Exploring models for the length of stay distribution.

Diagnosis Related Groups (DRG) are frequently used to standardize the comparison of consumption variables, such as length of stay (LOS). In order to be reliable, this comparison must control for the presence of outliers, i.e. values far removed from the pattern set by the majority of the data. Indeed, outliers can distort the usual statistical summaries, such as means and variances. A common practice is to trim LOS values according to various empirical rules, but there is little theoretical support for choosing between alternative procedures. This pilot study explores the possibility of describing LOS distributions with parametric models which provide the necessary framework for the use of robust methods.

Health risk behavior pattern among students from Cartagena, Colombia: prevalence and associated variables

The aim of the study was to determine the prevalence and variables associated with the pattern of risky health behavior (PRHB) among adolescent students in Cartagena, Colombia. A cross-sectional study was designed to investigate PRHB in a random cluster sample of students from middle and high schools. The associations were adjusted by logistic regression. A total of 2,625 students participated in this research, with ages from 10 to 20 years, mean=13.8 years (SD=2.0), and 54.3% were women. A total of 332 students reported PRHB (12.7%, 95%CI 11.4–14.0). Age over 15 years (OR=2.19, 95%CI 1.72–2.79), not being heterosexual (OR=1.98, 95%CI 1.36-2.87), poor/mediocre academic performance (OR=1.87, 95%CI 1.47–2.38), family dysfunction (OR=1.78, 95%CI 1.40–2.28) and male gender (OR=1.58, 95%CI 1.24–2.01) were associated with PRHB. One in every eight students presented a PRHB. It is important to pay greater attention to students who are over 15 years of age, male, not heterosexual, with a poor/mediocre academic performance and a dysfunctional family.

Factors associated with vaccination against Influenza A (H1N1) in the elderly

This study aimed to investigate the sociodemographic, clinical and behavioral factors and receiving information about the vaccine against pandemic influenza A (H1N1) associated with vaccination of elderly people. Study of quantitative and transversal nature, in which 286 elderly residents in Fortaleza, CE, Brazil participated. The association between variables was analyzed by the Pearson chi-square test, considering a 95% confidence interval and significance level (p≤0.05). The results revealed that, unlike the sociodemographic characteristics, many clinical, behavioral and informational aspects correlated significantly with adherence to Influenza A (H1N1) vaccination. It is believed that the findings can be used in strategies to control and prevent infection by viral subtypes within the elderly population, extensible even to other vaccine-preventable diseases, especially in light of possible future pandemics.

Analysis of variables that are not directly observable: influence on decision-making during the research process

The sample dimension, types of variables, format used for measurement, and construction of instruments to collect valid and reliable data must be considered during the research process. In the social and health sciences, and more specifically in nursing, data-collection instruments are usually composed of latent variables or variables that cannot be directly observed. Such facts emphasize the importance of deciding how to measure study variables (using an ordinal scale or a Likert or Likert-type scale). Psychometric scales are examples of instruments that are affected by the type of variables that comprise them, which could cause problems with measurement and statistical analysis (parametric tests versus non-parametric tests). Hence, investigators using these variables must rely on suppositions based on simulation studies or recommendations based on scientific evidence in order to make the best decisions.

Pheomelanin-based colouration is correlated with indices of flying strategies in the barn owl

Resource polymorphism refers to individuals from the same population foraging in alternative habitats or on alternative food. Food specialization can be associated with adaptations such as colour polymorphism, with pale and dark colours conferring differential camouflage in different habitats. Pale and dark-reddish pheomelanic Barn Owls (Tyto alba) forage on different prey species in closed and open habitats, respectively. We show here that darker-reddish owls have heavier stomach content when found dead, and their 5th secondary wing feather is more deeply anchored inside the integument. These correlations suggest that their feathers bend less when flying, and that darker-reddish Barn Owls are able sustain more intense flying than their paler conspecifics.

