Gene expression time series (GETS) analysis aims to characterize sets of genes according to their longitudinal patterns of expression. Due to the large number of genes evaluated in GETS analysis, an useful strategy to summarize biological functional processes and regulatory mechanisms is through clustering of genes that present similar expression pattern over time. Traditional cluster methods usually ignore the challenges in GETS, such as the lack of data normality and small number of temporal observations. Independent Component Analysis (ICA) is a statistical procedure that uses a transformation to convert raw time series data into sets of values of independent variables, which can be used for cluster analysis to identify sets of genes with similar temporal expression patterns. ICA allows clustering small series of distribution-free data while accounting for the dependence between subsequent time-points. Using temporal simulated and real (four libraries of two pig breeds at 21, 40, 70 and 90 days of gestation) RNA-seq data set we present a methodology (ICAclust) that jointly considers independent components analysis (ICA) and a hierarchical method for clustering GETS. We compare ICAclust results with those obtained for K-means clustering. ICAclust presented, on average, an absolute gain of 5.15% over the best K-means scenario. Considering the worst scenario for K-means, the gain was of 84.85%, when compared with the best ICAclust result. For the real data set, genes were grouped into six distinct clusters with 89, 51, 153, 67, 40, and 58 genes each, respectively. In general, it can be observed that the 6 clusters presented very distinct expression patterns. Overall, the proposed two-step clustering method (ICAclust) performed well compared to K-means, a traditional method used for cluster analysis of temporal gene expression data. In ICAclust, genes with similar expression pattern over time were clustered together.

Genomic selection (GS) is a variant of marker-assisted selection, in which genetic markers covering the whole genome predict individual genetic merits for breeding. GS increases the accuracy of breeding values (BV) prediction. Although a variety of statistical models have been proposed to estimate BV in GS, few methodologies have examined statistical challenges based on non-normal phenotypic distributions, e.g., skewed distributions. Traditional GS models estimate changes in the phenotype distribution mean, i.e., the function is defined for the expected value of trait-conditional on markers, E(Y|X). We proposed an approach based on regularized quantile regression (RQR) for GS to improve the estimation of marker effects and the consequent genomic estimated BV (GEBV). The RQR model is based on conditional quantiles, Qt(Y|X), enabling models that fit all portions of a trait probability distribution. This allows RQR to choose one quantile function that "best" represents the relationship between the dependent and independent variables. Data were simulated for 1000 individuals. The genome included 1500 markers; most had a small effect and only a few markers with a sizable effect were simulated. We evaluated three scenarios according to symmetrical, positively, and negatively skewed distributions. Analyses were performed using Bayesian LASSO (BLASSO) and RQR considering three quantiles (0.25, 0.50, and 0.75). The use of RQR to estimate GEBV was efficient; the RQR method achieved better results than BLASSO, at least for one quantile model fit for all evaluated scenarios. The gains in relation to BLASSO were 86.28 and 55.70% for positively and negatively skewed distributions, respectively.

We propose and evaluate a novel approach for forecasting gene expression over non-observed times in longitudinal trials under a Bayesian viewpoint. One of the aims is to cluster genes that share similar expression patterns over time and then use this similarity to predict relative expression at time points of interest. Expression values of 106 genes expressed during the cell cycle of Saccharomyces cerevisiae were used and genes were partitioned into five distinct clusters of sizes 33, 32, 21, 16, and 4. After removing the last observed time point, the agreements of signals (upregulated or downregulated) considering the predicted expression level were 72.7, 81.3, 76.2, 68.8, and 50.0%, respectively, for each cluster. The percentage of credibility intervals that contained the true values of gene expression for a future time was similar to 90%. The methodology performed well, providing a valid forecast of gene expression values by fitting an autoregressive panel data model. This approach is easily implemented with other time-series models and when Poisson and negative binomial probability distributions are assumed for the gene expression data.