Missing value imputation in high-dimensional phenomic data: imputable or not, and how?

Abstract

Background: In modern biomedical research of complex diseases, a large number of demographic and clinical variables, herein called phenomic data, are often collected and missing values (MVs) are inevitable in the data collection process. Since many downstream statistical and bioinformatics methods require complete data matrix, imputation is a common and practical solution. In high-throughput experiments such as microarray experiments, continuous intensities are measured and many mature missing value imputation methods have been developed and widely applied. Numerous methods for missing data imputation of microarray data have been developed. Large phenomic data, however, contain continuous, nominal, binary and ordinal data types, which void application of most methods. Though several methods have been developed in the past few years, not a single complete guideline is proposed with respect to phenomic missing data imputation.

Results: In this paper, we investigated existing imputation methods for phenomic data, proposed a self-training selection (STS) scheme to select the best imputation method and provide a practical guideline for general applications. We introduced a novel concept of "imputability measure" (IM) to identify missing values that are fundamentally inadequate to impute. In addition, we also developed four variations of K-nearest-neighbor (KNN) methods and compared with two existing methods, multivariate imputation by chained equations (MICE) and missForest. The four variations are imputation by variables (KNN-V), by subjects (KNN-S), their weighted hybrid (KNN-H) and an adaptively weighted hybrid (KNN-A). We performed simulations and applied different imputation methods and the STS scheme to three lung disease phenomic datasets to evaluate the methods. An R package "phenomeImpute" is made publicly available.

Conclusions: Simulations and applications to real datasets showed that MICE often did not perform well; KNN-A, KNN-H and random forest were among the top performers although no method universally performed the best. Imputation of missing values with low imputability measures increased imputation errors greatly and could potentially deteriorate downstream analyses. The STS scheme was accurate in selecting the optimal method by evaluating methods in a second layer of missingness simulation. All source files for the simulation and the real data analyses are available on the author's publication website.

Figure 1

Heatmap of distance matrix in simulation I. (a) Variable and (b) Subject distance matrixes of Simulation I. (black: small distance/high correlation; white: large distance/low correlation).

Figure 2

Diagram of evaluating performance of STS scheme in a real complete data set (CD). Missing data sets are randomly generated for 20 times (MD₁, ⋅⋅⋅, MD₂₀). The STS scheme is applied to learn the best method from STS simulation (denoted as M_b,STS for the b-th missing data set MD_b). The true best (in terms of RMSE) method for MD_b is denoted as M_b* and the STS best (in terms of RMSE across MD_b,1, …, MD_b,20) method is denoted as M_b,STS. When M_b,STS = M_b*, the STS scheme successfully selects the optimal method.

Figure 3

Boxplots of RMSE/PFC for (a) Simulation I and (b) Simulation II and (c) Simulation III. KNN-based methods: KNN-V, KNN-S, KNN-H and KNN-A; RF: MissForest algorithim; MICE: multivariate imputation by chained equations; MeanImp: mean imputation.

Figure 4

Boxplots of RMSE/PFC for (a) COPD; (b) SARP and (c) LTRC. KNN-based methods: KNN-V, KNN-S, KNN-H and KNN-A; RF: MissForest algorithm; MeanImp: Mean imputation.

Figure 5

Boxplots of RMSE/PFC evaluated using (1) all imputed values and (2) only imputable values in LTRC dataset. Boxplots of RMSE/PFC evaluated using (1) all imputed values and (2) only imputable values in LTRC dataset with m =5% missingness. Color: grey (evaluation using all imputed values); white (evaluation using only imputable values).

Figure 6

An application guideline to apply the STS scheme for a real dataset with missing values.