Bioclimatic constraints to Andean cat distribution: a modelling application for rare species

AimTo identify the bioclimatic niche of the endangered Andean cat (Leopardus jacobita), one of the rarest and least known felids in the world, by developing a species distribution model.LocationSouth America, High Andes and Patagonian steppe. Peru, Bolivia, Chile, Argentina.MethodsWe used 108 Andean cat records to build the models, and 27 to test them, applying the Maxent algorithm to sets of uncorrelated bioclimatic variables from global databases, including elevation. We based our biogeographical interpretations on the examination of the predicted geographic range, the modelled response curves and latitudinal variations in climatic variables associated with the locality data.ResultsSimple bioclimatic models for Andean cats were highly predictive with only 3-4 explanatory variables. The climatic niche of the species was defined by extreme diurnal variations in temperature, cold minimum and moderate maximum temperatures, and aridity, characteristic not only of the Andean highlands but also of the Patagonian steppe. Argentina had the highest representation of suitable climates, and Chile the lowest. The most favourable conditions were centrally located and spanned across international boundaries. Discontinuities in suitable climatic conditions coincided with three biogeographical barriers associated with climatic or topographic transitions.Main conclusionsSimple bioclimatic models can produce useful predictions of suitable climatic conditions for rare species, including major biogeographical constraints. In our study case, these constraints are also known to affect the distribution of other Andean species and the genetic structure of Andean cat populations. We recommend surveys of areas with suitable climates and no Andean cat records, including the corridor connecting two core populations. The inclusion of landscape variables at finer scales, crucially the distribution of Andean cat prey, would contribute to refine our predictions for conservation applications.

New anthropometry-based age- and sex-specific reference values for urinary 24-hour creatinine excretion based on the adult Swiss population (epublish)

BACKGROUND: Urinary creatinine excretion is used as a marker of completeness of timed urine collections, which are a keystone of several metabolic evaluations in clinical investigations and epidemiological surveys. METHODS: We used data from two independent Swiss cross-sectional population-based studies with standardised 24-hour urinary collection and measured anthropometric variables. Only data from adults of European descent, with estimated glomerular filtration rate (eGFR) ≥60 ml/min/1.73 m2 and reported completeness of the urinary collection were retained. A linear regression model was developed to predict centiles of the 24-hour urinary creatinine excretion in 1,137 participants from the Swiss Survey on Salt and validated in 994 participants from the Swiss Kidney Project on Genes in Hypertension. RESULTS: The mean urinary creatinine excretion was 193 ± 41 μmol/kg/24 hours in men and 151 ± 38 μmol/kg/24 hours in women in the Swiss Survey on Salt. The values were inversely correlated with age and body mass index (BMI). CONCLUSIONS: We propose a validated prediction equation for 24-hour urinary creatinine excretion in the general European population, based on readily available variables such as age, sex and BMI, and a few derived normograms to ease its clinical application. This should help healthcare providers to interpret the completeness of a 24-hour urine collection in daily clinical practice and in epidemiological population studies.

Assessment of diesel exhaust particulate exposure and surface characteristics in association with levels of oxidative stress biomarkers

Exposure to PM10 and PM2.5 (particulate matter with aerodynamic diameter smaller than 10 μm and 2.5 μm, respectively) is associated with a range of adverse health effects, including cancer, pulmonary and cardiovascular diseases. Surface characteristics (chemical reactivity, surface area) are considered of prime importance to understand the mechanisms which lead to harmful effects. A hypothetical mechanism to explain these adverse effects is the ability of components (organics, metal ions) adsorbed on these particles to generate Reactive Oxygen Species (ROS), and thereby to cause oxidative stress in biological systems (Donaldson et al., 2003). ROS can attack almost any cellular structure, like DNA or cellular membrane, leading to the formation of a wide variety of degradation products which can be used as a biomarker of oxidative stress. The aim of the present research project is to test whether there is a correlation between the exposure to Diesel Exhaust Particulate (DEP) and the oxidative stress status. For that purpose, a survey has been conducted in real occupational situations where workers were exposed to DEP (bus depots). Different exposure variables have been considered: - particulate number, size distribution and surface area (SMPS); - particulate mass - PM2.5 and PM4 (gravimetry); - elemental and organic carbon (coulometry); - total adsorbed heavy metals - iron, copper, manganese (atomic adsorption); - surface functional groups present on aerosols (Knudsen flow reactor). (Demirdjian et al., 2005). Several biomarkers of oxidative stress (8-hydroxy-2'-deoxyguanosine and several aldehydes) have been determined either in urine or serum of volunteers. Results obtained during the sampling campaign in several bus depots indicated that the occupational exposure to particulates in these places was rather low (40-50 μg/m3 for PM4). Size distributions indicated that particles are within the nanometric range. Surface characteristics of sampled particles varied strongly, depending on the bus depot. They were usually characterized by high carbonyl and low acidic sites content. Among the different biomarkers which have been analyzed within the framework of this study, mean levels of 8- hydroxy-2'-deoxyguanosine and several aldehydes (hexanal, heptanal, octanal, nonanal) increased during two consecutive days of exposure for non-smokers. In order to bring some insight into the relation between the particulate characteristics and the formation of ROS by-products, biomarkers levels will be discussed in relation with exposure variables.

