Small Number Of Replicates Research Articles

Population size rescaling significantly biases outcomes of forward-in-time population genetic simulations.

Simulations are an essential tool in all areas of population genetic research, used in tasks such as the validation of theoretical analysis and the study of complex evolutionary models. Forward-in-time simulations are especially flexible, allowing for various types of natural selection, complex genetic architectures, and non-Wright-Fisher dynamics. However, their intense computational requirements can be prohibitive to simulating large populations and genomes. A popular method to alleviate this burden is to scale down the population size by some scaling factor while scaling up the mutation rate, selection coefficients, and recombination rate by the same factor. However, this rescaling approach may in some cases bias simulation results. To investigate the manner and degree to which rescaling impacts simulation outcomes, we carried out simulations with different demographic histories and distributions of fitness effects using several values of the rescaling factor, , and compared the deviation of key outcomes (fixation times, allele frequencies, linkage disequilibrium, and the fraction of mutations that fix during the simulation) between the scaled and unscaled simulations. Our results indicate that scaling introduces substantial biases to each of these measured outcomes, even at small values of . Moreover, the nature of these effects depends on the evolutionary model and scaling factor being examined. While increasing the scaling factor tends to increase the observed biases, this relationship is not always straightforward, thus it may be difficult to know the impact of scaling on simulation outcomes a priori. However, it appears that for most models, only a small number of replicates was needed to accurately quantify the bias produced by rescaling for a given . In summary, while rescaling forward-in-time simulations may be necessary in many cases, researchers should be aware of the rescaling procedure's impact on simulation outcomes and consider investigating its magnitude in smaller scale simulations of the desired model(s) before selecting an appropriate value of .

Scalable Bayesian Transport Maps for High-Dimensional Non-Gaussian Spatial Fields

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian processes. This enables regularization and uncertainty quantification of the map estimation, while resulting in a closed-form and invertible posterior map. We then focus on inferring the distribution of a nonstationary spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible and are motivated by the behavior of a large class of stochastic processes. Our approach is scalable to high-dimensional distributions due to data-dependent sparsity and parallel computations. We also discuss extensions, including Dirichlet process mixtures for flexible marginals. We present numerical results to demonstrate the accuracy, scalability, and usefulness of our methods, including statistical emulation of non-Gaussian climate-model output. Supplementary materials for this article are available online.

High-content phenotyping of Parkinson's disease patient stem cell-derived midbrain dopaminergic neurons using machine learning classification.

SummaryCombining multiple Parkinson's disease (PD) relevant cellular phenotypes might increase the accuracy of midbrain dopaminergic neuron (mDAN) in vitro models. We differentiated patient-derived induced pluripotent stem cells (iPSCs) with a LRRK2 G2019S mutation, isogenic control, and genetically unrelated iPSCs into mDANs. Using automated fluorescence microscopy in 384-well-plate format, we identified elevated levels of α-synuclein (αSyn) and serine 129 phosphorylation, reduced dendritic complexity, and mitochondrial dysfunction. Next, we measured additional image-based phenotypes and used machine learning (ML) to accurately classify mDANs according to their genotype. Additionally, we show that chemical compound treatments, targeting LRRK2 kinase activity or αSyn levels, are detectable when using ML classification based on multiple image-based phenotypes. We validated our approach using a second isogenic patient-derived SNCA gene triplication mDAN model which overexpresses αSyn. This phenotyping and classification strategy improves the practical exploitability of mDANs for disease modeling and the identification of novel LRRK2-associated drug targets.

