Estimators in capture–recapture studies with two sources

This paper investigates the applications of capture–recapture methods to human populations. Capture–recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln–Petersen estimator and its modified version, the Chapman estimator, Chao’s lower bound estimator, the Zelterman’s estimator, McKendrick’s moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao’s estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao’s and Chapman’s estimator. Results indicate that Chao’s estimator is less biased than Chapman’s estimator unless both sources are independent. Chao’s estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

Estimators in capture-recapture studies with two sources

This paper investigates the applications of capture-recapture methods to human populations. Capture-recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln-Petersen estimator and its modified version, the Chapman estimator, Chao's lower bound estimator, the Zelterman's estimator, McKendrick's moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao's estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao's and Chapman's estimator. Results indicate that Chao's estimator is less biased than Chapman's estimator unless both sources are independent. Chao's estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

Bayesian retrieval of complete posterior PDFs of oceanic rain rate from microwave observations

A new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) over the ocean is presented, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain-rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes’s theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance the understanding of theoretical benefits of the Bayesian approach, sensitivity analyses have been conducted based on two synthetic datasets for which the “true” conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism, but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak owing to saturation effects. It is also suggested that both the choice of the estimators and the prior information are crucial to the retrieval. In addition, the performance of the Bayesian algorithm herein is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Comparing hybrid data assimilation methods on the Lorenz 1963 model with increasing nonlinearity

We systematically compare the performance of ETKF-4DVAR, 4DVAR-BEN and 4DENVAR with respect to two traditional methods (4DVAR and ETKF) and an ensemble transform Kalman smoother (ETKS) on the Lorenz 1963 model. We specifically investigated this performance with increasing nonlinearity and using a quasi-static variational assimilation algorithm as a comparison. Using the analysis root mean square error (RMSE) as a metric, these methods have been compared considering (1) assimilation window length and observation interval size and (2) ensemble size to investigate the influence of hybrid background error covariance matrices and nonlinearity on the performance of the methods. For short assimilation windows with close to linear dynamics, it has been shown that all hybrid methods show an improvement in RMSE compared to the traditional methods. For long assimilation window lengths in which nonlinear dynamics are substantial, the variational framework can have diffculties fnding the global minimum of the cost function, so we explore a quasi-static variational assimilation (QSVA) framework. Of the hybrid methods, it is seen that under certain parameters, hybrid methods which do not use a climatological background error covariance do not need QSVA to perform accurately. Generally, results show that the ETKS and hybrid methods that do not use a climatological background error covariance matrix with QSVA outperform all other methods due to the full flow dependency of the background error covariance matrix which also allows for the most nonlinearity.

Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Buff XII regression models. (C) 2008 Published by Elsevier B.V.

Thermoset matrix reinforced with sisal fibers: Effect of the cure cycle on the properties of the biobased composite

Thermoset phenolic composites reinforced with sisal fibers were prepared to optimize the cure step. In the present study, processing parameters such as pressure, temperature, and time interval were varied to control the vaporization of the water generated as a byproduct during the crosslinking reaction. These molecules can vaporize forming voids, which in turn affect the final material properties. The set of results on impact strength revealed that the application of higher pressure before the gel point of the phenolic matrix produced composites with better properties. The SEM images showed that the cure cycle corresponding to the application of higher values of molding pressure at the gel point of the phenolic resin led to the reduction of voids in the matrix. In addition, the increase in the molding pressure during the cure step increased the resin interdiffusion. Better filling of the fiber channels decreased the possibility of water molecules diffusing through the internal spaces of the fibers. These molecules then diffused mainly through the bulk of the thermoset matrix, which led to a decrease in the water diffusion coefficient (D) at all three temperatures (25, 55 and 70 degrees C) considered in the experiments. (C) 2009 Elsevier Ltd. All rights reserved.

Fast Acquisition of (13)C NMR Spectra using the Steady-state Free Precession Sequence

In this paper, we show that the steady-state free precession sequence can be used to acquire (13)C high-resolution nuclear magnetic resonance spectra and applied to qualitative analysis. The analysis of brucine sample using this sequence with 60 degrees flip angle and time interval between pulses equal to 300 ms (acquisition time, 299.7 ms; recycle delay, 300 ms) resulted in spectrum with twofold enhancement in signal-to-noise ratio, when compared to standard (13)C sequence. This gain was better when a much shorter time interval between pulses (100 ms) was applied. The result obtained was more than fivefold enhancement in signal-to-noise ratio, equivalent to more than 20-fold reduction in total data recording time. However, this short time interval between pulses produces a spectrum with severe phase and truncation anomalies. We demonstrated that these anomalies can be minimized by applying an appropriate apodization function and plotting the spectrum in the magnitude mode.

