  The literature on differential privacy almost invariably assumes that the
data to be analyzed are fully observed. In most practical applications this is
an unrealistic assumption. A popular strategy to address this problem is
imputation, in which missing values are replaced by estimated values given the
observed data. In this paper we evaluate various approaches to answering
queries on an imputed dataset in a differentially private manner, as well as
discuss trade-offs as to where along the pipeline privacy is considered. We
show that if imputation is done without consideration to privacy, the
sensitivity of certain queries can increase linearly with the number of
incomplete records. On the other hand, for a general class of imputation
strategies, these worst case scenarios can be greatly reduced by ensuring
privacy already during the imputation stage. We use a simulated dataset to
demonstrate these results across a number of imputation schemes (both private
and non-private) and examine their impact on the utility of a private query on
the data.