Variation in CO2 and CH4 fluxes among land cover types in heterogeneous Arctic tundra in northeastern Siberia

Abstract. Arctic tundra is facing unprecedented warming, resulting in shifts in the vegetation, thaw regimes, and potentially in the ecosystem–atmosphere exchange of carbon (C). However, the estimates of regional carbon dioxide (CO2) and methane (CH4) budgets are highly uncertain. We measured CO2 and CH4 fluxes, vegetation composition and leaf area index (LAI), thaw depth, and soil wetness in Tiksi (71∘ N, 128∘ E), a heterogeneous site located within the prostrate dwarf-shrub tundra zone in northeastern Siberia. Using the closed chamber method, we determined the net ecosystem exchange (NEE) of CO2, ecosystem respiration in the dark (ER), ecosystem gross photosynthesis (Pg), and CH4 flux during the growing season. We applied a previously developed high-spatial-resolution land cover map over an area of 35.8 km2 for spatial extrapolation. Among the land cover types varying from barren to dwarf-shrub tundra and tundra wetlands, the NEE and Pg at the photosynthetically active photon flux density of 800 µmol m−2 h−1 (NEE800 and Pg800) were greatest in the graminoid-dominated habitats, i.e., streamside meadow and fens, with NEE800 and Pg800 of up to −21 (uptake) and 28 mmol m−2 h−1, respectively. Vascular LAI was a robust predictor of both NEE800 and Pg800 and, on a landscape scale, the fens were disproportionately important for the summertime CO2 sequestration. Dry tundra, including the dwarf-shrub and lichen tundra, had smaller CO2 exchange rates. The fens were the largest source of CH4, while the dry mineral soil tundra consumed atmospheric CH4, which on a landscape scale amounted to −9 % of the total CH4 balance during the growing season. The largest seasonal mean CH4 consumption rate of 0.02 mmol m−2 h−1 occurred in sand- and stone-covered barren areas. The high consumption rate agrees with the estimate based on the eddy covariance measurements at the same site. We acknowledge the uncertainty involved in spatial extrapolations due to a small number of replicates per land cover type. This study highlights the need to distinguish different land cover types including the dry tundra habitats to account for their different CO2 and CH4 flux patterns, especially the consumption of atmospheric CH4, when estimating tundra C exchange on a larger spatial scale.

Gene-based association tests using GWAS summary statistics and incorporating eQTL

Although genome-wide association studies (GWAS) have been successfully applied to a variety of complex diseases and identified many genetic variants underlying complex diseases via single marker tests, there is still a considerable heritability of complex diseases that could not be explained by GWAS. One alternative approach to overcome the missing heritability caused by genetic heterogeneity is gene-based analysis, which considers the aggregate effects of multiple genetic variants in a single test. Another alternative approach is transcriptome-wide association study (TWAS). TWAS aggregates genomic information into functionally relevant units that map to genes and their expression. TWAS is not only powerful, but can also increase the interpretability in biological mechanisms of identified trait associated genes. In this study, we propose a powerful and computationally efficient gene-based association test, called Overall. Using extended Simes procedure, Overall aggregates information from three types of traditional gene-based association tests and also incorporates expression quantitative trait locus (eQTL) information into a gene-based association test using GWAS summary statistics. We show that after a small number of replications to estimate the correlation among the integrated gene-based tests, the p values of Overall can be calculated analytically. Simulation studies show that Overall can control type I error rates very well and has higher power than the tests that we compared with. We also apply Overall to two schizophrenia GWAS summary datasets and two lipids GWAS summary datasets. The results show that this newly developed method can identify more significant genes than other methods we compared with.

Retrograde Analysis of Calcium Signaling by CaMPARI2 Shows Cytosolic Calcium in Chondrocytes Is Unaffected by Parabolic Flights.

Calcium (Ca2+) elevation is an essential secondary messenger in many cellular processes, including disease progression and adaptation to external stimuli, e.g., gravitational load. Therefore, mapping and quantifying Ca2+ signaling with a high spatiotemporal resolution is a key challenge. However, particularly on microgravity platforms, experiment time is limited, allowing only a small number of replicates. Furthermore, experiment hardware is exposed to changes in gravity levels, causing experimental artifacts unless appropriately controlled. We introduce a new experimental setup based on the fluorescent Ca2+ reporter CaMPARI2, onboard LED arrays, and subsequent microscopic analysis on the ground. This setup allows for higher throughput and accuracy due to its retrograde nature. The excellent performance of CaMPARI2 was demonstrated with human chondrocytes during the 75th ESA parabolic flight campaign. CaMPARI2 revealed a strong Ca2+ response triggered by histamine but was not affected by the alternating gravitational load of a parabolic flight.

