I get the impression that this is not the case. Is there something I am missing about MI that prevents bias?
Thanks.
 A: First, recognize that other methods of dealing with missing data either introduce bias (depending on the type of "missingness") or mis-estimate the standard errors of estimates. See Table 1.1 of Stef van Buuren's Flexible Imputation of Missing Data.
Second, although multiple imputation (MI) might lead to bias in some circumstances, that does not arise from "using the same initial data set" multiple times, as you seem to fear. Consider the situation in which there are no missing data: estimating a parameter value from multiple copies of the data set will give exactly the same results each time. If you had multiple complete data sets sampled from the population, there will be different parameter estimates from data sample to data sample. Unless the estimation method itself has bias, however, the average among those estimates from multiple data sets in the limit should equal the true population value. That's unbiased. It's possible that the estimate based on any single complete data set will produce a parameter estimate far from the true value, but the definition of "bias" in statistics is in terms of the expected value of the parameter estimate rather than the error in any one estimate.
So the question is whether the combination of the pattern of the missing data and the methods used for multiple imputation lead to bias in a particular situation. Chapter 2.5.2 of van Buuren's book shows how to evaluate that possibility.
