Jode W. Edwards

Power and sample size estimation in high dimensional biology

Genomic scientists often test thousands of hypotheses in a single experiment. One example is a microarray experiment that seeks to determine differential gene expression among experimental groups. Planning such experiments involves a determination of sample size that will allow meaningful interpretations. Traditional power analysis methods may not be well suited to this task when thousands of hypotheses are tested in a discovery oriented basic research. We introduce the concept of expected discovery rate (EDR) and an approach that combines parametric mixture modelling with parametric bootstrapping to estimate the sample size needed for a desired accuracy of results. While the examples included are derived from microarray studies, the methods, herein, are ‘extraparadigmatic’ in the approach to study design and are applicable to most high dimensional biological situations. Pilot data from three different microarray experiments are used to extrapolate EDR as well as the related false discovery rate at different sample sizes and thresholds.

The PowerAtlas : a power and sample size atlas for microarray experimental design and research

BackgroundMicroarrays permit biologists to simultaneously measure the mRNA abundance of thousands of genes. An important issue facing investigators planning microarray experiments is how to estimate the sample size required for good statistical power. What is the projected sample size or number of replicate chips needed to address the multiple hypotheses with acceptable accuracy? Statistical methods exist for calculating power based upon a single hypothesis, using estimates of the variability in data from pilot studies. There is, however, a need for methods to estimate power and/or required sample sizes in situations where multiple hypotheses are being tested, such as in microarray experiments. In addition, investigators frequently do not have pilot data to estimate the sample sizes required for microarray studies.ResultsTo address this challenge, we have developed a Microrarray PowerAtlas [1]. The atlas enables estimation of statistical power by allowing investigators to appropriately plan studies by building upon previous studies that have similar experimental characteristics. Currently, there are sample sizes and power estimates based on 632 experiments from Gene Expression Omnibus (GEO). The PowerAtlas also permits investigators to upload their own pilot data and derive power and sample size estimates from these data. This resource will be updated regularly with new datasets from GEO and other databases such as The Nottingham Arabidopsis Stock Center (NASC).ConclusionThis resource provides a valuable tool for investigators who are planning efficient microarray studies and estimating required sample sizes.

Applications of Bayesian Statistical Methods in Microarray Data Analysis

Microarray technology allows one to measure gene expression levels simultaneously on the whole-genome scale. The rapid progress generates both a great wealth of information and challenges in making inferences from such massive data sets. Bayesian statistical modeling offers an alternative approach to frequentist methodologies, and has several features that make these methods advantageous for the analysis of microarray data. These include the incorporation of prior information, flexible exploration of arbitrarily complex hypotheses, easy inclusion of nuisance parameters, and relatively well developed methods to handle missing data.Recent developments in Bayesian methodology generated a variety of techniques for the identification of differentially expressed genes, finding genes with similar expression profiles, and uncovering underlying gene regulatory networks. Bayesian methods will undoubtedly become more common in the future because of their great utility in microarray analysis.

The effect of artificial selection on phenotypic plasticity in maize

Remarkable productivity has been achieved in crop species through artificial selection and adaptation to modern agronomic practices. Whether intensive selection has changed the ability of improved cultivars to maintain high productivity across variable environments is unknown. Understanding the genetic control of phenotypic plasticity and genotype by environment (G × E) interaction will enhance crop performance predictions across diverse environments. Here we use data generated from the Genomes to Fields (G2F) Maize G × E project to assess the effect of selection on G × E variation and characterize polymorphisms associated with plasticity. Genomic regions putatively selected during modern temperate maize breeding explain less variability for yield G × E than unselected regions, indicating that improvement by breeding may have reduced G × E of modern temperate cultivars. Trends in genomic position of variants associated with stability reveal fewer genic associations and enrichment of variants 0–5000 base pairs upstream of genes, hypothetically due to control of plasticity by short-range regulatory elements.Breeding has increased crop productivity, but whether it has also changed phenotypic plasticity is unclear. Here, the authors find maize genomic regions selected for high productivity show reduced contribution to genotype by environment variation and provide evidence for regulatory control of phenotypic stability.

