BACKGROUND: Often researchers are interested in comparing multiple experimental groups (e.g. tumor size) with a reference group (e.g. normal tissue) on the basis of thousands of features (e.g. genes) and determine if a differentially expressed feature is up or down regulated in a pairwise comparison. There are two sources of false discoveries, one due to multiple testing involving several pairwise comparisons and the second due to falsely declaring a feature to be up (or down) regulated when it is not (known as directional error). Together, the total error rate is called the mixed directional false discovery rate (mdFDR). RESULTS: We develop a general powerful mdFDR controlling testing procedure and illustrate the methodology by analyzing uterine fibroid gene expression data (PLoS ONE 8:63909, 2013). We identify several differentially expressed genes (DEGs) and pathways that are specifically enriched according to the size of a uterine fibroid. CONCLUSIONS: The proposed general procedure strongly controls mdFDR. Several specific methodologies can be derived from this general methodology by using appropriate testing procedures at different steps of the general procedure. Thus we are providing a general framework for making multiple pairwise comparisons. Our analysis of the uterine fibroid growth gene expression data suggests that molecular characteristics of a fibroid changes with size. Our powerful methodology allowed us to draw several interesting conclusions regarding the molecular characteristics of uterine fibroids. For example, IL-1 signaling pathway (Sci STKE 2003:3, 2003), associated with inflammation and known to activate prostaglandins that are implicated in the progression of fibroids, is significantly enriched only in small tumors (volume < 5.7 cm (3)). It appears that the molecular apparatus necessary for fibroid growth and development is established during tumor development. A complete list of all DEGs and the corresponding enriched pathways according to tumor size is provided for researchers to mine these data. Identification of these DEGs and the pathways may potentially have clinical implications.

It is acknowledged that some obesity trajectories are set early in life, and that rapid weight gain in infancy is a risk factor for later development of obesity. Identifying modifiable factors associated with early rapid weight gain is a prerequisite for curtailing the growing worldwide obesity epidemic. Recently, much attention has been given to findings indicating that gut microbiota may play a role in obesity development. We aim at identifying how the development of early gut microbiota is associated with expected infant growth. We developed a novel procedure that allows for the identification of longitudinal gut microbiota patterns (corresponding to the gut ecosystem developing), which are associated with an outcome of interest, while appropriately controlling for the false discovery rate. Our method identified developmental pathways of Staphylococcus species and Escherichia coli that were associated with expected growth, and traditional methods indicated that the detection of Bacteroides species at day 30 was associated with growth. Our method should have wide future applicability for studying gut microbiota, and is particularly important for translational considerations, as it is critical to understand the timing of microbiome transitions prior to attempting to manipulate gut microbiota in early life.

BACKGROUND: Based on available biological information, genomic data can often be partitioned into pre-defined sets (e.g. pathways) and subsets within sets. Biologists are often interested in determining whether some pre-defined sets of variables (e.g. genes) are differentially expressed under varying experimental conditions. Several procedures are available in the literature for making such determinations, however, they do not take into account information regarding the subsets within each set. Secondly, variables (e.g. genes) belonging to a set or a subset are potentially correlated, yet such information is often ignored and univariate methods are used. This may result in loss of power and/or inflated false positive rate. RESULTS: We introduce a multiple testing-based methodology which makes use of available information regarding biologically relevant subsets within each pre-defined set of variables while exploiting the underlying dependence structure among the variables. Using this methodology, a biologist may not only determine whether a set of variables are differentially expressed between two experimental conditions, but may also test whether specific subsets within a significant set are also significant. CONCLUSIONS: The proposed methodology; (a) is easy to implement, (b) does not require inverting potentially singular covariance matrices, and (c) controls the family wise error rate (FWER) at the desired nominal level, (d) is robust to the underlying distribution and covariance structures. Although for simplicity of exposition, the methodology is described for microarray gene expression data, it is also applicable to any high dimensional data, such as the mRNA seq data, CpG methylation data etc.

BACKGROUND: For gene expression data obtained from a time-course microarray experiment, Liu et al. developed a new algorithm for clustering genes with similar expression profiles over time. Performance of their proposal was compared with three other methods including the order-restricted inference based methodology of Peddada et al. In this note we point out several inaccuracies in Liu et al. and conclude that the order-restricted inference based methodology of Peddada et al. (programmed in the software ORIOGEN) indeed operates at the desired nominal Type 1 error level, an important feature of a statistical decision rule, while being computationally substantially faster than indicated by Liu et al. RESULTS: Application of ORIOGEN to the well-known breast cancer cell line data of Lobenhofer et al. revealed that ORIOGEN software took only 21 minutes to run (using 100,000 bootstraps with p = 0.0025), substantially faster than the 72 hours found by Liu et al. using Matlab. Also, based on a data simulated according to the model and parameters of simulation 1 (sigma2 = 1, M = 5) in [1] we found that ORIOGEN took less than 30 seconds to run in stark contrast to Liu et al. who reported that their implementation of the same algorithm in R took 2979.29 seconds. Furthermore, for the simulation studies reported in [1], unlike the claims made by Liu et al., ORIOGEN always maintained the desired false positive rate. According to Figure three in Liu et al. their algorithm had a false positive rate ranging approximately from 0.20 to 0.70 for the scenarios that they simulated. CONCLUSIONS: Our comparisons of run times indicate that the implementations of ORIOGEN's algorithm in Matlab and R by Liu et al. is inefficient compared to the publicly available JAVA implementation. Our results on the false positive rate of ORIOGEN suggest some error in Figure three of Liu et al., perhaps due to a programming error.

