Motivation: Affymetrix GeneChip arrays require summarization in order to combine the probe-level intensities into one value representing the expression level of a gene. However, probe intensity measurements are expected to be affected by different levels of non-specific- and cross-hybridization to non-specific transcripts. Here, we present a new summarization technique, the Distribution Free Weighted method (DFW), which uses information about the variability in probe behavior to estimate the extent of non-specific and cross-hybridization for each probe. The contribution of the probe is weighted accordingly during summarization, without making any distributional assumptions for the probe-level data. Results: We compare DFW with several popular summarization methods on spike-in datasets, via both our own calculations and the ‘Affycomp II’ competition. The results show that DFW outperforms other methods when sensitivity and specificity are considered simultaneously. With the Affycomp spike-in datasets, the area under the receiver operating characteristic curve for DFW is nearly 1.0 (a perfect value), indicating that DFW can identify all differentially expressed genes with a few false positives. The approach used is also computationally faster than most other methods in current use. Availability: The R code for DFW is available upon request. Contact:mmcgee@smu.edu Supplementary information: Supplementary data are available at Bioinformatics online.

When the distributional assumptions for a t-test are not met, the default position of many analysts is to resort to a rank-based test, such as the Wilcoxon-Mann-Whitney Test to compare the difference in means between two samples. The Wilcoxon-Mann-Whitney Test presents no danger of tied observations when the observations in the data are continuous. However, in practice, observations are discretized due various logical reasons, or the data are ordinal in nature. When ranks are tied, most textbooks recommend using mid-ranks to replace the tied ranks, a practice that affects the distribution of the Wilcoxon-Mann-Whitney Test under the null hypothesis. Other methods for breaking ties have also been proposed. In this study, we examine four tie-breaking methods—average-scores, mid-ranks, jittering, and omission—for their effects on Type I and Type II error of the Wilcoxon-Mann-Whitney Test and the two-sample t-test for various combinations of sample sizes, underlying population distributions, and percentages of tied observations. We use the results to determine the maximum percentage of ties for which the power and size are seriously affected, and for which method of tie-breaking results in the best Type I and Type II error properties. Not surprisingly, the underlying population distribution of the data has less of an effect on the Wilcoxon-Mann-Whitney Test than on the t-test. Surprisingly, we find that the jittering and omission methods tend to hold Type I error at the nominal level, even for small sample sizes, with no substantial sacrifice in terms of Type II error. Furthermore, the t-test and the Wilcoxon-Mann-Whitney Test are equally effected by ties in terms of Type I and Type II error; therefore, we recommend omitting tied observations when they occur for both the two-sample t-test and the Wilcoxon-Mann-Whitney due to the bias in Type I error that is created when tied observations are left in the data, in the case of the t-test, or adjusted using mid-ranks or average-scores, in the case of the Wilcoxon-Mann-Whitney.

There are many methods of correcting microarray data for non-biological sources of error. Authors routinely supply software or code so that interested analysts can implement their methods. Even with a thorough reading of associated references, it is not always clear how requisite parts of the method are calculated in the software packages. However, it is important to have an understanding of such details, as this understanding is necessary for proper use of the output, or for implementing extensions to the model. In this paper, the calculation of parameter estimates used in Robust Multichip Average (RMA), a popular preprocessing algorithm for Affymetrix GeneChip brand microarrays, is elucidated. The background correction method for RMA assumes that the perfect match (PM) intensities observed result from a convolution of the true signal, assumed to be exponentially distributed, and a background noise component, assumed to have a normal distribution. A conditional expectation is calculated to estimate signal. Estimates of the mean and variance of the normal distribution and the rate parameter of the exponential distribution are needed to calculate this expectation. Simulation studies show that the current estimates are flawed; therefore, new ones are suggested. We examine the performance of preprocessing under the exponential-normal convolution model using several different methods to estimate the parameters.

Flow cytometry (FCM) is a fluorescence‐based single‐cell experimental technology that is routinely applied in biomedical research for identifying cellular biomarkers of normal physiological responses and abnormal disease states. While many computational methods have been developed that focus on identifying cell populations in individual FCM samples, very few have addressed how the identified cell populations can be matched across samples for comparative analysis. This article presents FlowMap‐FR, a novel method for cell population mapping across FCM samples. FlowMap‐FR is based on the Friedman–Rafsky nonparametric test statistic (FR statistic), which quantifies the equivalence of multivariate distributions. As applied to FCM data by FlowMap‐FR, the FR statistic objectively quantifies the similarity between cell populations based on the shapes, sizes, and positions of fluorescence data distributions in the multidimensional feature space. To test and evaluate the performance of FlowMap‐FR, we simulated the kinds of biological and technical sample variations that are commonly observed in FCM data. The results show that FlowMap‐FR is able to effectively identify equivalent cell populations between samples under scenarios of proportion differences and modest position shifts. As a statistical test, FlowMap‐FR can be used to determine whether the expression of a cellular marker is statistically different between two cell populations, suggesting candidates for new cellular phenotypes by providing an objective statistical measure. In addition, FlowMap‐FR can indicate situations in which inappropriate splitting or merging of cell populations has occurred during gating procedures. We compared the FR statistic with the symmetric version of Kullback–Leibler divergence measure used in a previous population matching method with both simulated and real data. The FR statistic outperforms the symmetric version of KL‐distance in distinguishing equivalent from nonequivalent cell populations. FlowMap‐FR was also employed as a distance metric to match cell populations delineated by manual gating across 30 FCM samples from a benchmark FlowCAP data set. An F‐measure of 0.88 was obtained, indicating high precision and recall of the FR‐based population matching results. FlowMap‐FR has been implemented as a standalone R/Bioconductor package so that it can be easily incorporated into current FCM data analytical workflows. © 2015 International Society for Advancement of Cytometry

Gamma-ray bursts (GRBs) are intense, short-lived bursts of gamma-ray radiation observed up to a high redshift (z ∼ 10) due to their luminosities. Thus, they can serve as cosmological tools to probe the early Universe. However, we need a large sample of high-z GRBs, currently limited due to the difficulty in securing time at the large aperture telescopes. Thus, it is painstaking to determine quickly whether a GRB is high-z or low-z, which hampers the possibility of performing rapid follow-up observations. Previous efforts to distinguish between high- and low-z GRBs using GRB properties and machine learning (ML) have resulted in limited sensitivity. In this study, we aim to improve this classification by employing an ensemble ML method on 251 GRBs with measured redshifts and plateaus observed by the Neil Gehrels Swift Observatory. Incorporating the plateau phase with the prompt emission, we have employed an ensemble of classification methods to unprecedentedly enhance the sensitivity. Additionally, we investigate the effectiveness of various classification methods using different redshift thresholds, z _threshold = z _t at z _t = 2.0, 2.5, 3.0, and 3.5. We achieve a sensitivity of 87% and 89% with a balanced sampling for both z _t = 3.0 and z _t = 3.5, respectively, representing a 9% and 11% increase in the sensitivity over random forest used alone. Overall, the best results are at z _t = 3.5, where the difference between the sensitivity of the training set and the test set is the smallest. This enhancement of the proposed method paves the way for new and intriguing follow-up observations of high-z GRBs.