Binomial Likelihood Research Articles

Nonparametric Bayesian Negative Binomial Factor Analysis

A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency for a covariate present in a sample to both repeat itself and excite related ones. To address this limitation, we construct negative binomial factor analysis (NBFA) to factorize the matrix under the negative binomial likelihood, and relate it to a Dirichlet-multinomial distribution based mixed-membership model. To support countably infinite factors, we propose the hierarchical gamma-negative binomial process. By exploiting newly proved connections between discrete distributions, we construct two blocked and a collapsed Gibbs sampler that all adaptively truncate their number of factors, and demonstrate that the blocked Gibbs sampler developed under a compound Poisson representation converges fast and has low computational complexity. Example results show that NBFA has a distinct mechanism in adjusting its number of inferred factors according to the sample lengths, and provides clear advantages in parsimonious representation, predictive power, and computational complexity over previously proposed discrete latent variable models, which either completely ignore burstiness, or model only the burstiness of the covariates but not that of the factors.

Different Methods for Modelling Severe Hypoglycaemic Events: Implications for Effectiveness and Cost-Effectiveness Analyses

ObjectivesPublished clinical trials report severe hypoglycaemic events in different ways. Some report number of patients who suffered at least one event out of total number randomised and others report number of events for a given total exposure. The different data types can be modelled in different ways; therefore, three models have been used in published Bayesian Network Meta Analyses (NMAs) of hypoglycaemic events; models with a binomial likelihood reporting odds ratios (using a logit link) or hazard ratios (using the complementary log log link) and models with a Poisson likelihood reporting hazard ratios. The objective of this paper is to establish the impact of using different models on effectiveness estimates and the outputs from cost-effectiveness models.MethodsWe analysed a dataset used in a recent NMA conducted to inform NICE guideline recommendations regarding insulin choice for patients with type 1 diabetes using the three previously used models, plus a shared parameter model combining different types of data.ResultsThe relative treatment effects are similar regardless of which model or scale is used. Differences were seen when the probability of having an event on the baseline treatment was calculated using the different models with the logit model giving a baseline probability of 0.07, the clog-log 0.17 and the Poisson 0.29. These translate into differences of up to £110 in the cost of a hypoglycaemic event and 0.004 in associated disutility when calculating the absolute probabilities of an event to use in an economic model.ConclusionsWhile choice of outcome measure may not have a significant impact on relative effects for this outcome, care should be taken to ensure that the baseline probabilities used in an economic model are realistic and accurate to avoid over or underestimating costs and effects.

Comparative effectiveness of different transarterial embolization therapies alone or in combination with local ablative or adjuvant systemic treatments for unresectable hepatocellular carcinoma: A network meta-analysis of randomized controlled trials.