Modelagem dos tempos de falhas ao longo do calendário

Um dos modos de avaliar a confiabilidade de um produto é verificando o comportamento das falhas em testes de uso contínuo. Contudo, essa informação não permite saber em que data a falha ocorrerá. Para resolver esse impasse abordamos na presente dissertação a modelagem dos tempos de falha ao longo do calendário. A modelagem desses tempos permite uma melhor administração do sistema de garantia e assistência técnica, além de possibilitar a empresa estimar e monitorar a confiabilidade do produto. Para proceder com a modelagem, é preciso, inicialmente, conhecer a distribuição de três variáveis: o tempo de vida do produto, em horas de uso contínuo; o tempo de uso do produto, em horas por dia; e o intervalo de tempo entre a manufatura e a venda, em dias. Conhecendo o comportamento dessa variáveis duas alternativas de solução são apresentadas: (a) Modelagem via simulação de Monte Carlo e (b) Modelagem através de solução matemática fechada. São discutidos os casos em que há um ou vários grupos de clientes que utilizam o produto.

Acidentes de trânsito fatais e sua associação com indicadores sociais e adolescência

Introdução - Os acidentes de trânsito são um grave problema de saúde pública universal, em países desenvolvidos e subdesenvolvidos, estando entre as primeiras causas de morte em quase todos os países do mundo (DEL CIAMPO & RICCO, 1996). No Brasil, assu-mem grande relevância, especialmente pela alta morbidade e mortalidade, predominância em populações jovens e/ou economicamente ativas, maior perda de anos de vida produtiva e ele-vado custo direto e indireto para a sociedade. Objetivo - Os objetivos deste trabalho foram descrever a magnitude da mortali-dade por acidentes de trânsito, avaliar sua correlação com indicadores sociais e proporção de jovens na população e testar a sua associação com adolescência, sexo masculino e consumo de álcool. Material e Métodos - Foi realizado, inicialmente, um estudo ecológico envolven-do todas as capitais das unidades da federação e Distrito Federal (exceto o município do Rio de Janeiro), com coleta de dados sobre acidentes de trânsito com vítimas no Departamento Nacional de Trânsito. Foram descritos os índices de acidentes de trânsito com vítimas p/ 1.000 veículos (IAT-V) e de feridos p/ 1.000 veículos (IF-V) referentes aos anos de 1995, 1997 e 1998 e o índice de mortos p/ 10.000 veículos (IM-V) referente ao período de 1995 a 1998. Em seguida, avaliou-se a existência de correlação entre o IM-V e taxa de mortalidade infantil (TMI), índice municipal de desenvolvimento humano (IDH-M), índice de condições de vida (ICV), proporção de condutores adolescentes envolvidos em acidentes de trânsito com vítimas (PCJ-ATV) e proporção de residentes jovens (PRJ) nas diferentes capitais. Em um segundo momento, realizou-se um estudo de caso controle, onde foram estudados 863 condu-tores envolvidos em acidentes de trânsito com vítimas atendidos no Departamento Médico Legal de Porto Alegre, no período de 1998 a 1999. Os condutores foram divididos em dois grupos: condutores envolvidos em acidentes de trânsito com vítima fatal (casos) e com vítima não fatal (controles). Os grupos foram comparados com relação a adolescência, sexo mascu-lino e consumo de álcool, através da razão de chances e seu intervalo de confiança, com signi-ficância determinada pelo teste de qui-quadrado. Resultados - No estudo ecológico, observou-se, no Brasil, uma tendência decres-cente quanto aos indicadores de eventos relacionados ao trânsito no período de 1995 a 1998. Nas capitais das unidades da federação e Distrito Federal, apesar da ampla variação apresenta-da, a maioria manteve a mesma tendência decrescente observada para o país como um todo. Na análise das correlações entre o IM-V e os indicadores sociais, observou-se forte correlação positiva com a TMI (r = 0,57; P = 0,002), ou seja, quanto maior a TMI, maior a mortalidade no trânsito, além de correlação negativa com o IDH-M (r = - 0,41; P = 0,038) e com o ICV (r = - 0,58; P = 0,02). Quando se avaliaram o IDH-M e o ICV separados em suas dimensões, a dimensão renda de ambos indicadores foi a única que não demonstrou correlação com o IM- -V. As demais dimensões do IDH-M e ICV demonstraram correlação negativa, sendo que a dimensão infância (r = - 0,62; P = 0,001) apresentou a maior correlação. A análise da asso-ciação entre o IM-V e a PCJ-ATV não demonstrou correlação, mas, quando avaliada a asso-ciação com a PRJ nas capitais, houve forte correlação positiva (r = 0,59; P = 0,002). No estudo de caso controle, quando avaliada a relação entre condutores envolvidos em acidentes com vítima fatal e adolescência, sexo masculino e consumo de álcool, não foi observada asso-ciação importante em nenhum dos fatores em estudo. Conclusões - Apesar de os indicadores de eventos relacionados ao trânsito (IAT- -V, IF-V e IM-V) terem apresentado uma tendência decrescente durante o período de estudo, acidentes de trânsito continuam sendo um grave problema de saúde pública. O estudo ecológico evidenciou a existência de relação entre o IM-V e os indicadores sociais (TMI, IDH-M e ICV), sendo que a dimensão renda não demonstrou correlação e a dimensão infância apresen-tou a correlação negativa de maior valor. Quanto à PCJ-ATV, não foi encontrada associação relevante entre este indicador e o IM-V. Entretanto, observou-se forte associação entre a PRJ e o IM-V. O estudo de caso controle não evidenciou associação entre adolescência e os de-mais fatores estudados e maior risco para acidente de trânsito fatal.

