Predicting the long-term impact of antiretroviral therapy scale-up on population incidence of tuberculosis.

OBJECTIVE: To investigate the impact of antiretroviral therapy (ART) on long-term population-level tuberculosis disease (TB) incidence in sub-Saharan Africa. METHODS: We used a mathematical model to consider the effect of different assumptions about life expectancy and TB risk during long-term ART under alternative scenarios for trends in population HIV incidence and ART coverage. RESULTS: All the scenarios we explored predicted that the widespread introduction of ART would initially reduce population-level TB incidence. However, many modelled scenarios projected a rebound in population-level TB incidence after around 20 years. This rebound was predicted to exceed the TB incidence present before ART scale-up if decreases in HIV incidence during the same period were not sufficiently rapid or if the protective effect of ART on TB was not sustained. Nevertheless, most scenarios predicted a reduction in the cumulative TB incidence when accompanied by a relative decline in HIV incidence of more than 10% each year. CONCLUSIONS: Despite short-term benefits of ART scale-up on population TB incidence in sub-Saharan Africa, longer-term projections raise the possibility of a rebound in TB incidence. This highlights the importance of sustaining good adherence and immunologic response to ART and, crucially, the need for effective HIV preventive interventions, including early widespread implementation of ART

Genomic approaches to research in lung cancer

The medical research community is experiencing a marked increase in the amount of information available on genomic sequences and genes expressed by humans and other organisms. This information offers great opportunities for improving our understanding of complex diseases such as lung cancer. In particular, we should expect to witness a rapid increase in the rate of discovery of genes involved in lung cancer pathogenesis and we should be able to develop reliable molecular criteria for classifying lung cancers and predicting biological properties of individual tumors. Achieving these goals will require collaboration by scientists with specialized expertise in medicine, molecular biology, and decision-based statistical analysis

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled activation subunits, while the DA was modeled using uncoupled activation subunits. Implementations of DA with coupled subunits, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable - allowing an easy and efficient DA implementation. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur

Sampling constrained probability distributions using Spherical Augmentation

Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained domains could be quite challenging for commonly used sampling algorithms. In this paper, we propose a novel augmentation technique that handles a wide range of constraints by mapping the constrained domain to a sphere in the augmented space. By moving freely on the surface of this sphere, sampling algorithms handle constraints implicitly and generate proposals that remain within boundaries when mapped back to the original space. Our proposed method, called {Spherical Augmentation}, provides a mathematically natural and computationally efficient framework for sampling from constrained probability distributions. We show the advantages of our method over state-of-the-art sampling algorithms, such as exact Hamiltonian Monte Carlo, using several examples including truncated Gaussian distributions, Bayesian Lasso, Bayesian bridge regression, reconstruction of quantized stationary Gaussian process, and LDA for topic modeling.Comment: 41 pages, 13 figure

The structure of iterative methods for symmetric linear discrete ill-posed problems

The iterative solution of large linear discrete ill-posed problems with an error contaminated data vector requires the use of specially designed methods in order to avoid severe error propagation. Range restricted minimal residual methods have been found to be well suited for the solution of many such problems. This paper discusses the structure of matrices that arise in a range restricted minimal residual method for the solution of large linear discrete ill-posed problems with a symmetric matrix. The exploitation of the structure results in a method that is competitive with respect to computer storage, number of iterations, and accuracy.Acknowledgments We would like to thank the referees for comments. The work of F. M. was supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain under grant MTM2012-36732-C03-01. Work of L. R. was supported by Universidad Carlos III de Madrid in the Department of Mathematics during the academic year 2010-2011 within the framework of the Chair of Excellence Program and by NSF grant DMS-1115385