BackgroundThe optimal transcatheter embolization strategy for patients with unresectable hepatocellular carcinoma (HCC) remains elusive. We conducted a systematic review and network meta-analysis (NMA) of different embolization options for unresectable HCC.MethodsMedical databases were searched for randomized controlled trials evaluating bland transarterial embolization (TAE), conventional TACE, drug-eluting bead chemoembolization (DEB-TACE), or transarterial radioembolization (TARE), either alone or combined with adjuvant chemotherapy, or local liver ablation, or external radiotherapy for unresectable HCC up to June 2017. Random effects Bayesian models with a binomial and normal likelihood were fitted (WinBUGS). Primary endpoint was patient survival expressed as hazard ratios (HR) and 95% credible intervals. An exponential model was used to fit patient survival curves. Safety and objective response were calculated as odds ratios (OR) and accompanying 95% credible intervals. Competing treatments were ranked with the SUCRA statistic. Heterogeneity-adjusted effective sample sizes were calculated to evaluate information size for each comparison. Quality of evidence (QoE) was assessed with the GRADE system adapted for NMA reports. All analyses complied with the ISPOR-AMCP-NCP Task Force Report for good practice in NMA.FindingsThe network of evidence included 55 RCTs (12 direct comparisons) with 5,763 patients with preserved liver function and unresectable HCC (intermediate to advanced stage). All embolization strategies achieved a significant survival gain over control treatment (HR range, 0.42–0.76; very low-to-moderate QoE). However, TACE, DEB-TACE, TARE and adjuvant systemic agents did not confer any survival benefit over bland TAE alone (moderate QoE, except low in case of TARE). There was moderate QoE that TACE combined with external radiation or liver ablation achieved the best patient survival (SUCRA 86% and 96%, respectively). Estimated median survival was 13.9 months in control, 18.1 months in TACE, 20.6 months with DEB-TACE, 20.8 months with bland TAE, 30.1 months in TACE plus external radiotherapy, and 33.3 months in TACE plus liver ablation. TARE was the safest treatment (SUCRA 77%), however, all examined therapies were associated with a significantly higher risk of toxicity over control (OR range, 6.35 to 68.5). TACE, DEB-TACE, TARE and adjuvant systemic agents did not improve objective response over bland embolization alone (OR range, 0.85 to 1.65). There was clinical diversity among included randomized controlled trials, but statistical heterogeneity was low.ConclusionsChemo- and radio-embolization for unresectable hepatocellular carcinoma may improve tumour objective response and patient survival, but are not more effective than bland particle embolization. Chemoembolization combined with external radiotherapy or local liver ablation may significantly improve tumour response and patient survival rates over embolization monotherapies. Quality of evidence remains mostly low to moderate because of clinical diversity.Systematic review registrationCRD42016035796 (http://www.crd.york.ac.uk/PROSPERO).

Network meta-analysis of liraglutide versus dipeptidyl peptidase-4 inhibitors for the treatment of type 2 diabetes in Japanese patients

Aims: To determine the comparative efficacy and safety of liraglutide and dipeptidyl peptidase-4 (DPP-4) inhibitors as antidiabetics for Japanese patients with uncontrolled type 2 diabetes (T2DM).Methods and materials: We searched for randomized controlled trials (RCTs) evaluating outcomes among Japanese adults with uncontrolled T2DM and including liraglutide or DPP-4 inhibitors up to August 2016. We extracted data on trial and patient characteristics, and the following outcomes: HbA1c, weight, patients meeting HbA1c <7%, patients experiencing hypoglycemic events, microalbuminuria, estimated glomerular filtration rate (eGFR) and creatinine. We synthesized data using network meta-analyses (NMA) using a Bayesian framework. Continuous outcomes were modeled using normal likelihoods and an identity link, while dichotomous outcomes were modeled using a binomial likelihood and a logit link.Results: The systematic literature review yielded 39 publications pertaining to 38 trials. A total of 27 trials (5032 patients) reported change in HbA1c at 12 weeks and at 24 weeks 9 trials (2091 patients). All treatments showed statistically significant reductions in HbA1c relative to placebo at 12 and 24 weeks. Liraglutide 0.9 mg was statistically superior to all DPP-4 interventions (vildagliptin, sitagliptin, linagliptin, alogliptin, teneligliptin, trelagliptin and omarigliptin) at 12 weeks and 24 weeks among those reporting. Treatments were not statistically differentiable with respect to weight change and risk of hypoglycemia. Finally, no comparisons of eGFR and microalbuminuria were conducted, as this data was reported in too few trials to conduct analyses.Limitations: Some important outcomes were limited by poor reporting (eGFR and microalbuminuria) or low event rates (hypoglycemia). The follow-up time was relatively short. Clinically, the 24 week time point is more important as it demonstrates more sustained results.Conclusions: Our research suggests that liraglutide 0.9 mg offers a more efficacious treatment option for T2DM than the DPP-4 inhibitors among adult Japanese patients and that it is a viable option for this population.

