Affinity analysis: methodologies and statistical inference

Affinity analysis (AA) is a group of methods for the study of the variation of degrees of compositional relatedness among all of the communities in a landscape. AA cab be used with statistical inference to compare mosaic diversities (89-1) among different landscapes, identify unusual sites within a landscape, and determine when a pair of sites are significantly different from each other. These procedures were done with a set of samples from meadows in the Danube River Valley near Ulm by using random simulations to provide expectations of the summary statistics. The sampling and statistical limitations of AA were discussed.     

Information measures: statistical confidence limits and inference

This paper presents tested statistical methods for reducing sampling bias in, for assigning approximate confidence bounds to, and for testing hypotheses about information-theoretic measures used in the study of animal communication and in behavioral sequence analysis. These procedures are also applicable in fields other than animal behavior, including psychology and ecology. Results of a Monte Carlo evaluation of the methods, including comparison of these techniques with possible alternative procedures, are presented.     

A stochastic SIR model with contact-tracing: large population limits and statistical inference

This paper is devoted to the presentation and study of a specific stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease. Precisely, one considers here the situation in which individuals identified as infected by the public health detection system may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The control strategy, which consists of examining each individual who has been able to be identified on the basis of the information collected within a certain time period, is expected to efficiently reinforce the standard random-screening-based detection and considerably ease the epidemic. In the novel modelling of the spread of a communicable infectious disease considered here, the population of interest evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size, roughly speaking, becomes larger. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relations of the model with the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out.     

A stochastic SIR model with contact-tracing: large population limits and statistical inference

This paper is devoted to the presentation and study of a specific stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease. Precisely, one considers here the situation in which individuals identified as infected by the public health detection system may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The control strategy, which consists of examining each individual who has been able to be identified on the basis of the information collected within a certain time period, is expected to efficiently reinforce the standard random-screening-based detection and considerably ease the epidemic. In the novel modelling of the spread of a communicable infectious disease considered here, the population of interest evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size, roughly speaking, becomes larger. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relations of the model with the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out.     

A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference

Gene expression studies generate large quantities of data with the defining characteristic that the number of genes (whose expression profiles are to be determined) exceed the number of available replicates by several orders of magnitude. Standard spot-by-spot analysis still seeks to extract useful information for each gene on the basis of the number of available replicates, and thus plays to the weakness of microarrays. On the other hand, because of the data volume, treating the entire data set as an ensemble, and developing theoretical distributions for these ensembles provides a framework that plays instead to the strength of microarrays. We present theoretical results that under reasonable assumptions, the distribution of microarray intensities follows the Gamma model, with the biological interpretations of the model parameters emerging naturally. We subsequently establish that for each microarray data set, the fractional intensities can be represented as a mixture of Beta densities, and develop a procedure for using these results to draw statistical inference regarding differential gene expression. We illustrate the results with experimental data from gene expression studies on Deinococcus radiodurans following DNA damage using cDNA microarrays.     

Large scale statistical inference of signaling pathways from RNAi and microarray data

Background  

The advent of RNA interference techniques enables the selective silencing of biologically interesting genes in an efficient way. In combination with DNA microarray technology this enables researchers to gain insights into signaling pathways by observing downstream effects of individual knock-downs on gene expression. These secondary effects can be used to computationally reverse engineer features of the upstream signaling pathway.     

NoRSE: noise reduction and state evaluator for high-frequency single event traces

NoRSE was developed to analyze high-frequency datasets collected from multistate, dynamic experiments, such as molecular adsorption and desorption onto carbon nanotubes. As technology improves sampling frequency, these stochastic datasets become increasingly large with faster dynamic events. More efficient algorithms are needed to accurately locate the unique states in each time trace. NoRSE adapts and optimizes a previously published noise reduction algorithm and uses a custom peak flagging routine to rapidly identify unique event states. The algorithm is explained using experimental data from our lab and its fitting accuracy and efficiency are then shown with a generalized model of stochastic datasets. The algorithm is compared to another recently published state finding algorithm and is found to be 27 times faster and more accurate over 55% of the generalized experimental space. NoRSE is written as an M-file for Matlab. AVAILABILITY: http://web.mit.edu/stranogroup/NoRSE.txt.     