Effects of initial spacing and species mix on stand developmental patterns in two field trials in central Oregon

Productivity, stand dynamics, and ecosystem processes characterizing mixed-species forests have been inferred from a mix of inventory data, observational studies, and designed experiments. Designed experiments are expensive to implement and maintain for a sufficiently long time in most temperate species, but associated treatment replication and randomization lower the risk of confounding from spatial correlations among species composition, environmental conditions, and productivity. Results from replicated mixed-species spacing trials in 45-yr-old Pinus ponderosa/Abies grandis plots and 53-yr-old P. ponderosa/P. contorta plots demonstrated main and interaction effects of spacing and species composition on growth and stand structure, as well as the change in these effects over time. Initial spacing ranged from 1.8 m to 5.5 m on a square grid. Mixtures of P. ponderosa and A. grandis at wide spacings offered A. grandis the opportunity to achieve cumulative height growth nearly equal to P. ponderosa and thereby form a uniform mixed canopy but lower cumulative stem volume growth. The same initial species mixture at closer spacing resulted in increasingly stratified mixtures with P. ponderosa dominating the overstory due largely to its more rapid juvenile height growth and wider crown, relegating shade tolerant A. grandis to the understory. A similar pattern emerged in the mixtures of P. ponderosa and P. contorta, but with more subtle gradients in vertical structure attributable to less extreme differences in juvenile height growth and shade tolerance. By the end of 2019 (plantation age 53), no significant overyielding or underyielding occurred in the mixed-species plots of P. ponderosa/P. contorta. In contrast, by the end of 2018 the mixed-species plots of P. ponderosa/A. grandis (plantation age 45 years) achieved some overyielding that was marginally significant (net volume production) or very significant (gross volume production) only at the narrowest (1.8-m) spacing. The timing and intensity of mortality shifted mixing effects on periodic annual increment slightly over time. Evidence for consistent overyielding among spacings was weak in these P. ponderosa/P. contorta and P. ponderosa/A. grandis spacing trials at total plantation age of 53 and 45 years, respectively. However, statistical power for detecting mixing effects was limited by the relatively small number of replications, and size differentiation continues to emerge at successively wider spacings on mixed-species plots.

A chip-based 128-channel potentiostat for high-throughput studies of bioelectrochemical systems: Optimal electrode potentials for anodic biofilms

The presence of microorganisms performing extracellular electron transfer has been established in many environments. Research to determine their role is moving slowly due to the high cost of potentiostats and the variance of data with small number of replicates. Here, we present a 128-channel potentiostat, connected to a 128 gold electrode array. Whereas the system is able to perform simultaneously 128 (bio)electrochemical measurements with an independent electrical signal input, the present manufacturing of the array limited the number of effective channels for this study to 77. We assessed the impact of 11 electrode potentials ranging from −0.45V to +0.2V vs. Ag/AgCl (7 replicates per potential) on the growth and electrochemical characteristics of anodic electroactive biofilms (EABs) formed by acetate-fed microbial communities. After 7 days of growth, maximum current was reached for electrodes poised at −0.3V, closely followed by −0.25V and −0.1V to +0.1V, a range well-fitting the midpoint potential of minerals naturally reduced by electroactive bacteria such as Geobacter Sulfurreducens. There was no significant difference in apparent midpoint potential of the EABs (−0.35V), suggesting that the mechanism of heterogeneous electron transfer was not affected by the electrode potential. The EABs poised below current plateau potential (≤−0.3V) exhibited slower growth but higher charge transfer parameters. The high-throughput and high reproducibility provided by the array may have a major facilitating impact on the field of electromicrobiology. Key aspects to improve are data processing algorithms to deal with the vast amount of generated data, and manufacturing of the electrode array itself.

