Analysis of feedback mechanisms with unknown delay using sparse multivariate autoregressive method

This paper discusses the study of two interacting processes in which a feedback mechanism exists between the processes. The study was motivated by problems such as the circadian oscillation of gene expression where two interacting protein transcriptions form both negative and positive feedback loops with long delays to equilibrium. Traditionally, data of this type could be examined using autoregressive analysis. However, in circadian oscillation the order of an autoregressive model cannot be determined a priori. We propose a sparse multivariate autoregressive method that incorporates mixed linear effects into regression analysis, and uses a forward-backward greedy search algorithm to select nonzero entries in the regression coefficients, the number of which is constrained not to exceed a pre-specified number. A small simulation study provides preliminary evidence of the validity of the method. Besides the circadian oscillation example, an additional example of blood pressure variations using data from an intervention study is used to illustrate the method and the interpretation of the results obtained from the sparse matrix method. These applications demonstrate how sparse representation can be used for handling high dimensional variables that feature dynamic, reciprocal relationships

Pooling, meta-analysis, and the evaluation of drug safety

BACKGROUND: The "integrated safety report" of the drug registration files submitted to health authorities usually summarizes the rates of adverse events observed for a new drug, placebo or active control drugs by pooling the safety data across the trials. Pooling consists of adding the numbers of events observed in a given treatment group across the trials and dividing the results by the total number of patients included in this group. Because it considers treatment groups rather than studies, pooling ignores validity of the comparisons and is subject to a particular kind of bias, termed "Simpson's paradox." In contrast, meta-analysis and other stratified analyses are less susceptible to bias. METHODS: We use a hypothetical, but not atypical, application to demonstrate that the results of a meta-analysis can differ greatly from those obtained by pooling the same data. In our hypothetical model, a new drug is compared to 1) a placebo in 4 relatively small trials in patients at high risk for a certain adverse event and 2) an active reference drug in 2 larger trials of patients at low risk for this event. RESULTS: Using meta-analysis, the relative risk of experiencing the adverse event with the new drug was 1.78 (95% confidence interval [1.02; 3.12]) compared to placebo and 2.20 [0.76; 6.32] compared to active control. By pooling the data, the results were, respectively, 1.00 [0.59; 1.70] and 5.20 [2.07; 13.08]. CONCLUSIONS: Because these findings could mislead health authorities and doctors, regulatory agencies should require meta-analyses or stratified analyses of safety data in drug registration files

The Topology of Parabolic Character Varieties of Free Groups

Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicat

Risk of Childhood Cancers Associated with Residence in Agriculturally Intense Areas in the United States

Background: The potential for widespread exposure to agricultural pesticides through drift during application raises concerns about possible health effects to exposed children living in areas of high agricultural activity. Objectives: We evaluated whether residence in a county with greater agricultural activity was associated with risk of developing cancer in children \u3c 15 years of age. Methods: Incidence data for U.S. children 0–14 years of age diagnosed with cancer between 1995 and 2001 were provided by member registries of the North American Association of Central Cancer Registries. We determined percent cropland for each county using agricultural census data, and used the overall study distribution to classify agriculturally intense counties. We estimated odds ratios and 95% confidence intervals for all ages and 5-year age groups for total cancers and selected cancer sites using logistic regression. Results: Our study results showed statistically significant increased risk estimates for many types of childhood cancers associated with residence at diagnosis in counties having a moderate to high level of agricultural activity, with a remarkably consistent dose–response effect seen for counties having ≥ 60% of the total county acreage devoted to farming. Risk for different cancers varied by type of crop. Conclusions: Although interpretation is limited by the ecologic design, in this study we were able to evaluate rarer childhood cancers across a diverse agricultural topography. The findings of this exploratory study support a continued interest in the possible impact of long-term, low-level pesticide exposure in communities located in agriculturally intense areas

The Analysis of Association Between Traits When Differences Between Trait States Matter

Because of their elementary significance in almost all fields of science, measures of association between two variables or traits are abundant and multiform. One aspect of association that is of considerable interest, especially in population genetics and ecology, seems to be widely ignored. This aspect concerns association between complex traits that show variable and arbitrarily defined state differences. Among such traits are genetic characters controlled by many and potentially polyploid loci, species characteristics, and environmental variables, all of which may be mutually and asymmetrically associated. A concept of directed association of one trait with another is developed here that relies solely on difference measures between the states of a trait. Associations are considered at three levels: between individual states of two variables, between an individual state of one variable and the totality of the other variable, and between two variables. Relations to known concepts of association are identified. In particular, measures at the latter two levels turn out to be interpretable as measures of differentiation. Examples are given for areas of application (search for functional relationships, distribution of variation over populations, genomic associations, spatiogenetic structure)

Simpson's Paradox, Lord's Paradox, and Suppression Effects are the same phenomenon – the reversal paradox