Risk analysis of new oral anticoagulants for gastrointestinal bleeding and intracranial hemorrhage in atrial fibrillation patients: a systematic review and network meta-analysis.

Antithrombotic therapy using new oral anticoagulants (NOACs) in patients with atrial fibrillation (AF) has been generally shown to have a favorable risk-benefit profile. Since there has been dispute about the risks of gastrointestinal bleeding (GIB) and intracranial hemorrhage (ICH), we sought to conduct a systematic review and network meta-analysis using Bayesian inference to analyze the risks of GIB and ICH in AF patients taking NOACs. We analyzed data from 20 randomized controlled trials of 91 671 AF patients receiving anticoagulants, antiplatelet drugs, or placebo. Bayesian network meta-analysis of two different evidence networks was performed using a binomial likelihood model, based on a network in which different agents (and doses) were treated as separate nodes. Odds ratios (ORs) and 95% confidence intervals (CIs) were modeled using Markov chain Monte Carlo methods. Indirect comparisons with the Bayesian model confirmed that aspirin+clopidogrel significantly increased the risk of GIB in AF patients compared to the placebo (OR 0.33, 95% CI 0.01-0.92). Warfarin was identified as greatly increasing the risk of ICH compared to edoxaban 30 mg (OR 3.42, 95% CI 1.22-7.24) and dabigatran 110 mg (OR 3.56, 95% CI 1.10-8.45). We further ranked the NOACs for the lowest risk of GIB (apixaban 5 mg) and ICH (apixaban 5 mg, dabigatran 110 mg, and edoxaban 30 mg). Bayesian network meta-analysis of treatment of non-valvular AF patients with anticoagulants suggested that NOACs do not increase risks of GIB and/or ICH, compared to each other.

Estimating efficacy in trials with selective crossover.

When one arm in a trial has a worse early endpoint such as recurrence, a data‐monitoring committee might recommend that all participants are offered the apparently superior treatment. The resultant crossover makes it difficult to measure differences between arms thereafter, including for longer‐term endpoints such as mortality and disease‐specific mortality. In this paper, we consider estimators of the efficacy of treatment on those who would not cross over if randomised to the apparently inferior arm. Binomial and proportional hazards maximum likelihood estimators are developed. The binomial estimator is applied to analysis of a breast cancer treatment trial and compared with intention‐to‐treat and inverse probability weighting estimators. Full and partial likelihood proportional‐hazard model estimators are assessed through computer simulations, where they had similar bias and variance. The new efficacy estimators extend those for all‐or‐none compliance to this important problem. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd

Univariate and bivariate likelihood-based meta-analysis methods performed comparably when marginal sensitivity and specificity were the targets of inference

ObjectivesTo compare statistical methods for meta-analysis of sensitivity and specificity of medical tests (e.g., diagnostic or screening tests). Study Design and SettingWe constructed a database of PubMed-indexed meta-analyses of test performance from which 2 × 2 tables for each included study could be extracted. We reanalyzed the data using univariate and bivariate random effects models fit with inverse variance and maximum likelihood methods. Analyses were performed using both normal and binomial likelihoods to describe within-study variability. The bivariate model using the binomial likelihood was also fit using a fully Bayesian approach. ResultsWe use two worked examples—thoracic computerized tomography to detect aortic injury and rapid prescreening of Papanicolaou smears to detect cytological abnormalities—to highlight that different meta-analysis approaches can produce different results. We also present results from reanalysis of 308 meta-analyses of sensitivity and specificity. Models using the normal approximation produced sensitivity and specificity estimates closer to 50% and smaller standard errors compared to models using the binomial likelihood; absolute differences of 5% or greater were observed in 12% and 5% of meta-analyses for sensitivity and specificity, respectively. Results from univariate and bivariate random effects models were similar, regardless of estimation method. Maximum likelihood and Bayesian methods produced almost identical summary estimates under the bivariate model; however, Bayesian analyses indicated greater uncertainty around those estimates. Bivariate models produced imprecise estimates of the between-study correlation of sensitivity and specificity. Differences between methods were larger with increasing proportion of studies that were small or required a continuity correction. ConclusionThe binomial likelihood should be used to model within-study variability. Univariate and bivariate models give similar estimates of the marginal distributions for sensitivity and specificity. Bayesian methods fully quantify uncertainty and their ability to incorporate external evidence may be useful for imprecisely estimated parameters.

