Bayesian tools for zero counts in compositional data

The log-ratio methodology makes available powerful tools for analyzing compositionaldata. Nevertheless, the use of this methodology is only possible for those data setswithout null values. Consequently, in those data sets where the zeros are present, aprevious treatment becomes necessary. Last advances in the treatment of compositionalzeros have been centered especially in the zeros of structural nature and in the roundedzeros. These tools do not contemplate the particular case of count compositional datasets with null values. In this work we deal with \count zeros" and we introduce atreatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichletprobability distribution as a prior and we estimate the posterior probabilities. Then weapply a multiplicative modi¯cation for the non-zero values. We present a case studywhere this new methodology is applied.Key words: count data, multiplicative replacement, composition, log-ratio analysis

Efficacy of prescribed injectable diacetylmorphine in the Andalusian trial: Bayesian analysis of responders and non-responders according to a multi domain outcome index.

BACKGROUND The objective of this research was to evaluate data from a randomized clinical trial that tested injectable diacetylmorphine (DAM) and oral methadone (MMT) for substitution treatment, using a multi-domain dichotomous index, with a Bayesian approach. METHODS Sixty two long-term, socially-excluded heroin injectors, not benefiting from available treatments were randomized to receive either DAM or MMT for 9 months in Granada, Spain. Completers were 44 and data at the end of the study period was obtained for 50. Participants were determined to be responders or non responders using a multi-domain outcome index accounting for their physical and mental health and psychosocial integration, used in a previous trial. Data was analyzed with Bayesian methods, using information from a similar study conducted in The Netherlands to select a priori distributions. On adding the data from the present study to update the a priori information, the distribution of the difference in response rates were obtained and used to build credibility intervals and relevant probability computations. RESULTS In the experimental group (n = 27), the rate of responders to treatment was 70.4% (95% CI 53.287.6), and in the control group (n = 23), it was 34.8% (95% CI 15.354.3). The probability of success in the experimental group using the a posteriori distributions was higher after a proper sensitivity analysis. Almost the whole distribution of the rates difference (the one for diacetylmorphine minus methadone) was located to the right of the zero, indicating the superiority of the experimental treatment. CONCLUSION The present analysis suggests a clinical superiority of injectable diacetylmorphine compared to oral methadone in the treatment of severely affected heroin injectors not benefiting sufficiently from the available treatments. TRIAL REGISTRATION Current Controlled Trials ISRCTN52023186.

Implementing statistical learning methods through Bayesian networks (Part 2): bayesian evaluations for results of black toner analyses in forensic document examination

This paper presents and discusses the use of Bayesian procedures - introduced through the use of Bayesian networks in Part I of this series of papers - for 'learning' probabilities from data. The discussion will relate to a set of real data on characteristics of black toners commonly used in printing and copying devices. Particular attention is drawn to the incorporation of the proposed procedures as an integral part in probabilistic inference schemes (notably in the form of Bayesian networks) that are intended to address uncertainties related to particular propositions of interest (e.g., whether or not a sample originates from a particular source). The conceptual tenets of the proposed methodologies are presented along with aspects of their practical implementation using currently available Bayesian network software.

Bayesian nash equilibrium in ''linear'' cournot models with private information about costs

Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesianf equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.

Using a Bayesian method to assign individuals to karyotypic taxa in shrew hybrid zones.

Individuals sampled in hybrid zones are usually analysed according to their sampling locality, morphology, behaviour or karyotype. But the increasing availability of genetic information more and more favours its use for individual sorting purposes and numerous assignment methods based on the genetic composition of individuals have been developed. The shrews of the Sorex araneus group offer good opportunities to test the genetic assignment on individuals identified by their karyotype. Here we explored the potential and efficiency of a Bayesian assignment method combined or not with a reference dataset to study admixture and individual assignment in the difficult context of two hybrid zones between karyotypic species of the Sorex araneus group. As a whole, we assigned more than 80% of the individuals to their respective karyotypic categories (i.e. 'pure' species or hybrids). This assignment level is comparable to what was obtained for the same species away from hybrid zones. Additionally, we showed that the assignment result for several individuals was strongly affected by the inclusion or not of a reference dataset. This highlights the importance of such comparisons when analysing hybrid zones. Finally, differences between the admixture levels detected in both hybrid zones support the hypothesis of an impact of chromosomal rearrangements on gene flow.

Probabilistic evidential assessment of gunshot residue particle evidence (Part II) : Bayesian parameter estimation for experimental count data.