Reliable Accuracy Estimates from k-Fold Cross Validation

It is popular to evaluate the performance of classification algorithms by k -fold cross validation. A reliable accuracy estimate will have a relatively small variance, and several studies therefore suggested to repeatedly perform k -fold cross validation. Most of them did not consider the correlation among the replications of k -fold cross validation, and hence the variance could be underestimated. The purpose of this study is to explore whether k -fold cross validation should be repeatedly performed for obtaining reliable accuracy estimates. The dependency relationships between the predictions of the same instance in two replications of k -fold cross validation are first analyzed for k -nearest neighbors with $k= 1$ k = 1 . Then, statistical methods are proposed to test the strength of the dependency level between the accuracy estimates resulting from two replications of k -fold cross validation. The experimental results on 20 data sets show that the accuracy estimates obtained from various replications of k -fold cross validation are generally highly correlated, and the correlation will be higher as the number of folds increases. The k -fold cross validation with a large number of folds and a small number of replications should be adopted for performance evaluation of classification algorithms.

Does no-tillage decrease nitrate leaching compared to ploughing under a long-term crop rotation in Switzerland?

The intensification of agriculture in the industrialized countries since the 1950s led to an increase not only in productivity but also in nitrate concentrations of ground and surface waters. In some countries, various policy measures aim at reducing agricultural nitrogen losses to waters. Still, nitrate concentrations of groundwater impair drinking water quality and nitrogen inputs to surface water are elevated in many areas. Since no-tillage (NT) is often promoted as a farming system that reduces nitrate leaching, we conducted a seven-year lysimeter trial at Berne-Liebefeld (Switzerland) to compare impacts of NT with mouldboard ploughing (MP) in a diverse crop rotation. Crop yields were 13 % lower and N removals by harvested products 5 % lower under NT than under MP. Seepage volumes under NT exceeded those under MP by 8 %. Larger seepage volumes under NT were found in nearly all crop-by-year combinations and months of the year. Mean nitrate concentrations of seepage water were 20 % lower under NT than under MP but still exceeded Swiss official limits for drinking water quality. On average, nitrate-leaching rates were more affected by nitrate concentrations than by seepage volumes because nitrate concentrations varied much more between tillage systems, crop types and years than seepage volumes. Mean annual rates of nitrate leached exceeded 50 kg N ha−1 in both tillage systems and crop rotations with a large range from 2 to 221 kg N ha−1 in individual years. NT showed 14 % lower leaching rates than MP. The differences between the two tillage systems were not statistically significant due to elevated coefficients of variation and the small number of replicates. Improvements in experimental design are suggested to increase the statistical power in future trials.

Towards a Better Understanding of Microbial Community Dynamics through High-Throughput Cultivation and Data Integration.

The investigation of microbial community dynamics is hampered by low resolution, a lack of control, and a small number of replicates. These deficiencies can be tackled with defined communities grown under well-controlled conditions in high-throughput automated cultivation devices. Besides delivering high-quality microbial community data, automated cultivation will also ease measurement of the basic parameters needed to parameterize mathematical models of microbial communities. Better experimental data will allow revisiting classical ecological questions, such as the impact of community structure on dynamics. In addition, such data will allow validation and comparison of community models and benchmarking of microbial data analysis software. In summary, high-throughput automated cultivation will lead to a deeper understanding of microbial community dynamics through better models and software.

See how they run: increased ranging behavior counters potential Allee effects in experimentally introduced house mice on an island

Whether the behaviors of individuals at low population densities differ from those at higher densities is critically informative for predictions of theoretical and experimental ecology, as well as for the conservation management of endangered or introduced species. The globally widespread house mouse Mus musculus is a frequently invasive species; detailed analyses of its low-density behavior will allow for better understanding of population dynamics at early stages of invasions and for generating clearer designs of timely management interventions. Opposite-sex pairs of house mice were released in a small number of replicates at opposite ends of a small, 6 ha island in New Zealand, that had been made experimentally rodent-free, to investigate spatial distributions and ranging behaviors at very low densities by simulating a new invasion of the island with each release trial. Successfully introduced mice (n = 15) of both sexes had twofold greater nightly movements, and tenfold larger range sizes, relative to mice trapped and tracked on the same island prior to eradication. This allowed new arrivals to rapidly and reliably overlap with the range of the opposite sex on the island, especially during the breeding season, suggesting that the driver behind increased ranging was mate searching. Despite the study’s small total sample size, the dramatically increased ranging behaviors exhibited by new arrivals on a mouse-free island imply that this species may avoid potential Allee effects through success in mate searching even at low density. Such behavioral shifts in ranging could contribute to the pervasive success of house mice in founding invasive populations even at extremely low initial densities.

