Comparative analysis of missing value imputation methods to improve clustering and interpretation of microarray experiments

Abstract

Background: Microarray technologies produced large amount of data. In a previous study, we have shown the interest of k-Nearest Neighbour approach for restoring the missing gene expression values, and its positive impact of the gene clustering by hierarchical algorithm. Since, numerous replacement methods have been proposed to impute missing values (MVs) for microarray data. In this study, we have evaluated twelve different usable methods, and their influence on the quality of gene clustering. Interestingly we have used several datasets, both kinetic and non kinetic experiments from yeast and human.

Results: We underline the excellent efficiency of approaches proposed and implemented by Bo and co-workers and especially one based on expected maximization (EM_array). These improvements have been observed also on the imputation of extreme values, the most difficult predictable values. We showed that the imputed MVs have still important effects on the stability of the gene clusters. The improvement on the clustering obtained by hierarchical clustering remains limited and, not sufficient to restore completely the correct gene associations. However, a common tendency can be found between the quality of the imputation method and the gene cluster stability. Even if the comparison between clustering algorithms is a complex task, we observed that k-means approach is more efficient to conserve gene associations.

Conclusions: More than 6.000.000 independent simulations have assessed the quality of 12 imputation methods on five very different biological datasets. Important improvements have so been done since our last study. The EM_array approach constitutes one efficient method for restoring the missing expression gene values, with a lower estimation error level. Nonetheless, the presence of MVs even at a low rate is a major factor of gene cluster instability. Our study highlights the need for a systematic assessment of imputation methods and so of dedicated benchmarks. A noticeable point is the specific influence of some biological dataset.

Figure 1

Principle of the method. The initial data matrix is analyzed. Each gene associated to at least one missing value (in pink) is excluded given a Reference matrix without any missing value. Then missing values are simulated (in red) with a fixed rate τ. This rate τ goes from 0.5% to 50% of missing values by step of 0.5%. 100 independent simulations are done each time. Missing values are then imputed (in blue) for each simulations by the selected methods. RMSE is computed between the estimated values of missing values and their true values.

Figure 2

Example of three methods. Distribution of predicted values (y-axis) in regards to true values (x-axis). Estimation of the missing values has been done (a) by kNN approach, (b) EM_gene and (c) EM_array. The dataset used is the Bohen set with τ values ranging from 0.5% to 50% of missing values with a step of 0.5. 10 independent simulations have been done for each τ value.

Figure 3

Missing value imputation. RMSE value for (a) G_Heat subset and (b) for OS for rate of missing value going from 0.5% to 50% by step of 0.5%. (b) 100 independent simulations are done at each level.

Figure 4

Extreme values (representing 1% of the missing values). Evolution of RMSE according to τ ranging (a) from 0.5% to 30% of the extreme values for the Bohen dataset and (b) from 0.5% to 50% of the extreme values) for the Ogawa dataset.

Figure 5

CPP of hierarchical clustering approach algorithm. (a) with complete, average, ward and McQuitty algorithm for OS with kNN and (b) with Ward algorithm for Ogawa dataset for the different imputation methods.

Figure 6

Summary of the comparison.