Part I of this series of articles focused on the construction of graphical probabilistic inference procedures, at various levels of detail, for assessing the evidential value of gunshot residue (GSR) particle evidence. The proposed models - in the form of Bayesian networks - address the issues of background presence of GSR particles, analytical performance (i.e., the efficiency of evidence searching and analysis procedures) and contamination. The use and practical implementation of Bayesian networks for case pre-assessment is also discussed. This paper, Part II, concentrates on Bayesian parameter estimation. This topic complements Part I in that it offers means for producing estimates useable for the numerical specification of the proposed probabilistic graphical models. Bayesian estimation procedures are given a primary focus of attention because they allow the scientist to combine (his/her) prior knowledge about the problem of interest with newly acquired experimental data. The present paper also considers further topics such as the sensitivity of the likelihood ratio due to uncertainty in parameters and the study of likelihood ratio values obtained for members of particular populations (e.g., individuals with or without exposure to GSR).

Is spinal stenosis assessment dependent on slice orientation? A magnetic resonance imaging study.

INTRODUCTION: Lumbar spinal stenosis (LSS) treatment is based primarily on the clinical criteria providing that imaging confirms radiological stenosis. The radiological measurement more commonly used is the dural sac cross-sectional area (DSCA). It has been recently shown that grading stenosis based on the morphology of the dural sac as seen on axial T2 MRI images, better reflects severity of stenosis than DSCA and is of prognostic value. This radiological prospective study investigates the variability of surface measurements and morphological grading of stenosis for varying degrees of angulation of the T2 axial images relative to the disc space as observed in clinical practice. MATERIALS AND METHODS: Lumbar spine TSE T2 three-dimensional (3D) MRI sequences were obtained from 32 consecutive patients presenting with either suspected spinal stenosis or low back pain. Axial reconstructions using the OsiriX software at 0°, 10°, 20° and 30° relative to the disc space orientation were obtained for a total of 97 levels. For each level, DSCA was digitally measured and stenosis was graded according to the 4-point (A-D) morphological grading by two observers. RESULTS: A good interobserver agreement was found in grade evaluation of stenosis (k = 0.71). DSCA varied significantly as the slice orientation increased from 0° to +10°, +20° and +30° at each level examined (P < 0.0001) (-15 to +32% at 10°, -24 to +143% at 20° and -29 to +231% at 30° of slice orientation). Stenosis definition based on the surface measurements changed in 39 out of the 97 levels studied, whereas the morphology grade was modified only in two levels (P < 0.01). DISCUSSION: The need to obtain continuous slices using the classical 2D MRI acquisition technique entails often at least a 10° slice inclination relative to one of the studied discs. Even at this low angulation, we found a significantly statistical difference between surface changes and morphological grading change. In clinical practice, given the above findings, it might therefore not be necessary to align the axial cuts to each individual disc level which could be more time-consuming than obtaining a single series of axial cuts perpendicular to the middle of the lumbar spine or to the most stenotic level. In conclusion, morphological grading seems to offer an alternative means of assessing severity of spinal stenosis that is little affected by image acquisition technique.

Single breath-hold slice-following CSPAMM myocardial tagging.

Myocardial tagging has shown to be a useful magnetic resonance modality for the assessment and quantification of local myocardial function. Many myocardial tagging techniques suffer from a rapid fading of the tags, restricting their application mainly to systolic phases of the cardiac cycle. However, left ventricular diastolic dysfunction has been increasingly appreciated as a major cause of heart failure. Subtraction based slice-following CSPAMM myocardial tagging has shown to overcome limitations such as fading of the tags. Remaining impediments to this technique, however, are extensive scanning times (approximately 10 min), the requirement of repeated breath-holds using a coached breathing pattern, and the enhanced sensitivity to artifacts related to poor patient compliance or inconsistent depths of end-expiratory breath-holds. We therefore propose a combination of slice-following CSPAMM myocardial tagging with a segmented EPI imaging sequence. Together with an optimized RF excitation scheme, this enables to acquire as many as 20 systolic and diastolic grid-tagged images per cardiac cycle with a high tagging contrast during a short period of sustained respiration.

Bayesian networks for evaluating forensic DNA profiling evidence: a review and guide to literature

Almost 30 years ago, Bayesian networks (BNs) were developed in the field of artificial intelligence as a framework that should assist researchers and practitioners in applying the theory of probability to inference problems of more substantive size and, thus, to more realistic and practical problems. Since the late 1980s, Bayesian networks have also attracted researchers in forensic science and this tendency has considerably intensified throughout the last decade. This review article provides an overview of the scientific literature that describes research on Bayesian networks as a tool that can be used to study, develop and implement probabilistic procedures for evaluating the probative value of particular items of scientific evidence in forensic science. Primary attention is drawn here to evaluative issues that pertain to forensic DNA profiling evidence because this is one of the main categories of evidence whose assessment has been studied through Bayesian networks. The scope of topics is large and includes almost any aspect that relates to forensic DNA profiling. Typical examples are inference of source (or, 'criminal identification'), relatedness testing, database searching and special trace evidence evaluation (such as mixed DNA stains or stains with low quantities of DNA). The perspective of the review presented here is not exclusively restricted to DNA evidence, but also includes relevant references and discussion on both, the concept of Bayesian networks as well as its general usage in legal sciences as one among several different graphical approaches to evidence evaluation.