Improved statistical inference from DNA microarray data using analysis of variance and a Bayesian statistical framework. Analysis of global gene expression in Escherichia coli K12

We describe statistical methods based on the t test that can be conveniently used on high density array data to test for statistically significant differences between treatments. These t tests employ either the observed variance among replicates within treatments or a Bayesian estimate of the variance among replicates within treatments based on a prior estimate obtained from a local estimate of the standard deviation. The Bayesian prior allows statistical inference to be made from microarray data even when experiments are only replicated at nominal levels. We apply these new statistical tests to a data set that examined differential gene expression patterns in IHF(+) and IHF(-) Escherichia coli cells (Arfin, S. M., Long, A. D., Ito, E. T., Tolleri, L., Riehle, M. M., Paegle, E. S., and Hatfield, G. W. (2000) J. Biol. Chem. 275, 29672-29684). These analyses identify a more biologically reasonable set of candidate genes than those identified using statistical tests not incorporating a Bayesian prior. We also show that statistical tests based on analysis of variance and a Bayesian prior identify genes that are up- or down-regulated following an experimental manipulation more reliably than approaches based only on a t test or fold change. All the described tests are implemented in a simple-to-use web interface called Cyber-T that is located on the University of California at Irvine genomics web site.     

A regulatory perspective on choice of margin and statistical inference issue in non-inferiority trials

Without a placebo arm, any non-inferiority inference involving assessment of the placebo effect under the active control trial setting is difficult. The statistical risk for falsely concluding non-inferiority cannot be evaluated unless the constancy assumption approximately holds that the effect of the active control under the historical trial setting where the control effect can be assessed carries to the noninferiority trial setting. The constancy assumption cannot be checked because of missing the placebo arm in the non-inferiority trial. Depending on how serious the violation of the assumption is thought to be, one may need to seek an alternative design strategy that includes a cushion for a very conservative non-inferiority analysis or shows superiority of the experimental treatment over the control. Determination of the non-inferiority margin depends on what objective the non-inferiority analysis is intended to achieve. The margin can be a fixed margin or a margin functionally defined. Between-trial differences always exist and need to be properly considered.     

Information maintenance and statistical dependence reduction in simple neural networks

This study compares the ability of excitatory, feed-forward neural networks to construct good transformations on their inputs. The quality of such a transformation is judged by the minimization of two information measures: the information loss of the transformation and the statistical dependency of the output. The networks that are compared differ from each other in the parametric properties of their neurons and in their connectivity. The particular network parameters studied are output firing threshold, synaptic connectivity, and associative modification of connection weights. The network parameters that most directly affect firing levels are threshold and connectivity. Networks incorporating neurons with dynamic threshold adjustment produce better transformations. When firing threshold is optimized, sparser synaptic connectivity produces a better transformation than denser connectivity. Associative modification of synaptic weights confers only a slight advantage in the construction of optimal transformations. Additionally, our research shows that some environments are better suited than others for recoding. Specifically, input environments high in statistical dependence, i.e. those environments most in need of recoding, are more likely to undergo successful transformations.     

CAPE: An R Package for Combined Analysis of Pleiotropy and Epistasis

Contemporary genetic studies are revealing the genetic complexity of many traits in humans and model organisms. Two hallmarks of this complexity are epistasis, meaning gene-gene interaction, and pleiotropy, in which one gene affects multiple phenotypes. Understanding the genetic architecture of complex traits requires addressing these phenomena, but interpreting the biological significance of epistasis and pleiotropy is often difficult. While epistasis reveals dependencies between genetic variants, it is often unclear how the activity of one variant is specifically modifying the other. Epistasis found in one phenotypic context may disappear in another context, rendering the genetic interaction ambiguous. Pleiotropy can suggest either redundant phenotype measures or gene variants that affect multiple biological processes. Here we present an R package, R/cape, which addresses these interpretation ambiguities by implementing a novel method to generate predictive and interpretable genetic networks that influence quantitative phenotypes. R/cape integrates information from multiple related phenotypes to constrain models of epistasis, thereby enhancing the detection of interactions that simultaneously describe all phenotypes. The networks inferred by R/cape are readily interpretable in terms of directed influences that indicate suppressive and enhancing effects of individual genetic variants on other variants, which in turn account for the variance in quantitative traits. We demonstrate the utility of R/cape by analyzing a mouse backcross, thereby discovering novel epistatic interactions influencing phenotypes related to obesity and diabetes. R/cape is an easy-to-use, platform-independent R package and can be applied to data from both genetic screens and a variety of segregating populations including backcrosses, intercrosses, and natural populations. The package is freely available under the GPL-3 license at http://cran.r-project.org/web/packages/cape.

This is a PLOS Computational Biology Software Article

     

powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions

Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years, effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight. In order to greatly decrease the barriers to using good statistical methods for fitting power law distributions, we developed the powerlaw Python package. This software package provides easy commands for basic fitting and statistical analysis of distributions. Notably, it also seeks to support a variety of user needs by being exhaustive in the options available to the user. The source code is publicly available and easily extensible.