Consideration of documentary records in the Annals of the Choson Dynasty for the frequency analysis of rainfall in Seoul, Korea

ABSTRACTIn this study, flood records in the Annals of the Choson Dynasty (1392–1910) were considered for the frequency analysis of rainfall in Seoul, Korea. The old Korean rain gauge (Chukwooki) data (1777–1907) were also used to evaluate major flood records in the Annals of the Choson Dynasty. The design rainfalls were estimated using the binomial censored data maximum likelihood estimator. The results can be summarized as follows. (1) The frequency analysis was done for 24 h rainfall amounts as this was assumed to represent the three different rainfall records well: the documentary records in the Annals of the Choson Dynasty, the Chukwooki data and the modern data. Also, given the possible uncertainty level of the classification results of the documentary records, only 19 catastrophic events (the highest level of flood) were considered in the frequency analysis. The threshold value was decided to be 388 mm by comparing the documentary records with the Chukwooki data. (2) The sensitivity analysis shows that the effects of the threshold value, the number of catastrophic records, and the accuracy level of the flood records in the Annals of the Choson Dynasty on the frequency analysis results are very limited. That is, the length of the flood records in the Annals of the Choson Dynasty was found to be long enough to overcome the possible uncertainty of the flood records. (3) The design rainfalls estimated by taking into account the flood records in the Annals of the Choson Dynasty were found to be very similar to those for the modern data. However, the confidence intervals estimated by considering all the records available were found to be just one third of those of the modern data.

Monitoring potential adverse event rate differences using data from blinded trials: the canary in the coal mine.

The development of drugs and biologicals whose mechanisms of action may extend beyond their target indications has led to a need to identify unexpected potential toxicities promptly even while blinded clinical trials are under way. One component of recently issued FDA rules regarding safety reporting requirements raises the possibility of breaking the blind for pre-identified serious adverse events that are not the clinical endpoints of a blinded study. Concern has been expressed that unblinding individual cases of frequently occurring adverse events could compromise the overall validity of the study. However, if external information is available about adverse event rates among patients not receiving the test product in populations similar to the study population, then it may be possible to address the potential for elevated risk without unblinding the trial. This article describes a Bayesian approach for determining the likelihood of elevated risk suitable binomial or Poisson likelihoods that applies regardless of the metric used to express the difference. The method appears to be particularly appropriate for routine monitoring of safety information for project development programs that include large blinded trials. Copyright © 2016 John Wiley & Sons, Ltd.

Association of Age, Systolic Blood Pressure, and Heart Rate with Adult Morbidity and Mortality after Urgent Care Visits.