Pharmacokinetic and pharmacogenetic factors influencing plasma and cellular antiretroviral drug disposition

Abstract: The improvement in antiretroviral drug therapy has transformed HIV infection into a chronic disease. However, treatment failure and drug toxicity are frequent. Inadequate response to treatment is clearly multifactorial and, therefore, dosage individualisation based on demographic factors, genetic markers and measurement of cellular and plasma drug level may enhance both drug efficacy and tolerability. At present, antiretroviral drugs levels are monitored in plasma, whereas only drugs penetrating into cells are able to exert an antiviral activity, suggesting that cellular drug determination may more confidently reflect drug exposure at the site of pharmacological action. The overall objective of this thesis is to provide a better understanding of the Pharmacokinetic and pharmacogenetic factors influencing the plasma and cellular disposition of antiretroviral drugs. To that endeavour, analytical methods for the measurements of plasma and cellular drug levels have been developed and validated using liquid chromatography methods coupled with ultraviolet and tandem mass spectrometry detection, respectively. Correlations between plasma and cellular exposures were assessed during observational and experimental studies. Cytochrome (CYP) 2B6, efflux transporters (ABCB1, ABCC1, ABCC2 and ABCG2) and orosomucoid (ORM) polymorphisms were determined and were related to plasma and cellular exposures, as well as toxicity of antiretroviral drugs. A Pharmacokinetic population model was developed to characterise inter- and intra-patient variability of atazanavir pharmacokinetics, and to identify covariates influencing drug disposition. In that context, a Pharmacokinetic interaction study between atazanavir and lopinavir, both boosted with ritonavir, has beén conducted to assess the safety and pharmacokinetics of this boosted double-protease inhibitors regimen. Well to moderately-correlated cellular and plasma drug levels are .observed or protease inhibitors, whereas for efavirenz and nevirapine these correlations are weak. Cellular exposure, and CYP2B6 genotype (516G>T) are predictors of efavirenz neuropsychological toxicity. Nevirapine plasma exposure is also influenced by CYPZB6 polymorphism. Nelfinavir cellular exposure appears to be significantly associated only with ABCB1 genotype (3435C>T and intron 26 + 80T>C). Indinavir and lopinavir clearance and lopinavir cellular/plasma exposure ratio are influenced by the concentration of the variant S of ORM, suggesting-a specific binding of these drugs to this variant. Nelfinavir and efavirenz are not influenced by ORM concentration and phenotype. The Pharmacokinetic parameters of atazanavir are adequately described by our population model. The atazanavir-lopinavir interaction study indicates no influence on plasma and cellular atazanavir pharmacokinetics, while limited decrease in lopinavir concentrations was observed after atazanavir addition. The residual variability unexplained by the considered variables suggests that other covariates either uncontrolled at present or remaining to be identified, such as genetic and environmental factors influence antiretroviral drug pharmacokinetics, with substantial impact on treatment efficacy and tolerability. In that context, a comprehensive approach taking into account drug pharmacokinetics and patient genetic background is expected to contribute to increase treatment success, and to reduce the occurrence of adverse drug reactions by stratifying patients in an individualised antiretroviral therapy approach. Résumé Facteurs pharmacocinétiques et pharmacogénétiques influençant l'exposition plasmatique et cellulaire des antirétroviraux Les progrès de la thérapie antirétrovirale ont transformé l'infection par le VIH d'une affection mortelle à une maladie chronique. En dépit de ce succès, l'échec thérapeutique et la toxicité médicamenteuse restent fréquents. Une réponse inadéquate au traitement est clairement multifactorielle et une individualisation de la posologie des médicaments qui se baserait sur les facteurs démographiques et génétiques des patients et sur les taux sanguins des médicaments pourrait améliorer à la fois l'efficacité et la tolérance de la thérapie. Par ailleurs, seules les concentrations plasmatiques sont actuellement considérées pour le suivi thérapeutique des médicaments, alors que les taux cellulaires pourraient mieux refléter l'activité de ses médicaments qui agissent au niveau intracellulaire. L'objectif global de cette thèse était de mieux comprendre les facteurs pharmacocinétiques et pharmacocénétiques influençant l'exposition plasmatique et cellulaire des médicaments antirétroviraux. A cet effet, des méthodes pour quantifier les concentrations plasmatiques et cellulaires des antirétroviraux ont été développées et validées en utilisant la chromatographie liquide couplée à la détection ultraviolette et la spectrométrie de masse en tandem, respectivement. La corrélation entre l'exposition cellulaire et plasmatique de ces médicaments a été étudiée lors d'études observationnelles et