Substantial advantage of a combined Bayesian and genotyping approach in testosterone doping tests.

Testosterone abuse is conventionally assessed by the urinary testosterone/epitestosterone (T/E) ratio, levels above 4.0 being considered suspicious. A deletion polymorphism in the gene coding for UGT2B17 is strongly associated with reduced testosterone glucuronide (TG) levels in urine. Many of the individuals devoid of the gene would not reach a T/E ratio of 4.0 after testosterone intake. Future test programs will most likely shift from population based- to individual-based T/E cut-off ratios using Bayesian inference. A longitudinal analysis is dependent on an individual's true negative baseline T/E ratio. The aim was to investigate whether it is possible to increase the sensitivity and specificity of the T/E test by addition of UGT2B17 genotype information in a Bayesian framework. A single intramuscular dose of 500mg testosterone enanthate was given to 55 healthy male volunteers with either two, one or no allele (ins/ins, ins/del or del/del) of the UGT2B17 gene. Urinary excretion of TG and the T/E ratio was measured during 15 days. The Bayesian analysis was conducted to calculate the individual T/E cut-off ratio. When adding the genotype information, the program returned lower individual cut-off ratios in all del/del subjects increasing the sensitivity of the test considerably. It will be difficult, if not impossible, to discriminate between a true negative baseline T/E value and a false negative one without knowledge of the UGT2B17 genotype. UGT2B17 genotype information is crucial, both to decide which initial cut-off ratio to use for an individual, and for increasing the sensitivity of the Bayesian analysis.

Assessment of volumetric bone mineral density of the femoral neck in postmenopausal women with and without vertebral fractures using quantitative multi-slice CT.

OBJECTIVE: To demonstrate the validity and reliability of volumetric quantitative computed tomography (vQCT) with multi-slice computed tomography (MSCT) and dual energy X-ray absorptiometry (DXA) for hip bone mineral density (BMD) measurements, and to compare the differences between the two techniques in discriminating postmenopausal women with osteoporosis-related vertebral fractures from those without. METHODS: Ninety subjects were enrolled and divided into three groups based on the BMD values of the lumbar spine and/or the femoral neck by DXA. Groups 1 and 2 consisted of postmenopausal women with BMD changes <-2SD, with and without radiographically confirmed vertebral fracture (n=11 and 33, respectively). Group 3 comprised normal controls with BMD changes > or =-1SD (n=46). Post-MSCT (GE, LightSpeed16) scan reconstructed images of the abdominal-pelvic region, 1.25 mm thick per slice, were processed by OsteoCAD software to calculate the following parameters: volumetric BMD values of trabecular bone (TRAB), cortical bone (CORT), and integral bone (INTGL) of the left femoral neck, femoral neck axis length (NAL), and minimum cross-section area (mCSA). DXA BMD measurements of the lumbar spine (AP-SPINE) and the left femoral neck (NECK) also were performed for each subject. RESULTS: The values of all seven parameters were significantly lower in subjects of Groups 1 and 2 than in normal postmenopausal women (P<0.05, respectively). Comparing Groups 1 and 2, 3D-TRAB and 3D-INTGL were significantly lower in postmenopausal women with vertebral fracture(s) [(109.8+/-9.61) and (243.3+/-33.0) mg/cm3, respectively] than in those without [(148.9+/-7.47) and (285.4+/-17.8) mg/cm(3), respectively] (P<0.05, respectively), but no significant differences were evident in AP-SPINE or NECK BMD. CONCLUSION: the femoral neck-derived volumetric BMD parameters using vQCT appeared better than the DXA-derived ones in discriminating osteoporotic postmenopausal women with vertebral fractures from those without. vQCT might be useful to evaluate the effect of osteoporotic vertebral fracture status on changes in bone mass in the femoral neck.

Panel index VAR models: Specification, Estimation, Testing and Leading Indicators

This paper proposes a method to conduct inference in panel VAR models with cross unit interdependencies and time variations in the coefficients. The approach can be used to obtain multi-unit forecasts and leading indicators and to conduct policy analysis in a multiunit setups. The framework of analysis is Bayesian and MCMC methods are used to estimate the posterior distribution of the features of interest. The model is reparametrized to resemble an observable index model and specification searches are discussed. As an example, we construct leading indicators for inflation and GDP growth in the Euro area using G-7 information.