IntroductionLittle data exists to help urgent care (UC) clinicians predict morbidity and mortality risk. Age, systolic blood pressure (SBP), and heart rate (HR) are easily obtainable and have been used in other settings to predict short-term risk of deterioration. We hypothesized that there is a relationship between advancing age, SBP, HR, and short-term health outcomes in the UC setting.MethodsWe collected retrospective data from 28 UC clinics and 22 hospitals in the Intermountain Healthcare system between years 2008–2013. Adult patients (≥18 years) were included if they had a unique UC visit and HR or SBP data. Three endpoints following UC visit were assessed: emergency department (ED) visit within three days, hospitalization within three days, and death within seven days. We analyzed associations between age, SBP, HR and endpoints using local regression with a binomial likelihood. Five age groups were chosen from previously published national surveys. Vital sign (VS) distributions were determined for each age group, and the central tendency was compared against previously published norms (90–120mmHg for SBP and 60–100bpm for HR.)ResultsA total of 1,720,207 encounters (714,339 unique patients) met the inclusion criteria; 51,446 encounters (2.99%) had ED visit within three days; 12,397 (0.72%) experienced hospitalization within three days; 302 (0.02%) died within seven days of UC visit. Heart rate and SBP combined with advanced age predicted the probability of ED visit (p<0.0001) and hospitalization (p<0.0001) following UC visit. Significant associations between advancing age and death (p<0.0001), and VS and death (p<0.0001) were observed. Odds ratios of risk were highest for elderly patients with lower SBP or higher HR. Observed distributions of SBP were higher than published normal ranges for all age groups.ConclusionAmong adults seeking care in the UC, associations between HR and SBP and likelihood of ED visits and hospitalization were more pronounced with advancing age. Death following UC visit had a more limited association with advancing age or the VS evaluated. Rapidly increasing risk below SBP of 100–110 mmHg in older patients suggests that accepted normal ranges for SBP may need to be redefined for patients treated in the UC clinic.

A general framework for the use of logistic regression models in meta-analysis.

Where individual participant data are available for every randomised trial in a meta-analysis of dichotomous event outcomes, "one-stage" random-effects logistic regression models have been proposed as a way to analyse these data. Such models can also be used even when individual participant data are not available and we have only summary contingency table data. One benefit of this one-stage regression model over conventional meta-analysis methods is that it maximises the correct binomial likelihood for the data and so does not require the common assumption that effect estimates are normally distributed. A second benefit of using this model is that it may be applied, with only minor modification, in a range of meta-analytic scenarios, including meta-regression, network meta-analyses and meta-analyses of diagnostic test accuracy. This single model can potentially replace the variety of often complex methods used in these areas. This paper considers, with a range of meta-analysis examples, how random-effects logistic regression models may be used in a number of different types of meta-analyses. This one-stage approach is compared with widely used meta-analysis methods including Bayesian network meta-analysis and the bivariate and hierarchical summary receiver operating characteristic (ROC) models for meta-analyses of diagnostic test accuracy.

Statistical Evidence Measured on a Properly Calibrated Scale for Multinomial Hypothesis Comparisons

Measurement of the strength of statistical evidence is a primary objective of statistical analysis throughout the biological and social sciences. Various quantities have been proposed as definitions of statistical evidence, notably the likelihood ratio, the Bayes factor and the relative belief ratio. Each of these can be motivated by direct appeal to intuition. However, for an evidence measure to be reliably used for scientific purposes, it must be properly calibrated, so that one “degree” on the measurement scale always refers to the same amount of underlying evidence, and the calibration problem has not been resolved for these familiar evidential statistics. We have developed a methodology for addressing the calibration issue itself, and previously applied this methodology to derive a calibrated evidence measure E in application to a broad class of hypothesis contrasts in the setting of binomial (single-parameter) likelihoods. Here we substantially generalize previous results to include the m-dimensional multinomial (multiple-parameter) likelihood. In the process we further articulate our methodology for addressing the measurement calibration issue, and we show explicitly how the more familiar definitions of statistical evidence are patently not well behaved with respect to the underlying evidence. We also continue to see striking connections between the calculating equations for E and equations from thermodynamics as we move to more complicated forms of the likelihood.