expérimentales. Les polymorphismes du cytochrome (CYP) 2B6, ainsi que des transporteurs d'efflux (ABCB1, ABCC1, ABCC2 et ABCG2) et de l'orosomucoïde (ORM) ont été déterminés et corrélés avec l'exposition plasmatique et cellulaire des antirétroviraux, ainsi qu'à leur toxicité. Un modèle de pharmacocinétique de population a été établi afin de caractériser la variabilité inter- et intra-individuelle de l'atazanavir, et d'identifier les covariables pouvant influencer le devenir de ce médicament. Dans ce contexte, une étude d'interaction entre l'atazanavir et le lopinavir a été effectuée afin de déterminer la sécurité et le profil pharmacocinétique de ce régime thérapeutique. Des corrélations modérées à bonnes ont été observées entre les taux cellulaires et plasmatiques des inhibiteurs de protéase, alors que pour l'efavirenz et la névirapine ces corrélations sont faibles. L'exposition cellulaire, ainsi que le génotype du CYP2B6 (516G>T) sont des indices de la toxicité neuropsychologique de l'efavirenz. L'exposition plasmatique de la névirapine est également influencée par le polymorphisme du CYPZB6. L'exposition cellulaire du nelfinavir est significativement associée au génotype du ABCB1 (3435C>T et intron 26 + 80T>C). La clairance de l'indinavir et du lopinavir, ainsi que le rapport entre exposition cellulaire et plasmatique du lopinavir sont influencés par la concentration du variant S de l'ORM, suggérant une liaison spécifique de ces médicaments à ce variant. La clairance du nelfinavir et de l'efavirenz n'est pas influencée ni par la concentration ni par le phénotype de l'ORM. Les paramètres pharmacocinétiques de l'atazanavir ont été décrits de façon adéquate par le modèle de population proposé. De plus, le lopinavir n'influence pas les concentrations plasmatiques et cellulaires de l'atazanavir; alors que celui-ci conduit à une baisse limitée des taux de lopinavir. L'importante variabilité pharmacocinétique des antirétroviraux suggère que d'autres facteurs génétiques et environnementaux -qui restent encore à découvrir- influencent également leur disponibilité. Dans un proche futur, une prise en charge qui tienne. compte de la pharmacocinétique des médicaments et des caractéristiques génétiques du patient devrait permettre d'individualiser le traitement, contribuant certainement à une amélioration de la réponse thérapeutique et à une diminution de la toxicité. Résumé grand public Facteurs pharmacocinétiques et pharmacogénétiques influençant l'exposition plasmatique et cellulaire des antirétroviraux Les progrès effectués dans le traitement de l'infection par le virus de l'immunodéficience humaine acquise (VIH), ont permis de transformer une maladie avec un pronostic sombre, en une maladie chronique traitable avec des médicaments de plus en plus efficaces. Malgré ce succès, de nombreux patients ne répondent pas de façon optimale à leur traitement et/ou souffrent d'effets indésirables médicamenteux entraînant fréquemment une modification de leur thérapie. Actuellement, le suivi de la réponse au traitement s'effectue par la mesure chez les patients de la quantité de virus et du nombre des cellules immunitaires dans le sang, ainsi que par la concentration sanguine des médicaments administrés. Cependant, comme le virus se réplique à l'intérieur de la cellule, la mesure des concentrations médicamenteuses au niveau intracellulaire pourrait mieux refléter l'activité pharmacologique au site d'action. De plus, il a été possible de mettre en évidence la grande variabilité des concentrations plasmatiques de médicaments chez des patients prenant pourtant la même dose de médicament. Comme cette variabilité est notamment due à des facteurs génétiques qui sont susceptibles d'influencer la réponse au traitement antirétroviral, des analyses génétiques ont été également effectuées chez ces patients. Cette thèse a eu pour objectif de mieux comprendre les facteurs pharmacologiques et génétiques influençant l'activité et la toxicité des médicaments antirétroviraux afin de réduire la variabilité de la réponse thérapeutique. A cet effet, une méthode de dosage permettant la quantification des médicaments anti-HIV au niveau intracellulaire a été développée. Par ailleurs, nos études ont également porté .sur les variations génétiques influençant la quantité et l'activité des protéines impliquées dans le métabolisme et dans le transport des médicaments antirétroviraux. Enfin, les conséquences de ces variations sur la réponse clinique et la toxicité du traitement ont été évaluées. Nos études ont mis en évidence des associations significatives entre les variations génétiques considérées et la concentration sanguine, cellulaire et la toxicité de quelques médicaments antirétroviraux. La complémentarité des connaissances pharmacologiques, génétiques et virales pourrait aboutir à une stratégie globale permettant d'individualiser le traitement et la dose administrée, en fonction des caractéristiques propres de chaque patient. Cette approche pourrait contribuer à une optimisation du traitement antirétroviral dans la perspective d'une meilleure- efficacité thérapeutique à long terme et d'une diminution des effets indésirables rencontrés.

