A generalized estimating equations approach to capture-recapture closed population models: methods

ABSTRACT; Wildlife population parameters, such as capture or detection probabilities, and density or population size, can be estimated from capture-recapture data. These estimates are of particular interest to ecologists and biologists who rely on ac- curate inferences for management and conservation of the population of interest. However, there are many challenges to researchers for making accurate inferences on population parameters. For instance, capture-recapture data can be considered as binary longitudinal observations since repeated measurements are collected on the same individuals across successive points in times, and these observations are often correlated over time. If these correlations are not taken into account when estimating capture probabilities, then parameter estimates will be biased, possibly producing misleading results. Also, an estimator of population size is generally biased under the presence of heterogeneity in capture probabilities. The use of covariates (or auxiliary variables), when available, has been proposed as an alternative way to cope with the problem of heterogeneous capture probabilities. In this dissertation, we are interested in tackling these two main problems, (i) when capture probabilities are dependent among capture occasions in closed population capture-recapture models, and (ii) when capture probabilities are heterogeneous among individuals. Hence, the capture-recapture literature can be improved, if we could propose an approach to jointly account for these problems. In summary, this dissertation proposes: (i) a generalized estimating equations (GEE) approach to model possible effects in capture-recapture closed population studies due to correlation over time and individual heterogeneity; (ii) the corresponding estimating equations for each closed population capture-recapture model; (iii) a comprehensive analysis on various real capture-recapture data sets using classical, GEE and generalized linear mixed models (GLMM); (iv) an evaluation of the effect of ac- counting for correlation structures on capture-recapture model selection based on the ‘Quasi-likelihood Information Criterion (QIC)’; (v) a comparison of the performance of population size estimators using GEE and GLMM approaches in the analysis of capture-recapture data. The performance of these approaches is evaluated by Monte Carlo (MC) simulation studies resembling real capture-recapture data. The proposed GEE approach provides a useful inference procedure for estimating population parameters, particularly when a large proportion of individuals are captured. For a low capture proportion, it is difficult to obtain reliable estimates for all approaches, but the GEE approach outperforms the other methods. Simulation results show that quasi-likelihood GEE provide lower standard error than partial likelihood based on generalized linear modelling (GLM) and GLMM approaches. The estimated population sizes vary on the nature of the existing correlation among capture occasions; RESUMO: Parâmetros populacionais em espécies de vida selvagens, como probabilidade captura ou deteção, e abundância ou densidade da população, podem ser estimados a partir de dados de captura-recaptura. Estas estimativas são de particular interesse para ecologistas e biólogos que dependem de inferências precisas a gestão e conservação das populações. No entanto, há muitos desafios par investigadores fazer inferências precisas de parâmetros populacionais. Por exemplo, os dados de captura-recaptura podem ser considerados como observa longitudinais binárias uma vez que são medições repetidas coletadas nos mesmos indivíduos em pontos sucessivos no tempo, e muitas vezes correlacionadas. Essas correlações não são levadas em conta ao estimar as probabilidades de tura, as estimativas dos parâmetros serão tendenciosas e possivelmente produz resultados enganosos. Também, um estimador do tamanho de uma população geralmente enviesado na presença de heterogeneidade das probabilidades de captura. A utilização de co-variáveis (ou variáveis auxiliares), quando disponível tem sido proposta como uma forma de lidar com o problema de probabilidade captura heterogéneas. Nesta dissertação, estamos interessados em abordar problemas principais em mode1os de captura-recapturar para população fecha (i) quando as probabilidades de captura são dependentes entre ocasiões de captura e (ii) quando as probabilidades de captura são heterogéneas entre os indivíduos Assim, a literatura de captura-recaptura pode ser melhorada, se pudéssemos por uma abordagem conjunta para estes problemas. Em resumo, nesta dissertação propõe-se: (i) uma abordagem de estimação de equações generalizadas (GEE) para modelar possíveis efeitos de correlação temporal e heterogeneidade individual nas probabilidades de captura; (ii) as correspondentes equações de estimação generalizadas para cada modelo de captura-recaptura em população fechadas; (iii) uma análise sobre vários conjuntos de dados reais de captura-recaptura usando a abordagem clássica, GEE e modelos linear generalizados misto (GLMM); (iv) uma avaliação do efeito das estruturas de correlação na seleção de modelos de captura-recaptura com base no ‘critério de informação da Quasi-verossimilhança (QIC); (v) uma comparação da performance das estimativas do tamanho da população usando GEE e GLMM. O desempenho destas abordagens ´e avaliado usando simulações Monte Carlo (MC) que se assemelham a dados de captura- recapture reais. A abordagem GEE proposto ´e um procedimento de inferência útil para estimar parâmetros populacionais, especialmente quando uma grande proporção de indivíduos ´e capturada. Para uma proporção baixa de capturas, ´e difícil obter estimativas fiáveis para todas as abordagens aplicadas, mas GEE supera os outros métodos. Os resultados das simulações mostram que o método da quase-verossimilhança do GEE fornece estimativas do erro padrão menor do que o método da verossimilhança parcial dos modelos lineares generalizados (GLM) e GLMM. As estimativas do tamanho da população variam de acordo com a natureza da correlação existente entre as ocasiões de captura