This article discusses three statistical paradoxes that pervade epidemiological research: Simpson's paradox, Lord's paradox, and suppression. These paradoxes have important implications for the interpretation of evidence from observational studies. This article uses hypothetical scenarios to illustrate how the three paradoxes are different manifestations of one phenomenon – the reversal paradox – depending on whether the outcome and explanatory variables are categorical, continuous or a combination of both; this renders the issues and remedies for any one to be similar for all three. Although the three statistical paradoxes occur in different types of variables, they share the same characteristic: the association between two variables can be reversed, diminished, or enhanced when another variable is statistically controlled for. Understanding the concepts and theory behind these paradoxes provides insights into some controversial or contradictory research findings. These paradoxes show that prior knowledge and underlying causal theory play an important role in the statistical modelling of epidemiological data, where incorrect use of statistical models might produce consistent, replicable, yet erroneous results

Extending colonic mucosal microbiome analysis - Assessment of colonic lavage as a proxy for endoscopic colonic biopsies

This study was supported through GI Research funds and MRC Grant Ref: MR/M00533X/1 to GH.Peer reviewedPublisher PD

Effects of habitat and land use on breeding season density of male Asian Houbara Chlamydotis macqueenii

Landscape-scale habitat and land-use influences on Asian Houbara Chlamydotis macqueenii (IUCN Vulnerable) remain unstudied, while estimating numbers of this cryptic, low-density, over-hunted species is challenging. In spring 2013, male houbara were recorded at 231 point counts, conducted twice, across a gradient of sheep density and shrub assemblages within 14,300 km² of the Kyzylkum Desert, Uzbekistan. Four sets of models related male abundance to: (1) vegetation structure (shrub height and substrate); (2) shrub assemblage; (3) shrub species composition (multidimensional scaling); (4) remote-sensed derived land-cover (GLOBCOVER, 4 variables). Each set also incorporated measures of landscape rugosity and sheep density. For each set, multi-model inference was applied to generalised linear mixed models of visit-specific counts that included important detectability covariates and point ID as a random effect. Vegetation structure received strongest support, followed by shrub species composition and shrub assemblage, with weakest support for the GLOBCOVER model set. Male houbara numbers were greater with lower mean shrub height, more gravel and flatter surfaces, but were unaffected by sheep density. Male density (mean 0.14 km-2, 95% CI, 0.12‒0.15) estimated by distance analysis differed substantially among shrub assemblages, being highest in vegetation dominated by Salsola rigida (0.22 [CI, 0.20‒0.25]), high in areas of S. arbuscula and Astragalus (0.14 [CI, 0.13‒0.16] and 0.15 [CI, 0.14‒0.17] respectively), lower (0.09 [CI, 0.08‒0.10]) in Artemisia and lowest (0.04 [CI, 0.04‒0.05]) in Calligonum. The study area was estimated to hold 1,824 males (CI: 1,645‒2,030). The spatial distribution of relative male houbara abundance, predicted from vegetation structure models, had the strongest correspondence with observed numbers in both model-calibration and the subsequent year’s data. We found no effect of pastoralism on male distribution but potential effects on nesting females are unknown. Density differences among shrub communities suggest extrapolation to estimate country- or range-wide population size must take account of vegetation composition

Simpson's paradox and calculation of number needed to treat from meta-analysis

BACKGROUND: Calculation of numbers needed to treat (NNT) is more complex from meta-analysis than from single trials. Treating the data as if it all came from one trial may lead to misleading results when the trial arms are imbalanced. DISCUSSION: An example is shown from a published Cochrane review in which the benefit of nursing intervention for smoking cessation is shown by formal meta-analysis of the individual trial results. However if these patients were added together as if they all came from one trial the direction of the effect appears to be reversed (due to Simpson's paradox). Whilst NNT from meta-analysis can be calculated from pooled Risk Differences, this is unlikely to be a stable method unless the event rates in the control groups are very similar. Since in practice event rates vary considerably, the use a relative measure, such as Odds Ratio or Relative Risk is advocated. These can be applied to different levels of baseline risk to generate a risk specific NNT for the treatment. SUMMARY: The method used to calculate NNT from meta-analysis should be clearly stated, and adding the patients from separate trials as if they all came from one trial should be avoided

Viral population estimation using pyrosequencing

The diversity of virus populations within single infected hosts presents a major difficulty for the natural immune response as well as for vaccine design and antiviral drug therapy. Recently developed pyrophosphate based sequencing technologies (pyrosequencing) can be used for quantifying this diversity by ultra-deep sequencing of virus samples. We present computational methods for the analysis of such sequence data and apply these techniques to pyrosequencing data obtained from HIV populations within patients harboring drug resistant virus strains. Our main result is the estimation of the population structure of the sample from the pyrosequencing reads. This inference is based on a statistical approach to error correction, followed by a combinatorial algorithm for constructing a minimal set of haplotypes that explain the data. Using this set of explaining haplotypes, we apply a statistical model to infer the frequencies of the haplotypes in the population via an EM algorithm. We demonstrate that pyrosequencing reads allow for effective population reconstruction by extensive simulations and by comparison to 165 sequences obtained directly from clonal sequencing of four independent, diverse HIV populations. Thus, pyrosequencing can be used for cost-effective estimation of the structure of virus populations, promising new insights into viral evolutionary dynamics and disease control strategies.Comment: 23 pages, 13 figure