BACKGROUND: Recent circadian clock studies using gene expression microarray in two different tissues of mouse have revealed not all circadian-related genes are synchronized in phase or peak expression times across tissues in vivo. Instead, some circadian-related genes may be delayed by 4-8 hrs in peak expression in one tissue relative to the other. These interesting biological observations prompt a statistical question regarding how to distinguish the synchronized genes from genes that are systematically lagged in phase/peak expression time across two tissues. RESULTS: We propose a set of techniques from circular statistics to analyze phase angles of circadian-related genes in two tissues. We first estimate the phases of a cycling gene separately in each tissue, which are then used to estimate the paired angular difference of the phase angles of the gene in the two tissues. These differences are modeled as a mixture of two von Mises distributions which enables us to cluster genes into two groups; one group having synchronized transcripts with the same phase in the two tissues, the other containing transcripts with a discrepancy in phase between the two tissues. For each cluster of genes we assess the association of phases across the tissue types using circular-circular regression. We also develop a bootstrap methodology based on a circular-circular regression model to evaluate the improvement in fit provided by allowing two components versus a one-component von-Mises model. CONCLUSION: We applied our proposed methodologies to the circadian-related genes common to heart and liver tissues in Storch et al. 2, and found that an estimated 80% of circadian-related transcripts common to heart and liver tissues were synchronized in phase, and the other 20% of transcripts were lagged about 8 hours in liver relative to heart. The bootstrap p-value for being one cluster is 0.063, which suggests the possibility of two clusters. Our methodologies can be extended to analyze peak expression times of circadian-related genes across more than two tissues, for example, kidney, heart, liver, and the suprachiasmatic nuclei (SCN) of the hypothalamus.

UNLABELLED: ORIOGEN is a user-friendly Java-based software package for selecting and clustering genes according to their profiles across various treatment groups. In particular, ORIOGEN is useful for analyzing data obtained from time-course or dose-response type experiments. AVAILABILITY: The ORIOGEN software can be downloaded freely from http://dir.niehs.nih.gov/dirbb/oriogen/index.cfm CONTACT: [email protected] (for statistical questions) and [email protected] (for software support) SUPPLEMENTARY INFORMATION: ORIOGEN has a full set of help files. Also, an example input file is provided with the download.

Differing arresting agents and protocols can be used to synchronize cells in cultures to specific phases of the cell when studying cell-cycle gene expressions. Often, data derived from individual experiments are analyzed separately, since no appropriate statistical methodology is available at the moment to analyze the data from all such experiments simultaneously. The focus of this paper is to determine the association and coherence of the relative activation times of cell-cycling genes under different experimental conditions. Using a circular-circular regression model, we define two parameters, a rotation parameter for the angular difference between cells' arresting times (phases) in two cell-cycle experiments, and an association parameter to describe the correspondence between the cycle times of maximal expression (phase angles) for a set of genes studied in two experiments. Further, we propose a procedure to assess coherence across multiple experiments, i.e. to what extent the circular ordering of the phase angles of genes is maintained across multiple experiments. Coherence of genes across experiments suggests that functionally these genes tend to respond in a stereotypically sequenced way under different experimental conditions. Our proposed methodology is illustrated by applying it to a HeLa cell-cycle gene-expression data.

We propose an algorithm for selecting and clustering genes according to their time-course or dose-response profiles using gene expression data. The proposed algorithm is based on the order-restricted inference methodology developed in statistics. We describe the methodology for time-course experiments although it is applicable to any ordered set of treatments. Candidate temporal profiles are defined in terms of inequalities among mean expression levels at the time points. The proposed algorithm selects genes when they meet a bootstrap-based criterion for statistical significance and assigns each selected gene to the best fitting candidate profile. We illustrate the methodology using data from a cDNA microarray experiment in which a breast cancer cell line was stimulated with estrogen for different time intervals. In this example, our method was able to identify several biologically interesting genes that previous analyses failed to reveal.

Often, in synthetic aperture radar (SAR) images of polar ice, one encounters shadow-like features across the images. Such features make it difficult to classify pixels into ice and water. Accordingly, it becomes a challenge to determine the true size and boundaries of ice floes in an SAR image of polar ice. We develop a simple statistical procedure which classifies pixels of an image by eliminating the effects of shadow-like features. Methodology developed in this paper is illustrated using some noisy SAR images of ice floes in the Arctic sea.

Due to variability in the assignment of gray scale values, most edge detection algorithms produce undesirable edges inside and outside the object of a gray scale image. Also, the points of the edges formed by these algorithms may not be in a linear order. In this communications, a new automated algorithm is provided which removes the undesirable edges and linearly orders the remaining boundary points.

Suppose we have two images /spl Iscr/ and /spl Jscr/ of a collection of ice floes taken at times t/sub 0/ and t/sub 1/, respectively. Given an ice floe I in /spl Iscr/, the authors develop a new automated tracking algorithm to track the position of I in image /spl Jscr/. The proposed least average residual algorithm (LARA) performs a constrained search for matching ice floes by determining an appropriate search space for each floe to be tracked. LARA takes a stepwise approach with suitable decision rules at various stages. It takes into account various distinguishing characteristics such as: i) the geometry of the ice field; ii) size of an ice floe; and iii) geometry of the floe. LARA also attempts to detect broken floes and amalgamated floes.