Estimation of Capture Probabilities Using a GEE Approach

Heterogeneity in capture probabilities represents a serious problem when estimating population size in capture-recapture studies. A generalized estimating equation (GEE) approach is applied to data from a capture-recapture experiment to model capture probabilities through a logit-link function of the covariates. The model accounts for heterogeneity resulting from individual characteristics as well as correlation among trapping occasions. In this paper, we build-up a model to use GEE in capture-recapture methodology and argue that heterogeneity and correlation among capture occasions should be accounted for. Quasi-likelihood Information Criterion (QIC) is used for selecting best fitting model. The estimates of capture probabilities may then be used to estimate population size and a real application is revisited for illustrative purposes

A generalized estimating equations approach for capture-recapture closed population models

The estimation of population density animal population parameters, such as capture probability, population size, or population density, is an important issue in many ecological applications. Capture–recapture data may be considered as repeated observations that are often correlated over time. If these correlations are not taken into account then parameter estimates may be biased, possibly producing misleading results. We propose a generalized estimating equations (GEE) approach to account for correlation over time instead of assuming independence as in the traditional closed population capture–recapture studies. We also account for heterogeneity among observed individuals and over-dispersion, modelling capture probabilities as a function of covariates. The GEE versions of all closed population capture–recapture models and their corresponding estimating equations are proposed. We evaluate the effect of accounting for correlation structures on capture–recapture model selection based on the quasi-likelihood information criterion (QIC). An example is used for an illustrative application and for comparison to currently used methodology. A Horvitz–Thompson-like estimator is used to obtain estimates of population size based on conditional arguments. A simulation study is conducted to evaluate the performance of the GEE approach in capture-recapture studies. The GEE approach performs well for estimating population parameters, particularly when capture probabilities are high. The simulation results also reveal that estimated population size varies on the nature of the existing correlation among capture occasions

Generalized linear models, generalized additive models and generalized estimating equations to capture-recapture closed population models

Estimation of animal population parameters is an important issue in ecological statistics. In this paper generalized linear models (GLM), generalized additive models (GAM) and generalized estimating equations (GEE) are used to account for individual heterogeneity, modelling capture probabilities as a function of individual observed covariates. The GEE also accounts for a correlation structure among capture occasions. We are interested in estimating closed population size, where only heterogeneity is considered, there is no time e ect or behavioral response to capture, and the capture probabilities depend on covariates. A real example is used for illustrative purposes. Conditional arguments are used to obtain a Horvitz-Thompson-like estimator for estimating population size. A simulation study is also conducted to show the performance of the estimation procedure and for comparison between methodologies. The GEE approach performs better than GLM or GAM approaches for estimating population size. The simulation study highlight the importance of considering correlation among capture occasions

2007, Determinants of Delivery Complications in Rural Bangladesh

Abstract: The maternal morbidity data in Bangladesh is scanty. In this paper an attempt is made to identify the possible risks of occurring delivery complications among the rural women of Bangladesh in relation to their selected delivery characteristics. Longitudinal data on Maternal Morbidity in rural Bangladesh, conducted by the Bangladesh Institute of Research for Promotion of Essential and Reproductive Health and Technologies (BIRPERHT) were employed in this study. A total of 1020 pregnant women (pregnancy less than 6 months) were interviewed. It was observed that women who had a higher risk of assisted deliveries had no formal education during delivery period compared to those who had formal education. Deliveries attended by untrained personnel reduced risk of having assisted delivery compared to those deliveries attended by trained personnel. The place of delivery is significantly associated with the nature of delivery. The duration of labor seems to have an association with the nature of delivery as well. Similarly, complications at the time of deliveries significantly increase subsequent complications during the postpartum period

Assessment of Heavy Metals in the Sediments of Chalan Beel Wetland Area in Bangladesh

This study aimed to determine the levels and possible sources of heavy metals (HMs) in the sediments of Chalan beel (a large lake-like aquatic ecosystem) area located in the northwestern part of Bangladesh. The mean concentrations (mg kg−1) of two HMs, Cd (6.22) and Pb (51.39) exceeded the world normal averages (WNA), whereas the mean concentrations (mg kg−1) of Ni (60.46), Zn (10.75), Mn (8.64) and Cu (4.71) were below the WNA. The sediments showed significant enrichment with Cd, Pb and Ni in the studied area. The geo-accumulation index values of Cd (3.72) and Pb (0.76) were significantly higher in the sediments. The contamination factor and potential ecological risk index values of Cd and Pb revealed that Chalan beel was extremely and moderately contaminated by these heavy metals, respectively. Analysis of dye complexes used in handlooms around the Chalan beel areas revealed that mean concentrations of Cd and Pb exceeded the WNA. Furthermore, analyses of principal component, cluster and correlation matrix indicated that the presence of the higher levels of Cd and Pb in the sediments might be linked to various anthropogenic activities like discharged dyes into the beel water from the nearby handloom dyeing factories