Analyzing Microarray Data With Transitive Directed Acyclic Graphs

Abstract

Post hoc assignment of patterns determined by all pairwise comparisons in microarray experiments with multiple treatments has been proven to be useful in assessing treatment effects. We propose the usage of transitive directed acyclic graphs (tDAG) as the representation of these patterns and show that such representation can be useful in clustering treatment effects, annotating existing clustering methods, and analyzing sample sizes. Advantages of this approach include: (1) unique and descriptive meaning of each cluster in terms of how genes respond to all pairs of treatments; (2) insensitivity of the observed patterns to the number of genes analyzed; and (3) a combinatorial perspective to address the sample size problem by observing the rate of contractible tDAG as the number of replicates increases. The advantages and overall utility of the method in elaborating drug structure activity relationships are exemplified in a controlled study with real and simulated data.

Clustering of high throughput gene expression data

“…Zhu et al (2005) use a hybrid distance matrix having both direct and shortest-path distances for clustering. Phan et al (2009) also use transitive directed acyclic graphs for representation of expression patterns. Once the data are clustered based on a distance measure, validation of the clustering algorithm's performance is essential.…”

Ensemble Clustering for Biological Datasets

“…NP-complete is a class of problems that are in NP and reducible to an NP-complete problem in polynomial time. Some examples of graph theory-based clustering approaches are: [30] and [24].…”

Pattern analysis

“…Researchers employed dozens to hundreds of treatments in their studies [1,6]. To deal with such many treatments, a number of post hoc approaches have been proposed [8,5,7]. While [8,5] used ternary digits to represent patterns of gene response to all treatment pairs, [7] used directed graphs to represent these patterns.…”

“…To deal with such many treatments, a number of post hoc approaches have been proposed [8,5,7]. While [8,5] used ternary digits to represent patterns of gene response to all treatment pairs, [7] used directed graphs to represent these patterns. In ternary digit representation, each pattern has a sequence of digits in which each digit represents how a gene respond to pairs of treatments.…”

“…However, while sample size calculated from these methods might be enough for many genes, it might not be for others, which respond more variably across samples. Moreover, determining significantly expressions genes might not be enough for microarray experiments including multiple treatments [7], [8]. Authors in [7] connected the analysis of sample size to a property of directed graphs known as contractibility.…”