A Bayesian hierarchical model for analyzing methylated RNA immunoprecipitation sequencing data.

The recently emerged technology of methylated RNA immunoprecipitation sequencing (MeRIP-seq) sheds light on the study of RNA epigenetics. This new bioinformatics question calls for effective and robust peaking calling algorithms to detect mRNA methylation sites from MeRIP-seq data. We propose a Bayesian hierarchical model to detect methylation sites from MeRIP-seq data. Our modeling approach includes several important characteristics. First, it models the zero-inflated and over-dispersed counts by deploying a zero-inflated negative binomial model. Second, it incorporates a hidden Markov model (HMM) to account for the spatial dependency of neighboring read enrichment. Third, our Bayesian inference allows the proposed model to borrow strength in parameter estimation, which greatly improves the model stability when dealing with MeRIP-seq data with a small number of replicates. We use Markov chain Monte Carlo (MCMC) algorithms to simultaneously infer the model parameters in a de novo fashion. The R Shiny demo is available at https://qiwei.shinyapps.io/BaySeqPeak and the R/C ++ code is available at https://github.com/liqiwei2000/BaySeqPeak. In simulation studies, the proposed method outperformed the competing methods exomePeak and MeTPeak, especially when an excess of zeros were present in the data. In real MeRIP-seq data analysis, the proposed method identified methylation sites that were more consistent with biological knowledge, and had better spatial resolution compared to the other methods. In this study, we develop a Bayesian hierarchical model to identify methylation peaks in MeRIP-seq data. The proposed method has a competitive edge over existing methods in terms of accuracy, robustness and spatial resolution.

Environmental DNA analysis for estimating the abundance and biomass of stream fish

Summary Environmental DNA (eDNA) analysis for detecting the presence of aquatic and terrestrial organisms is an established method, and the eDNA concentration of a species can reflect its abundance/biomass at a site. However, attempts to estimate the abundance/biomass of aquatic species using eDNA concentrations in large stream and river ecosystems have received little attention. We determined the eDNA concentration and abundance/biomass of a stream fish, Plecoglossus altivelis, by conducting a snorkelling survey in the Saba River, Japan. Furthermore, we evaluated the relationship between eDNA concentrations and the estimated abundance/biomass of P. altivelis, and determined its spatial distribution within the river. Across the three seasons from spring to autumn, we found significant correlations between the eDNA concentration of P. altivelis and its abundance/biomass at study sites within the river. We detected the eDNA at the sites where we found only feeding traces on stones (where P. altivelis was not directly observed), but not at sites without feeding traces. Additionally, we tested the optimal number of qPCR replicates needed for the eDNA evaluation of P. altivelis abundance and biomass; only a small number of replicates was required when the eDNA concentration was high. Our findings suggest that eDNA analysis is a useful tool to estimate fish abundance/biomass as well as their spatial distribution in rivers.

Harmonization Study Between LC-MS/MS and Diasorin RIA for Measurement of 25-Hydroxyvitamin D Concentrations in a Large Population Survey.