Clinical, polysomnographic and genome-wide association analyses of narcolepsy with cataplexy: a European Narcolepsy Network study.

The aim of this study was to describe the clinical and PSG characteristics of narcolepsy with cataplexy and their genetic predisposition by using the retrospective patient database of the European Narcolepsy Network (EU-NN). We have analysed retrospective data of 1099 patients with narcolepsy diagnosed according to International Classification of Sleep Disorders-2. Demographic and clinical characteristics, polysomnography and multiple sleep latency test data, hypocretin-1 levels, and genome-wide genotypes were available. We found a significantly lower age at sleepiness onset (men versus women: 23.74 ± 12.43 versus 21.49 ± 11.83, P = 0.003) and longer diagnostic delay in women (men versus women: 13.82 ± 13.79 versus 15.62 ± 14.94, P = 0.044). The mean diagnostic delay was 14.63 ± 14.31 years, and longer delay was associated with higher body mass index. The best predictors of short diagnostic delay were young age at diagnosis, cataplexy as the first symptom and higher frequency of cataplexy attacks. The mean multiple sleep latency negatively correlated with Epworth Sleepiness Scale (ESS) and with the number of sleep-onset rapid eye movement periods (SOREMPs), but none of the polysomnographic variables was associated with subjective or objective measures of sleepiness. Variant rs2859998 in UBXN2B gene showed a strong association (P = 1.28E-07) with the age at onset of excessive daytime sleepiness, and rs12425451 near the transcription factor TEAD4 (P = 1.97E-07) with the age at onset of cataplexy. Altogether, our results indicate that the diagnostic delay remains extremely long, age and gender substantially affect symptoms, and that a genetic predisposition affects the age at onset of symptoms.

Adherence to nutritional recommendations and sociodemographic variables in patients with diabetes mellitus

OBJECTIVETo determine if there is a relationship between adherence to nutritional recommendations and sociodemographic variables in Brazilian patients with type 2 diabetes mellitus.METHODSCross-sectional observational study using a stratified random sample of 423 individuals. The Food Frequency Questionnaire (FFQ) was used, and the Fisher's exact test was applied with 95% confidence interval (p<0.05).RESULTSOf the 423 subjects, 66.7% were women, mean age of 62.4 years (SD = 11.8), 4.3 years of schooling on average (SD = 3.6) and family income of less than two minimum wages. There was association between the female gender and adherence to diet with adequate cholesterol content (OR: 2.03; CI: 1.23; 3.34), between four and more years of education and adherence to fractionation of meals (OR: 1 92 CI: 1.19; 3.10), and income of less than two minimum wages and adherence to diet with adequate cholesterol content (OR: 1.74; CI: 1.03, 2.95).CONCLUSIONAdherence to nutritional recommendations was associated with the female gender, more than four years of education and family income of less than two minimum wages.