Endoscopic and Open Release Similarly Safe for the Treatment of Carpal Tunnel Syndrome. A Systematic Review and Meta-Analysis

BackgroundThe Endoscopic Release of Carpal Tunnel Syndrome (ECTR) is a minimal invasive approach for the treatment of Carpal Tunnel Syndrome. There is scepticism regarding the safety of this technique, based on the assumption that this is a rather “blind” procedure and on the high number of severe complications that have been reported in the literature.PurposeTo evaluate whether there is evidence supporting a higher risk after ECTR in comparison to the conventional open release.MethodsWe searched MEDLINE (January 1966 to November 2013), EMBASE (January 1980 to November 2013), the Cochrane Neuromuscular Disease Group Specialized Register (November 2013) and CENTRAL (2013, issue 11 in The Cochrane Library). We hand-searched reference lists of included studies. We included all randomized or quasi-randomized controlled trials (e.g. study using alternation, date of birth, or case record number) that compare any ECTR with any OCTR technique. Safety was assessed by the incidence of major, minor and total number of complications, recurrences, and re-operations.The total time needed before return to work or to return to daily activities was also assessed. We synthesized data using a random-effects meta-analysis in STATA. We conducted a sensitivity analysis for rare events using binomial likelihood. We judged the conclusiveness of meta-analysis calculating the conditional power of meta-analysis.ConclusionsECTR is associated with less time off work or with daily activities. The assessment of major complications, reoperations and recurrence of symptoms does not favor either of the interventions. There is an uncertain advantage of ECTR with respect to total minor complications (more transient paresthesia but fewer skin-related complications). Future studies are unlikely to alter these findings because of the rarity of the outcome. The effect of a learning curve might be responsible for reduced recurrences and reoperations with ECTR in studies that are more recent, although formal statistical analysis failed to provide evidence for such an association. Level of evidence: I.

Risk of serious infection in biological treatment of patients with rheumatoid arthritis: a systematic review and meta-analysis

Serious infections are a major concern for patients considering treatments for rheumatoid arthritis. Evidence is inconsistent as to whether biological drugs are associated with an increased risk of serious infection compared with traditional disease-modifying antirheumatic drugs (DMARDs). We did a systematic review and meta-analysis of serious infections in patients treated with biological drugs compared with those treated with traditional DMARDs. We did a systematic literature search with Medline, Embase, Cochrane Central Register of Controlled Trials, and ClinicalTrials.gov from their inception to Feb 11, 2014. Search terms included "biologics", "rheumatoid arthritis" and their synonyms. Trials were eligible for inclusion if they included any of the approved biological drugs and reported serious infections. We assessed the risk of bias with the Cochrane Risk of Bias Tool. We did a Bayesian network meta-analysis of published trials using a binomial likelihood model to assess the risk of serious infections in patients with rheumatoid arthritis who were treated with biological drugs, compared with those treated with traditional DMARDs. The odds ratio (OR) of serious infection was the primary measure of treatment effect and calculated 95% credible intervals using Markov Chain Monte Carlo methods. The systematic review identified 106 trials that reported serious infections and included patients with rheumatoid arthritis who received biological drugs. Compared with traditional DMARDs, standard-dose biological drugs (OR 1.31, 95% credible interval [CrI] 1.09-1.58) and high-dose biological drugs (1.90, 1.50-2.39) were associated with an increased risk of serious infections, although low-dose biological drugs (0.93, 0.65-1.33) were not. The risk was lower in patients who were methotrexate naive compared with traditional DMARD-experienced or anti-tumour necrosis factor biological drug-experienced patients. The absolute increase in the number of serious infections per 1000 patients treated each year ranged from six for standard-dose biological drugs to 55 for combination biological therapy, compared with traditional DMARDs. Standard-dose and high-dose biological drugs (with or without traditional DMARDs) are associated with an increase in serious infections in rheumatoid arthritis compared with traditional DMARDs, although low-dose biological drugs are not. Clinicians should discuss the balance between benefit and harm with the individual patient before starting biological treatment for rheumatoid arthritis. Rheumatology Division at the University of Alabama at Birmingham.

Universal surrogate likelihood functions for nonnegative continuous data

In independent and identically distributed situations, we show that one can properly correct the Poisson and the negative binomial likelihood functions to become asymptotically identical to the profile likelihood function for the mean parameter of nonnegative continuous distributions under mild conditions. We present theoretical justifications and use data analyses to demonstrate the merit of our new robust likelihood method.