BackgroundPopulation‐based research on vitamin D has increased dramatically in recent years. Such studies are typically reliant on assay procedures to measure reliable and comparable levels of 25‐hydroxyvitamin D [25(OH)D] concentrations.MethodsConcentrations of 25(OH)D3 and 25(OH)D2 were measured using LC‐MS/MS in 5,915 participants (aged 31 years) of Northern Finland Birth Cohort 1966. Blood samples were assayed in batches over a course of 18 months. As anomalies were present in the measurements, 200 samples were reassayed using Diasorin RIA. Agreement between measurements was assessed by Passing–Bablok regression and limits of agreement (LoA). To harmonize LC‐MS/MS with Diasorin RIA measurements, formulae were derived from the LoA.ResultsConcentrations measured by LC‐MS/MS were much higher than those measured by Diasorin RIA, with a mean difference of 12.9 ng/ml. Constant variation was evident between batch measurements after log transformation. Statistical formula was applied separately for each batch of LC‐MS/MS measurements, enabling us to remove both the constant and proportional bias that was evident prior to the transformation.ConclusionDespite the introduction of schemes/programs to improve accuracy of assays to measure 25(OH)D, significant differences can still happen. In these instances, methods to harmonize measurements based on a relatively small number of replicates can be successfully applied to establish confidence and to enable between‐study comparisons.

LPEseq: Local-Pooled-Error Test for RNA Sequencing Experiments with a Small Number of Replicates.

RNA-Sequencing (RNA-Seq) provides valuable information for characterizing the molecular nature of the cells, in particular, identification of differentially expressed transcripts on a genome-wide scale. Unfortunately, cost and limited specimen availability often lead to studies with small sample sizes, and hypothesis testing on differential expression between classes with a small number of samples is generally limited. The problem is especially challenging when only one sample per each class exists. In this case, only a few methods among many that have been developed are applicable for identifying differentially expressed transcripts. Thus, the aim of this study was to develop a method able to accurately test differential expression with a limited number of samples, in particular non-replicated samples. We propose a local-pooled-error method for RNA-Seq data (LPEseq) to account for non-replicated samples in the analysis of differential expression. Our LPEseq method extends the existing LPE method, which was proposed for microarray data, to allow examination of non-replicated RNA-Seq experiments. We demonstrated the validity of the LPEseq method using both real and simulated datasets. By comparing the results obtained using the LPEseq method with those obtained from other methods, we found that the LPEseq method outperformed the others for non-replicated datasets, and showed a similar performance with replicated samples; LPEseq consistently showed high true discovery rate while not increasing the rate of false positives regardless of the number of samples. Our proposed LPEseq method can be effectively used to conduct differential expression analysis as a preliminary design step or for investigation of a rare specimen, for which a limited number of samples is available.

Analysis of Differential Gene Expression Based on Bayesian Estimation of Variance

Gene expression is arguably the most important indicator of biological function. Thus identifying differentially expressed genes is one of the main aims of high throughout studies that use microarray and RNAseq platforms to study deregulated cellular pathways. There are many tools for analysing differentia gene expression from transciptomic datasets. The major challenge of this topic is to estimate gene expression variance due to the high amount of ‘background noise’ that is generated from biological equipment and the lack of biological replicates. Bayesian inference has been widely used in the bioinformatics field. In this work, we reveal that the prior knowledge employed in the Bayesian framework also helps to improve the accuracy of differential gene expression analysis when using a small number of replicates. We have developed a differential analysis tool that uses Bayesian estimation of the variance of gene expression for use with small numbers of biological replicates. Our method is more consistent when compared to the widely used cyber-t tool that successfully introduced the Bayesian framework to differential analysis. We also provide a user-friendly web based Graphic User Interface for biologists to use with microarray and RNAseq data. Bayesian inference can compensate for the instability of variance caused when using a small number of biological replicates by using pseudo replicates as prior knowledge. We also show that our new strategy to select pseudo replicates will improve the performance of the analysis. - See more at: http://www.eurekaselect.com/node/138761/article#sthash.VeK9xl5k.dpuf

An assessment of the information content of likelihood ratios derived from complex mixtures