Analysis of testosterone pulsatility in women with ovulatory menstrual cycles

Objetivo: Avaliar o padrão pulsátil da secreção da testosterona em mulheres normais. Métodos: Oito mulheres saudáveis com ciclos ovulatórios foram selecionadas. Amostras sanguíneas foram coletadas a cada dez minutos durante seis horas, começando entre 7 e 8 h da manhã, após dez horas de jejum, nas três fases do ciclo menstrual: folicular média (Dia 7), folicular tardia (Dia 12) e lútea (Dia 21). Foram mensurados: testosterona, LH e, no basal, também SHBG. Resultados: A frequência dos pulsos de testosterona, média da amplitude do pulso, porcentagem do incremento da amplitude, duração e intervalos dos pulsos foram similares nas três fases (p > 0,05). A pulsatilidade do LH foi estatisticamente diferente entre as três fases (p < 0,001), caracterizando padrão característico do ciclo ovulatório normal. Conclusões: Esses dados aumentam o conhecimento sobre o padrão de secreção da testosterona no ciclo menstrual humano e representam uma contribuição para a investigação clínica, tanto no hiperandrogenismo como na síndrome de insuficiência androgênica __________________________________________________ ABSTRACT Objective: To evaluate the pattern of the pulsatile secretion of testosterone in normal menstrual cycle. Methods: Eight healthy women with ovulatory menstrual cycles were enrolled. Blood samples were collected at ten-minute intervals for six hours, starting between 7 and 8 am, after a ten-hour fasting, in three phases: mid-follicular (Day 7), late follicular (Day 12) and mid-luteal phase (Day 21). Samples were assayed for testosterone, LH and the baseline also for SHBG. Results: Testosterone pulse frequency, mean amplitude pulse, percentage of increment in pulse amplitude, mean duration of pulses and pulse interval were similar in the three phases. LH pulsatility was statistically different among the three phases (p < 0.001) representing normal ovulatory cycles. Conclusions: These data increase the knowledge about the testosterone secretion profile in the human menstrual cycle and can be used as a contribution to clinical investigation in both hyperandrogenism and androgen insufficiency syndrome

Influência de fatores biopsicossociais sobre a mortalidade de idosos no município de Santa Cruz/RN: um estudo prospectivo

The aging process if characterizes for a complex events network, from multidimensional nature, that encloses biological, social, psychic and functional aspects. The alteration of one or more aspects can speed up the aging process, anticipating limitations and until the death in the aged. For an adjusted confrontation of this question is necessary an interdisciplinary vision, in which the some areas of the knowledge can interact and with this to intervenes of the best possible form. Then, information derived from studies of aspects related to incidence, morbidity-mortality and transition patterns, involved in the health-illness process can more accurately identify risk groups thereby establishing links between social factors, illness, incapacity and death. Thus, this study aimed to identify, by a multidimensional vision, the risk factors of mortality in a coorth of elderly in a city in the interior of the state of Rio Grande do Norte (RN), Brazil. A prospective study carried out in Santa Cruz RN, where 310 elderly were randomly selected to form a baseline. The follow-up was 53 months. The predictive variables were divided into sociodemographic, physical health, neuropsychiatric and functional capacity. The statistical analysis carried out by bivariate analysis, survival analysis, followed by binary logistic regression and Cox regression, in the multivariate analysis, considering significant levels p < 0.05 and confidence interval (CI) of 95%. A total of 60 (19.3%) elderly died during the follow-up, where cardiovascular disease was the main cause. The survival was approximately 24.8 months. The study of general survival showed, at 12, 24, 36, and 48 months of observation, a survival rate of 97%, 54%, 31%, and 5% respectively, with a statistical difference in survival only observed for the variables of cognitive function and Basic Activities of Daily Living. In the logistic regression analysis, the risk factors identified were cognitive deficits (OR = 8.74), poor perception of health (OR = 3.89) and dependence for Basic Activities of Daily Living (OR = 3.96). In the Cox analysis, as well as dependence for Basic Activities of Daily Living (HR = 3.17), cognitive deficit (HR = 4.30) and stroke (CVA) (HR = 3.49) continued as independent risk factors for death. The risk factors found in the study can be interpreted as the primary predictors for death among elderly members of the community. Therefore, improvements in health conditions, with actions towards sustaining an autonomous life with special attention for elderly with cognitive impairment, could mean additional healthy quality of life, resulting in the reduction of premature mortality in this population