The Effect of Four-Lane to Three-Lane Conversion on the Number of Crashes and Crash Rates in Iowa Roads, June 2005

We analyze crash data collected by the Iowa Department of Transportation using Bayesian methods. The data set includes monthly crash numbers, estimated monthly traffic volumes, site length and other information collected at 30 paired sites in Iowa over more than 20 years during which an intervention experiment was set up. The intervention consisted in transforming 15 undivided road segments from four-lane to three lanes, while an additional 15 segments, thought to be comparable in terms of traffic safety-related characteristics were not converted. The main objective of this work is to find out whether the intervention reduces the number of crashes and the crash rates at the treated sites. We fitted a hierarchical Poisson regression model with a change-point to the number of monthly crashes per mile at each of the sites. Explanatory variables in the model included estimated monthly traffic volume, time, an indicator for intervention reflecting whether the site was a “treatment” or a “control” site, and various interactions. We accounted for seasonal effects in the number of crashes at a site by including smooth trigonometric functions with three different periods to reflect the four seasons of the year. A change-point at the month and year in which the intervention was completed for treated sites was also included. The number of crashes at a site can be thought to follow a Poisson distribution. To estimate the association between crashes and the explanatory variables, we used a log link function and added a random effect to account for overdispersion and for autocorrelation among observations obtained at the same site. We used proper but non-informative priors for all parameters in the model, and carried out all calculations using Markov chain Monte Carlo methods implemented in WinBUGS. We evaluated the effect of the four to three-lane conversion by comparing the expected number of crashes per year per mile during the years preceding the conversion and following the conversion for treatment and control sites. We estimated this difference using the observed traffic volumes at each site and also on a per 100,000,000 vehicles. We also conducted a prospective analysis to forecast the expected number of crashes per mile at each site in the study one year, three years and five years following the four to three-lane conversion. Posterior predictive distributions of the number of crashes, the crash rate and the percent reduction in crashes per mile were obtained for each site for the months of January and June one, three and five years after completion of the intervention. The model appears to fit the data well. We found that in most sites, the intervention was effective and reduced the number of crashes. Overall, and for the observed traffic volumes, the reduction in the expected number of crashes per year and mile at converted sites was 32.3% (31.4% to 33.5% with 95% probability) while at the control sites, the reduction was estimated to be 7.1% (5.7% to 8.2% with 95% probability). When the reduction in the expected number of crashes per year, mile and 100,000,000 AADT was computed, the estimates were 44.3% (43.9% to 44.6%) and 25.5% (24.6% to 26.0%) for converted and control sites, respectively. In both cases, the difference in the percent reduction in the expected number of crashes during the years following the conversion was significantly larger at converted sites than at control sites, even though the number of crashes appears to decline over time at all sites. Results indicate that the reduction in the expected number of sites per mile has a steeper negative slope at converted than at control sites. Consistent with this, the forecasted reduction in the number of crashes per year and mile during the years after completion of the conversion at converted sites is more pronounced than at control sites. Seasonal effects on the number of crashes have been well-documented. In this dataset, we found that, as expected, the expected number of monthly crashes per mile tends to be higher during winter months than during the rest of the year. Perhaps more interestingly, we found that there is an interaction between the four to three-lane conversion and season; the reduction in the number of crashes appears to be more pronounced during months, when the weather is nice than during other times of the year, even though a reduction was estimated for the entire year. Thus, it appears that the four to three-lane conversion, while effective year-round, is particularly effective in reducing the expected number of crashes in nice weather.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

The world distribution of income (estimated from individual country distributions)

We estimate the world distribution of income by integrating individualincome distributions for 125 countries between 1970 and 1998. Weestimate poverty rates and headcounts by integrating the density functionbelow the $1/day and $2/day poverty lines. We find that poverty ratesdecline substantially over the last twenty years. We compute povertyheadcounts and find that the number of one-dollar poor declined by 235million between 1976 and 1998. The number of $2/day poor declined by 450million over the same period. We analyze poverty across different regionsand countries. Asia is a great success, especially after 1980. LatinAmerica reduced poverty substantially in the 1970s but progress stoppedin the 1980s and 1990s. The worst performer was Africa, where povertyrates increased substantially over the last thirty years: the number of$1/day poor in Africa increased by 175 million between 1970 and 1998,and the number of $2/day poor increased by 227. Africa hosted 11% ofthe world s poor in 1960. It hosted 66% of them in 1998. We estimatenine indexes of income inequality implied by our world distribution ofincome. All of them show substantial reductions in global incomeinequality during the 1980s and 1990s.