Gene expression microarray experiments can generate data sets with multiple missing expression values. Unfortunately, many algorithms for gene expression analysis require a complete matrix of gene array values as input. For example, methods such as hierarchical clustering and K-means clustering are not robust to missing data, and may lose effectiveness even with a few missing values. Methods for imputing missing data are needed, therefore, to minimize the effect of incomplete data sets on analyses, and to increase the range of data sets to which these algorithms can be applied. In this report, we investigate automated methods for estimating missing data. We present a comparative study of several methods for the estimation of missing values in gene microarray data. We implemented and evaluated three methods: a Singular Value Decomposition (SVD) based method (SVDimpute), weighted K-nearest neighbors (KNNimpute), and row average. We evaluated the methods using a variety of parameter settings and over different real data sets, and assessed the robustness of the imputation methods to the amount of missing data over the range of 1--20% missing values. We show that KNNimpute appears to provide a more robust and sensitive method for missing value estimation than SVDimpute, and both SVDimpute and KNNimpute surpass the commonly used row average method (as well as filling missing values with zeros). We report results of the comparative experiments and provide recommendations and tools for accurate estimation of missing microarray data under a variety of conditions.

Machine Learning, 24(2), 123-140

Rubin's multiple imputation is a three-step method for handling complex missing data, or more generally, incomplete-data problems, which arise frequently in medical studies. At the first step, m (> 1) completed-data sets are created by imputing the unobserved data m times using m independent draws from an imputation model, which is constructed to reasonably approximate the true distributional relationship between the unobserved data and the available information, and thus reduce potentially very serious nonresponse bias due to systematic difference between the observed data and the unobserved ones. At the second step, m complete-data analyses are performed by treating each completed-data set as a real complete-data set, and thus standard complete-data procedures and software can be utilized directly. At the third step, the results from the m complete-data analyses are combined in a simple, appropriate way to obtain the so-called repeated-imputation inference, which properly takes into account the uncertainty in the imputed values. This paper reviews three applications of Rubin's method that are directly relevant for medical studies. The first is about estimating the reporting delay in acquired immune deficiency syndrome (AIDS) surveillance systems for the purpose of estimating survival time after AIDS diagnosis. The second focuses on the issue of missing data and noncompliance in randomized experiments, where a school choice experiment is used as an illustration. The third looks at handling nonresponse in United States National Health and Nutrition Examination Surveys (NHANES). The emphasis of our review is on the building of imputation models (i.e. the first step), which is the most fundamental aspect of the method.