With the increasing sensitivity of DNA typing methodologies, as well as increasing awareness by law enforcement of the perceived capabilities of DNA typing, complex mixtures consisting of DNA from two or more contributors are increasingly being encountered. However, insufficient research has been conducted to characterize the ability to distinguish a true contributor (TC) from a known non-contributor (KNC) in these complex samples, and under what specific conditions. In order to investigate this question, sets of six 15-locus Caucasian genotype profiles were simulated and used to create mixtures containing 2–5 contributors. Likelihood ratios were computed for various situations, including varying numbers of contributors and unknowns in the evidence profile, as well as comparisons of the evidence profile to TCs and KNCs. This work was intended to illustrate the best-case scenario, in which all alleles from the TC were detected in the simulated evidence samples. Therefore the possibility of drop-out was not modeled in this study. The computer program DNAMIX was then used to compute LRs comparing the evidence profile to TCs and KNCs. This resulted in 140,000 LRs for each of the two scenarios. These complex mixture simulations show that, even when all alleles are detected (i.e. no drop-out), TCs can generate LRs less than 1 across a 15-locus profile. However, this outcome was rare, 7 of 140,000 replicates (0.005%), and associated only with mixtures comprising 5 contributors in which the numerator hypothesis includes one or more unknown contributors. For KNCs, LRs were found to be greater than 1 in a small number of replicates (75 of 140,000 replicates, or 0.05%). These replicates were limited to 4 and 5 person mixtures with 1 or more unknowns in the numerator. Only 5 of these 75 replicates (0.004%) yielded an LR greater than 1,000. Thus, overall, these results imply that the weight of evidence that can be derived from complex mixtures containing up to 5 contributors, under a scenario in which no drop-out is required to explain any of the contributors, is remarkably high. This is a useful benchmark result on top of which to layer the effects of additional factors, such as drop-out, peak height, and other variables.

Simultaneous rank tests for detecting differentially expressed genes

Rank tests are known to be robust to outliers and violation of distributional assumptions. Two major issues besetting microarray data are violation of the normality assumption and contamination by outliers. In this article, we formulate the normal theory simultaneous tests and their aligned rank transformation (ART) analog for detecting differentially expressed genes. These tests are based on the least-squares estimates of the effects when data follow a linear model. Application of the two methods are then demonstrated on a real data set. To evaluate the performance of the aligned rank transform method with the corresponding normal theory method, data were simulated according to the characteristics of a real gene expression data. These simulated data are then used to compare the two methods with respect to their sensitivity to the distributional assumption and to outliers for controlling the family-wise Type I error rate, power, and false discovery rate. It is demonstrated that the ART generally possesses the robustness of validity property even for microarray data with small number of replications. Although these methods can be applied to more general designs, in this article the simulation study is carried out for a dye-swap design since this design is broadly used in cDNA microarray experiments.

Identification of Significant Features by the Global Mean Rank Test

With the introduction of omics-technologies such as transcriptomics and proteomics, numerous methods for the reliable identification of significantly regulated features (genes, proteins, etc.) have been developed. Experimental practice requires these tests to successfully deal with conditions such as small numbers of replicates, missing values, non-normally distributed expression levels, and non-identical distributions of features. With the MeanRank test we aimed at developing a test that performs robustly under these conditions, while favorably scaling with the number of replicates. The test proposed here is a global one-sample location test, which is based on the mean ranks across replicates, and internally estimates and controls the false discovery rate. Furthermore, missing data is accounted for without the need of imputation. In extensive simulations comparing MeanRank to other frequently used methods, we found that it performs well with small and large numbers of replicates, feature dependent variance between replicates, and variable regulation across features on simulation data and a recent two-color microarray spike-in dataset. The tests were then used to identify significant changes in the phosphoproteomes of cancer cells induced by the kinase inhibitors erlotinib and 3-MB-PP1 in two independently published mass spectrometry-based studies. MeanRank outperformed the other global rank-based methods applied in this study. Compared to the popular Significance Analysis of Microarrays and Linear Models for Microarray methods, MeanRank performed similar or better. Furthermore, MeanRank exhibits more consistent behavior regarding the degree of regulation and is robust against the choice of preprocessing methods. MeanRank does not require any imputation of missing values, is easy to understand, and yields results that are easy to interpret. The software implementing the algorithm is freely available for academic and commercial use.