Computation of the Likelihood in Biallelic Diffusion Models Using Orthogonal Polynomials

In population genetics, parameters describing forces such as mutation, migration and drift are generally inferred from molecular data. Lately, approximate methods based on simulations and summary statistics have been widely applied for such inference, even though these methods waste information. In contrast, probabilistic methods of inference can be shown to be optimal, if their assumptions are met. In genomic regions where recombination rates are high relative to mutation rates, polymorphic nucleotide sites can be assumed to evolve independently from each other. The distribution of allele frequencies at a large number of such sites has been called “allele-frequency spectrum” or “site-frequency spectrum” (SFS). Conditional on the allelic proportions, the likelihoods of such data can be modeled as binomial. A simple model representing the evolution of allelic proportions is the biallelic mutation-drift or mutation-directional selection-drift diffusion model. With series of orthogonal polynomials, specifically Jacobi and Gegenbauer polynomials, or the related spheroidal wave function, the diffusion equations can be solved efficiently. In the neutral case, the product of the binomial likelihoods with the sum of such polynomials leads to finite series of polynomials, i.e., relatively simple equations, from which the exact likelihoods can be calculated. In this article, the use of orthogonal polynomials for inferring population genetic parameters is investigated.

Estimating the scaled mutation rate and mutation bias with site frequency data

The distribution of allele frequencies of a large number of biallelic sites is known as “allele-frequency spectrum” or “site-frequency spectrum” (SFS). Without selection and in regions of relatively high recombination rates, sites may be assumed to be independently and identically distributed. With a beta equilibrium distribution of allelic proportions and binomial sampling, a beta–binomial compound likelihood for each site results. The likelihood of the data and the posterior distribution of two parameters, scaled mutation rate θ and mutation bias α, is investigated in the general case and for small scaled mutation rates θ. In the general case, an expectation–maximization (EM) algorithm is derived to obtain maximum likelihood estimates of both parameters. With an appropriate prior distribution, a Markov chain Monte Carlo sampler to integrate the posterior distribution is also derived. As far as I am aware, previous maximum likelihood or Bayesian estimators of θ, explicitly or implicitly assume small scaled mutation rates, i.e., θ≪1. For θ≪1, maximum-likelihood estimators are also derived for both parameters using a Taylor series expansion of the beta–binomial distribution. The estimator of θ is a variant of the Ewens–Watterson estimator and of the maximum likelihood estimator derived with the Poisson Random Field approach. With a conjugate prior distribution, marginal and conditional beta posterior distributions are also derived for both parameters.

Treatment outcomes of childhood tuberculous meningitis: a systematic review and meta-analysis

Tuberculous meningitis disproportionately affects young children. We aimed to characterise treatment outcomes for this deadliest and most debilitating form of tuberculosis. We did a systematic review and meta-analysis of childhood tuberculous meningitis studies published up to Oct 12, 2012. We included study reports that applied predefined diagnostic criteria and described treatment regimens and outcomes. We pooled risks of death during treatment and neurological sequelae among survivors. As secondary objectives, we assessed study-level characteristics as sources of heterogeneity, and we pooled frequencies of presenting symptoms and diagnostic findings. For all meta-analyses we used random-effects models with the exact binomial likelihood method. 19 studies met our inclusion criteria, with reported treatment outcomes for 1636 children. Risk of death was 19·3% (95% CI 14·0-26·1) and probability of survival without neurological sequelae was 36·7% (27·9-46·4). Among survivors, risk of neurological sequelae was 53·9% (95% CI 42·6-64·9). Diagnosis in the most advanced disease stage (3) occurred in 307 (47%) of 657 patients and was associated with worse outcomes than was earlier diagnosis. The most common findings at presentation were cerebrospinal fluid (CSF) leucocytosis (frequency 99·9%, 95% CI 68·5-100·0), CSF lymphocytosis (97·9%, 51·9-100·0), fever (89·8%, 79·8-95·2), and hydrocephalus (86·1%, 68·6-94·6). Frequency of CSF acid-fast-bacilli smear positivity was 8·9% (95% CI 5·0-15·4), and frequency of CSF culture positivity for Mycobacterium tuberculosis was 35·1% (16·8-59·2). Despite treatment, childhood tuberculous meningitis has very poor outcomes. Poor prognosis and difficult early diagnosis emphasise the importance of preventive therapy for child contacts of patients with tuberculosis and low threshold for empirical treatment of tuberculous meningitis suspects. Implementation of consensus definitions, standardised reporting of data, and high-quality clinical trials are needed to clarify optimum therapy. None.

