  Missing data present challenges in data analysis. Naive analyses such as
complete-case and available-case analysis may introduce bias and loss of
efficiency, and produce unreliable results. Multiple imputation (MI) is one of
the most widely used methods for handling missing data which can be partly
attributed to its ease of use. However, existing MI methods implemented in most
statistical software are not applicable to or do not perform well in
high-dimensional settings where the number of predictors is large relative to
the sample size. To remedy this issue, we develop an MI approach that uses
dimension reduction techniques. Specifically, in constructing imputation models
in the presence of high-dimensional data our approach uses sure independent
screening followed by either sparse principal component analysis (sPCA) or
sufficient dimension reduction (SDR) techniques. Our simulation studies,
conducted for high-dimensional data, demonstrate that using SIS followed by
sPCA to perform MI achieves better performance than the other imputation
methods including several existing imputation approaches. We apply our approach
to analysis of gene expression data from a prostate cancer study.
