Predicting possible directed-graph patterns of gene expressions in studies involving multiple treatments

Analysis of gene expression data from studies to assess patterns of gene expression to multiple treatments is usually challenging due to the inadequacy of sample size. We introduce an approach of representing gene expression response to multiple treatments using directed graphs and establish a relationship between sample size and a graph property known as contractibility. We exploit this relationship to predict patterns of gene response using synthetic replicates generated from real samples to produce most probable patterns for each pattern observed based on experimental replicates. Prediction based on gene expression simulation was validated with 4 different distribution models of gene expression, including Gaussian, Gaussian mixture, Weibull, and log normal. Across all distributions, we showed that predicting comparison outcomes was quite accurate, with accuracy generally above 0.85. Further, we showed how to apply this method to analyze gene responses to multiple treatments with few samples.