Silhouette Scores for Arbitrary Defined Groups in Gene Expression Data and Insights into Differential Expression...

Hierarchical Sample clustering (HSC) is widely performed to examine associations within expression data obtained from microarrays and RNA sequencing (RNA-seq). Researchers have investigated the HSC results with several possible criteria for grouping (e.g., sex, age, and disease types). However, the evaluation of arbitrary defined groups still counts in subjective visual inspection.

To objectively evaluate the degree of separation between groups of interest in the HSC dendrogram, we propose to use Silhouette scores. Silhouettes was originally developed as a graphical aid for the validation of data clusters. It provides a measure of how well a sample is classified when it was assigned to a cluster by according to both the tightness of the clusters and the separation between them. It ranges from 1.0 to - 1.0, and a larger value for the average silhouette (AS) over all samples to be analyzed indicates a higher degree of cluster separation. The basic idea to use an AS is to replace the term cluster by group when calculating the scores. We investigated the validity of this score using simulated and real data designed for differential expression (DE) analysis. We found that larger (or smaller) AS values agreed well with both higher (or lower) degrees of separation between different groups and higher percentages of differentially expressed genes (P_DEG). We also found that the AS values were generally independent on the number of replicates (N_rep). Although the P_DEG values depended on N_rep, we confirmed that both AS and P_DEG values were close to zero when samples in the data showed an intermingled nature between the groups in the HSC dendrogram.

Silhouettes is useful for exploring data with predefined group labels. It would help provide both an objective evaluation of HSC dendrograms and insights into the DE results with regard to the compared groups.