MOTIVATION: In genetic association studies, linear mixed models (LMMs) are used to test for associations between phenotypes and candidate single nucleotide polymorphisms (SNPs). These same models are also used to estimate heritability, which is central not only to evolutionary biology but also to the prediction of the response to selection in plant and animal breeding, as well as the prediction of disease risk in humans. However, when one or more of the underlying assumptions are violated, the estimation of variance components may be compromised and therefore so may the estimates of heritability and any other functions of these. Considering that datasets obtained from real life experiments are prone to several sources of contamination, which usually induce the violation of the assumption of the normality of the errors, a robust derivative-free restricted-maximum likelihood framework (DF-REML) together with a robust coefficient of determination are proposed for the LMM in the context of genetic studies of continuous traits. RESULTS: The proposed approach, in addition to the robust estimation of variance components and robust computation of the coefficient of determination, allows in particular for the robust estimation of SNP-based heritability by reducing the bias and increasing the precision of its estimates. The performance of both classical and robust DF-REML approaches is compared via a Monte Carlo simulation study. Additionally, three examples of application of the methodologies to real datasets are given in order to validate the usefulness of the proposed robust approach. Although the main focus of this article is on plant breeding applications, the proposed methodology is applicable to both human and animal genetic studies. AVAILABILITY AND IMPLEMENTATION: Source code implemented in R is available in the Supplementary Material. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Gene set analysis (GSA) has become a successful tool to interpret gene expression profiles in terms of biological functions, molecular pathways, or genomic locations. GSA performs statistical tests for independent microarray samples at the level of gene sets rather than individual genes. Nowadays, an increasing number of microarray studies are conducted to explore the dynamic changes of gene expression in a variety of species and biological scenarios. In these longitudinal studies, gene expression is repeatedly measured over time such that a GSA needs to take into account the within-gene correlations in addition to possible between-gene correlations. RESULTS: We provide a robust nonparametric approach to compare the expressions of longitudinally measured sets of genes under multiple treatments or experimental conditions. The limiting distributions of our statistics are derived when the number of genes goes to infinity while the number of replications can be small. When the number of genes in a gene set is small, we recommend permutation tests based on our nonparametric test statistics to achieve reliable type I error and better power while incorporating unknown correlations between and within-genes. Simulation results demonstrate that the proposed method has a greater power than other methods for various data distributions and heteroscedastic correlation structures. This method was used for an IL-2 stimulation study and significantly altered gene sets were identified. CONCLUSIONS: The simulation study and the real data application showed that the proposed gene set analysis provides a promising tool for longitudinal microarray analysis. R scripts for simulating longitudinal data and calculating the nonparametric statistics are posted on the North Dakota INBRE website http://ndinbre.org/programs/bioinformatics.php. Raw microarray data is available in Gene Expression Omnibus (National Center for Biotechnology Information) with accession number GSE6085.

MOTIVATION: The analysis of spotted cDNA microarrays involves scanning of color signals from fluorescent dyes. A common problem is that a given scanning intensity is not usually optimal for all spotted cDNAs. Specifically, some spots may be at the saturation limit, resulting in poor separation of signals from different tissues or conditions. The problem may be addressed by multiple scans with varying scanning intensities. Multiple scanning intensities raise the question of how to combine different signals from the same spot, particularly when measurement error is not negligible. RESULTS: This paper suggests a non-linear latent regression model for this purpose. It corrects for biases caused by the saturation limit and efficiently combines data from multiple scans. Combining multiple scans also allows reduction of technical error particularly for cDNA spots with low signal. The procedure is exemplified using cDNA expression data from maize. AVAILABILITY: All methods were implemented using standard procedures available in the SAS/STAT module of the SAS System. Programming statements are available from the first author upon request. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: The supplementary data are available at Bioinformatics online.