Avaliação genética de características de escores visuais de bovinos da raça Nelore da desmama até a maturidade

Os objetivos neste estudo foram estimar parâmetros genéticos das características categóricas musculosidade, estrutura física, aspectos raciais, conformação, ônfalo, pigmentação e sacro e predizer os valores genéticos utilizando-se a estatística bayesiana sob modelo animal de limiar, considerando diferentes idades de bovinos da raça Nelore. As informações de escores visuais foram obtidas nos anos de 2000 a 2005 de bovinos provenientes de 13 fazendas participantes do Programa Nelore Brasil. Nas análises bicaracterísticas, foram utilizados 500.000 até 1.100.000 ciclos para alcançar a convergência da cadeia de Gibbs. O descarte inicial e o intervalo amostral foram de 100.000 e 1.000 ciclos, respectivamente. As características de escores visuais avaliadas aos 8 e 22 meses de idade apresentaram estimativas de herdabilidades moderadas, indicando resposta rápida à seleção direta. Os escores visuais indicaram possibilidade de resposta rápida à seleção direta e, portanto, devem ser incorporados em programas de melhoramento genético como critérios de seleção. As estimativas de correlações genéticas entre musculosidade, estrutura física e conformação também indicam que a seleção direta para uma destas características trará progresso genético às outras. Recomenda-se utilizar os escores visuais como critérios de seleção em pelo menos duas fases de vida do animal, na desmama e ao sobreano.

Avaliação dos desempenhos produtivo e reprodutivo de um rebanho bubalino no Estado do Ceará

Foram avaliados os desempenhos produtivo e reprodutivo de um rebanho bubalino, localizado no município de Paracuru, litoral oeste do Estado do Ceará. Os animais foram mantidos em sistema intensivo e submetidos a duas ordenhas diárias. Foram analisadas informações de 87 fêmeas da raça Murrah, entre os anos de 1984 e 1998. As análises estatísticas foram efetuadas por meio do procedimento GLM (SAS, 1990), usando um modelo linear misto. As médias observadas para produção total de leite, duração da lactação, produção de leite no pico de lactação, idade ao primeiro parto e intervalo de partos foram: 2130,80+535,60kg, 301,41+49,30dias, 9,78+1,95kg, 1132,69+166,99dias e 430,79+100,44dias, respectivamente. Alta porcentagem de parições das ocorreu no período chuvoso (79,3%) e apenas 20,7%, no período seco. A produção total de leite e a produção no pico de lactação foram influenciadas pelos efeitos do ano e ordem de parto. A duração da lactação foi influenciada pelos efeitos do ano e mês de parto. A idade ao primeiro parto foi influenciada pelo efeito do ano de nascimento da búfala. O intervalo de partos foi influenciado pelo mês do parto anterior, além dos efeitos do mês dentro do ano de parto e mês de nascimento da búfala.

Uma fundamentação para sinais e sistemas intervalares

In this work we use Interval Mathematics to establish interval counterparts for the main tools used in digital signal processing. More specifically, the approach developed here is oriented to signals, systems, sampling, quantization, coding and Fourier transforms. A detailed study for some interval arithmetics which handle with complex numbers is provided; they are: complex interval arithmetic (or rectangular), circular complex arithmetic, and interval arithmetic for polar sectors. This lead us to investigate some properties that are relevant for the development of a theory of interval digital signal processing. It is shown that the sets IR and R(C) endowed with any correct arithmetic is not an algebraic field, meaning that those sets do not behave like real and complex numbers. An alternative to the notion of interval complex width is also provided and the Kulisch- Miranker order is used in order to write complex numbers in the interval form enabling operations on endpoints. The use of interval signals and systems is possible thanks to the representation of complex values into floating point systems. That is, if a number x 2 R is not representable in a floating point system F then it is mapped to an interval [x;x], such that x is the largest number in F which is smaller than x and x is the smallest one in F which is greater than x. This interval representation is the starting point for definitions like interval signals and systems which take real or complex values. It provides the extension for notions like: causality, stability, time invariance, homogeneity, additivity and linearity to interval systems. The process of quantization is extended to its interval counterpart. Thereafter the interval versions for: quantization levels, quantization error and encoded signal are provided. It is shown that the interval levels of quantization represent complex quantization levels and the classical quantization error ranges over the interval quantization error. An estimation for the interval quantization error and an interval version for Z-transform (and hence Fourier transform) is provided. Finally, the results of an Matlab implementation is given