Optimally splitting cases for training and testing high dimensional classifiers

<p>Abstract</p> <p>Background</p> <p>We consider the problem of designing a study to develop a predictive classifier from high dimensional data. A common study design is to split the sample into a training set and an independent test set, where the former is used to develop the classifier and the latter to evaluate its performance. In this paper we address the question of what proportion of the samples should be devoted to the training set. How does this proportion impact the mean squared error (MSE) of the prediction accuracy estimate?</p> <p>Results</p> <p>We develop a non-parametric algorithm for determining an optimal splitting proportion that can be applied with a specific dataset and classifier algorithm. We also perform a broad simulation study for the purpose of better understanding the factors that determine the best split proportions and to evaluate commonly used splitting strategies (1/2 training or 2/3 training) under a wide variety of conditions. These methods are based on a decomposition of the MSE into three intuitive component parts.</p> <p>Conclusions</p> <p>By applying these approaches to a number of synthetic and real microarray datasets we show that for linear classifiers the optimal proportion depends on the overall number of samples available and the degree of differential expression between the classes. The optimal proportion was found to depend on the full dataset size (n) and classification accuracy - with higher accuracy and smaller <it>n </it>resulting in more assigned to the training set. The commonly used strategy of allocating 2/3rd of cases for training was close to optimal for reasonable sized datasets (<it>n </it>≥ 100) with strong signals (i.e. 85% or greater full dataset accuracy). In general, we recommend use of our nonparametric resampling approach for determing the optimal split. This approach can be applied to any dataset, using any predictor development method, to determine the best split.</p

Detection of regulator genes and eQTLs in gene networks

Genetic differences between individuals associated to quantitative phenotypic traits, including disease states, are usually found in non-coding genomic regions. These genetic variants are often also associated to differences in expression levels of nearby genes (they are "expression quantitative trait loci" or eQTLs for short) and presumably play a gene regulatory role, affecting the status of molecular networks of interacting genes, proteins and metabolites. Computational systems biology approaches to reconstruct causal gene networks from large-scale omics data have therefore become essential to understand the structure of networks controlled by eQTLs together with other regulatory genes, and to generate detailed hypotheses about the molecular mechanisms that lead from genotype to phenotype. Here we review the main analytical methods and softwares to identify eQTLs and their associated genes, to reconstruct co-expression networks and modules, to reconstruct causal Bayesian gene and module networks, and to validate predicted networks in silico.Comment: minor revision with typos corrected; review article; 24 pages, 2 figure

Tuberculosis Incidence Rates during 8 Years of Follow-Up of an Antiretroviral Treatment Cohort in South Africa: Comparison with Rates in the Community

BACKGROUND: Although antiretroviral therapy (ART) is known to be associated with time-dependent reductions in tuberculosis (TB) incidence, the long-term impact of ART on incidence remains imprecisely defined due to limited duration of follow-up and incomplete CD4 cell count recovery in existing studies. We determined TB incidence in a South African ART cohort with up to 8 years of follow-up and stratified rates according to CD4 cell count recovery. We compared these rates with those of HIV-uninfected individuals living in the same community. METHODOLOGY/PRINCIPAL FINDINGS: Prospectively collected clinical data on patients receiving ART in a community-based cohort in Cape Town were analysed. 1544 patients with a median follow-up of 5.0 years (IQR 2.4-5.8) were included in the analysis. 484 episodes of incident TB (73.6% culture-confirmed) were diagnosed in 424 patients during 6506 person-years (PYs) of follow-up. The TB incidence rate during the first year of ART was 12.4 (95% CI 10.8-14.4) cases/100PYs and decreased to 4.92 (95% CI 3.64-8.62) cases/100PYs between 5 and 8 years of ART. During person-time accrued within CD4 cell strata 0-100, 101-200, 201-300, 301-400, 401-500, 501-700 and ≥700 cells/µL, TB incidence rates (95% CI) were 25.5 (21.6-30.3), 11.2 (9.4-13.5), 7.9 (6.4-9.7), 5.0 (3.9-6.6), 5.1 (3.8-6.8), 4.1 (3.1-5.4) and 2.7 (1.7-4.5) cases/100PYs, respectively. Overall, 75% (95% CI 70.9-78.8) of TB episodes were recurrent cases. Updated CD4 cell count and viral load measurements were independently associated with long-term TB risk. TB rates during person-time accrued in the highest CD4 cell count stratum (>700 cells/µL) were 4.4-fold higher that the rate in HIV uninfected individuals living in the same community (2.7 versus 0.62 cases/100PYs; 95%CI 0.58-0.65). CONCLUSIONS/SIGNIFICANCE: TB rates during long-term ART remained substantially greater than rates in the local HIV uninfected populations regardless of duration of ART or attainment of CD4 cell counts exceeding 700 cells/µL