Gene Sets Net Correlations Analysis (GSNCA): a multivariate differential coexpression test for gene sets

Motivation: To date, Gene Set Analysis (GSA) approaches primarily focus on identifying differentially expressed gene sets (pathways). Methods for identifying differentially coexpressed pathways also exist but are mostly based on aggregated pairwise correlations, or other pairwise measures of coexpression. Instead, we propose Gene Sets Net Correlations Analysis (GSNCA), a multivariate differential coexpression test that accounts for the complete correlation structure between genes.

Results: In GSNCA, weight factors are assigned to genes in proportion to the genes' cross-correlations (intergene correlations). The problem of finding the weight vectors is formulated as an eigenvector problem with a unique solution. GSNCA tests the null hypothesis that for a gene set there is no difference in the weight vectors of the genes between two conditions. In simulation studies and the analyses of experimental data, we demonstrate that GSNCA, indeed, captures changes in the structure of genes' cross-correlations rather than differences in the averaged pairwise correlations. Thus, GSNCA infers differences in coexpression networks, however, bypassing method-dependent steps of network inference. As an additional result from GSNCA, we define hub genes as genes with the largest weights and show that these genes correspond frequently to major and specific pathway regulators, as well as to genes that are most affected by the biological difference between two conditions. In summary, GSNCA is a new approach for the analysis of differentially coexpressed pathways that also evaluates the importance of the genes in the pathways, thus providing unique information that may result in the generation of novel biological hypotheses.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Progress on core outcomes sets for critical care research

Purpose of review: Appropriate selection and definition of outcome measures are essential for clinical trials to be maximally informative. Core outcome sets (an agreed, standardized collection of outcomes measured and reported in all trials for a specific clinical area) were developed due to established inconsistencies in trial outcome selection. This review discusses the rationale for, and methods of, core outcome set development, as well as current initiatives in critical care.

Recent findings: Recent systematic reviews of reported outcomes and measurement instruments relevant to the critically ill highlight inconsistencies in outcome selection, definition, and measurement, thus establishing the need for core outcome sets. Current critical care initiatives include development of core outcome sets for trials aimed at reducing mechanical ventilation duration; rehabilitation following critical illness; long-term outcomes in acute respiratory failure; and epidemic and pandemic studies of severe acute respiratory infection.

Summary: Development and utilization of core outcome sets for studies relevant to the critically ill is in its infancy compared to other specialties. Notwithstanding, core outcome set development frameworks and guidelines are available, several sets are in various stages of development, and there is strong support from international investigator-led collaborations including the International Forum for Acute Care Trialists.

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

COS-STAR: a reporting guideline for studies developing core outcome sets (protocol)

BACKGROUND: Core outcome sets can increase the efficiency and value of research and, as a result, there are an increasing number of studies looking to develop core outcome sets (COS). However, the credibility of a COS depends on both the use of sound methodology in its development and clear and transparent reporting of the processes adopted. To date there is no reporting guideline for reporting COS studies. The aim of this programme of research is to develop a reporting guideline for studies developing COS and to highlight some of the important methodological considerations in the process.

METHODS/DESIGN: The study will include a reporting guideline item generation stage which will then be used in a Delphi study. The Delphi study is anticipated to include two rounds. The first round will ask stakeholders to score the items listed and to add any new items they think are relevant. In the second round of the process, participants will be shown the distribution of scores for all stakeholder groups separately and asked to re-score. A final consensus meeting will be held with an expert panel and stakeholder representatives to review the guideline item list. Following the consensus meeting, a reporting guideline will be drafted and review and testing will be undertaken until the guideline is finalised. The final outcome will be the COS-STAR (Core Outcome Set-STAndards for Reporting) guideline for studies developing COS and a supporting explanatory document.

DISCUSSION: To assess the credibility and usefulness of a COS, readers of a COS development report need complete, clear and transparent information on its methodology and proposed core set of outcomes. The COS-STAR guideline will potentially benefit all stakeholders in COS development: COS developers, COS users, e.g. trialists and systematic reviewers, journal editors, policy-makers and patient groups.

Core outcome sets and trial registries

Some reasons for registering trials might be considered as self-serving, such as satisfying the requirements of a journal in which the researchers wish to publish their eventual findings or publicising the trial to boost recruitment. Registry entries also help others, including systematic reviewers, to know about ongoing or unpublished studies and contribute to reducing research waste by making it clear what studies are ongoing. Other sources of research waste include inconsistency in outcome measurement across trials in the same area, missing data on important outcomes from some trials, and selective reporting of outcomes. One way to reduce this waste is through the use of core outcome sets: standardised sets of outcomes for research in specific areas of health and social care. These do not restrict the outcomes that will be measured, but provide the minimum to include if a trial is to be of the most use to potential users. We propose that trial registries, such as ISRCTN, encourage researchers to note their use of a core outcome set in their entry. This will help people searching for trials and those worried about selective reporting in closed trials. Trial registries can facilitate these efforts to make new trials as useful as possible and reduce waste. The outcomes section in the entry could prompt the researcher to consider using a core outcome set and facilitate the specification of that core outcome set and its component outcomes through linking to the original core outcome set. In doing this, registries will contribute to the global effort to ensure that trials answer important uncertainties, can be brought together in systematic reviews, and better serve their ultimate aim of improving health and well-being through improving health and social care.

Inference in Polytrees with Sets of Probabilities

Inferences in directed acyclic graphs associated with probability intervals and sets of probabilities are NP-hard, even for polytrees. We propose: 1) an improvement on Tessem’s A/R algorithm for inferences on polytrees associated with probability intervals; 2) a new algorithm for approximate inferences based on local search; 3) branch-and-bound algorithms that combine the previous techniques. The first two algorithms produce complementary approximate solutions, while branch-and-bound procedures can generate either exact or approximate solutions. We report improvements on existing techniques for inference with probability sets and intervals, in some cases reducing computational effort by several orders of magnitude.

Prior knowledge transfer across transcriptional data sets and technologies using compositional statistics yields new mislabelled ovarian cell line

Here, we describe gene expression compositional assignment (GECA), a powerful, yet simple method based on compositional statistics that can validate the transfer of prior knowledge, such as gene lists, into independent data sets, platforms and technologies. Transcriptional profiling has been used to derive gene lists that stratify patients into prognostic molecular subgroups and assess biomarker performance in the pre-clinical setting. Archived public data sets are an invaluable resource for subsequent in silico validation, though their use can lead to data integration issues. We show that GECA can be used without the need for normalising expression levels between data sets and can outperform rank-based correlation methods. To validate GECA, we demonstrate its success in the cross-platform transfer of gene lists in different domains including: bladder cancer staging, tumour site of origin and mislabelled cell lines. We also show its effectiveness in transferring an epithelial ovarian cancer prognostic gene signature across technologies, from a microarray to a next-generation sequencing setting. In a final case study, we predict the tumour site of origin and histopathology of epithelial ovarian cancer cell lines. In particular, we identify and validate the commonly-used cell line OVCAR-5 as non-ovarian, being gastrointestinal in origin. GECA is available as an open-source R package.