Fast spatial ancestry via flexible allele frequency surfaces.

Unique modeling and computational challenges arise in locating the geographic origin of individuals based on their genetic backgrounds. Single-nucleotide polymorphisms (SNPs) vary widely in informativeness, allele frequencies change non-linearly with geography and reliable localization requires evidence to be integrated across a multitude of SNPs. These problems become even more acute for individuals of mixed ancestry. It is hardly surprising that matching genetic models to computational constraints has limited the development of methods for estimating geographic origins. We attack these related problems by borrowing ideas from image processing and optimization theory. Our proposed model divides the region of interest into pixels and operates SNP by SNP. We estimate allele frequencies across the landscape by maximizing a product of binomial likelihoods penalized by nearest neighbor interactions. Penalization smooths allele frequency estimates and promotes estimation at pixels with no data. Maximization is accomplished by a minorize-maximize (MM) algorithm. Once allele frequency surfaces are available, one can apply Bayes' rule to compute the posterior probability that each pixel is the pixel of origin of a given person. Placement of admixed individuals on the landscape is more complicated and requires estimation of the fractional contribution of each pixel to a person's genome. This estimation problem also succumbs to a penalized MM algorithm. We applied the model to the Population Reference Sample (POPRES) data. The model gives better localization for both unmixed and admixed individuals than existing methods despite using just a small fraction of the available SNPs. Computing times are comparable with the best competing software. Software will be freely available as the OriGen package in R. ranolaj@uw.edu or klange@ucla.edu Supplementary data are available at Bioinformatics online.

Methods for time series analysis of RNA-seq data with application to human Th17 cell differentiation.

Motivation: Gene expression profiling using RNA-seq is a powerful technique for screening RNA species’ landscapes and their dynamics in an unbiased way. While several advanced methods exist for differential expression analysis of RNA-seq data, proper tools to anal.yze RNA-seq time-course have not been proposed.Results: In this study, we use RNA-seq to measure gene expression during the early human T helper 17 (Th17) cell differentiation and T-cell activation (Th0). To quantify Th17-specific gene expression dynamics, we present a novel statistical methodology, DyNB, for analyzing time-course RNA-seq data. We use non-parametric Gaussian processes to model temporal correlation in gene expression and combine that with negative binomial likelihood for the count data. To account for experiment-specific biases in gene expression dynamics, such as differences in cell differentiation efficiencies, we propose a method to rescale the dynamics between replicated measurements. We develop an MCMC sampling method to make inference of differential expression dynamics between conditions. DyNB identifies several known and novel genes involved in Th17 differentiation. Analysis of differentiation efficiencies revealed consistent patterns in gene expression dynamics between different cultures. We use qRT-PCR to validate differential expression and differentiation efficiencies for selected genes. Comparison of the results with those obtained via traditional timepoint-wise analysis shows that time-course analysis together with time rescaling between cultures identifies differentially expressed genes which would not otherwise be detected.Availability: An implementation of the proposed computational methods will be available at http://research.ics.aalto.fi/csb/software/Contact: tarmo.aijo@aalto.fi or harri.lahdesmaki@aalto.fiSupplementary information: Supplementary data are available at Bioinformatics online.