Empirical Bayes estimation of gene-specific effects in micro-array research

Micro-array technology allows investigators the opportunity to measure expression levels of thousands of genes simultaneously. However, investigators are also faced with the challenge of simultaneous estimation of gene expression differences for thousands of genes with very small sample sizes. Traditional estimators of differences between treatment means (ordinary least squares estimators or OLS) are not the best estimators if interest is in estimation of gene expression differences for an ensemble of genes. In the case that gene expression differences are regarded as exchangeable samples from a common population, estimators are available that result in much smaller average mean-square error across the population of gene expression difference estimates. We have simulated the application of such an estimator, namely an empirical Bayes (EB) estimator of random effects in a hierarchical linear model (normal-normal). Simulation results revealed mean-square error as low as 0.05 times the mean-square error of OLS estimators (i.e., the difference between treatment means). We applied the analysis to an example dataset as a demonstration of the shrinkage of EB estimators and of the reduction in mean-square error, i.e., increase in precision, associated with EB estimators in this analysis. The method described here is available in software that is available at http://www.soph.uab.edu/ssg.asp?id=1087.

Association Mapping of Flowering and Height Traits in Germplasm Enhancement of Maize Doubled Haploid (GEM-DH) Lines

Genome‐wide association mapping in exotic derived double haploid maize lines. Genomic areas collocate with previously identified QTLs and candidate genes for flowering and height. Novel regions identified allow for future research of adapting exotic maize to the central‐U.S. Corn‐Belt.

Selection Signatures Underlying Dramatic Male Inflorescence Transformation During Modern Hybrid Maize Breeding

Inflorescence capacity plays a crucial role in reproductive fitness in plants, and in production of hybrid crops. Maize is a monoecious species bearing separate male and female flowers (tassel and ear, respectively). The switch from open-pollinated populations of maize to hybrid-based breeding schemes in the early 20th century was accompanied by a dramatic reduction in tassel size, and the trend has continued with modern breeding over the recent decades. The goal of this study was to identify selection signatures in genes that may underlie this dramatic transformation. Using a population of 942 diverse inbred maize accessions and a nested association mapping population comprising three 200-line biparental populations, we measured 15 tassel morphological characteristics by manual and image-based methods. Genome-wide association studies identified 242 single nucleotide polymorphisms significantly associated with measured traits. We compared 41 unselected lines from the Iowa Stiff Stalk Synthetic (BSSS) population to 21 highly selected lines developed by modern commercial breeding programs, and found that tassel size and weight were reduced significantly. We assayed genetic differences between the two groups using three selection statistics: cross population extended haplotype homozogysity, cross-population composite likelihood ratio, and fixation index. All three statistics show evidence of selection at genomic regions associated with tassel morphology relative to genome-wide null distributions. These results support the tremendous effect, both phenotypic and genotypic, that selection has had on maize male inflorescence morphology.

Maize Genomes to Fields: 2014 and 2015 field season genotype, phenotype, environment, and inbred ear image datasets

ObjectivesCrop improvement relies on analysis of phenotypic, genotypic, and environmental data. Given large, well-integrated, multi-year datasets, diverse queries can be made: Which lines perform best in hot, dry environments? Which alleles of specific genes are required for optimal performance in each environment? Such datasets also can be leveraged to predict cultivar performance, even in uncharacterized environments. The maize Genomes to Fields (G2F) Initiative is a multi-institutional organization of scientists working to generate and analyze such datasets from existing, publicly available inbred lines and hybrids. G2F’s genotype by environment project has released 2014 and 2015 datasets to the public, with 2016 and 2017 collected and soon to be made available.Data descriptionDatasets include DNA sequences; traditional phenotype descriptions, as well as detailed ear, cob, and kernel phenotypes quantified by image analysis; weather station measurements; and soil characterizations by site. Data are released as comma separated value spreadsheets accompanied by extensive README text descriptions. For genotypic and phenotypic data, both raw data and a version with outliers removed are reported. For weather data, two versions are reported: a full dataset calibrated against nearby National Weather Service sites and a second calibrated set with outliers and apparent artifacts removed.