Rheumatoid arthritis (RA) is a chronic disease characterized by an overactive immune system and joint inflammation. Population-based administrative health data (AHD) are widely used for RA outcomes research and surveillance. However, AHD may not completely capture all cases of RA in the population. Capture-recapture (CR) methods have been proposed to describe the completeness of AHD for estimating disease population size, but AHD may not conform to the assumptions that underlie CR models. A Monte Carlo simulation study was used to investigate the effects of violations of the assumptions for two-source CR methods: dependence between data sources and heterogeneity of capture probabilities. We compared the Chapman estimator and an estimator based on the multinomial logistic regression model (MLRM) to study relative bias (RB), coverage probability (CP) of 95% confidence intervals, width of 95% confidence intervals (WCI), and root-mean-square-error (RMSE) in prevalence estimates. The effects of misspecification of the MLRM were also investigated. In addition, the Chapman and MLRM estimators were used to estimate RA prevalence using AHD data from Saskatchewan, Canada. Population sizes were consistently underestimated for CR methods when the assumptions were violated. The estimated population size for both of the estimators did not differ substantially except for the RMSE values. Parameter estimates became biased when the MLRM model was misspecified, but there was little impact on population size estimates. In conclusion, CR methods are recommended to reduce bias in prevalence estimates based on AHDS. Because these methods may be sensitive to assumption violations, researchers should consider potential dependence between data sources. As well, sufficient overlap in the cases captured by each data source (e.g., 50% of the cases are captured by both data sources) or balanced capture probability in each data source is needed to effectively implement these methods. Researchers who estimate population size using CR methods in AHDs should favour the MLRM estimator over the Chapman estimator.

Nesta tese propomos dois modelos espaciais de captura-recaptura para estimação da abundância populacional em população aberta. Os modelos estatísticos propostos ajustam-se a dados obtidos via amostragem de captura-recaptura com marcação individual realizada em diferentes locais dentro do habitat, levando em consideração as taxas de nascimentos e mortes durante o período de estudo e as localizações geográficas das capturas. No primeiro modelo, propomos uma modelagem hierárquica para os tamanhos populacionais locais a fim de obter a distribuição preditiva da abundância populacional para regiões não visitadas pela amostragem. Nesta etapa, uma estrutura para dados zero-inflacionados foi adotada para acomodar situações quando realizam-se amostragens em locais sem a presença da espécie. O segundo modelo proposto leva em consideração o deslocamento dos animais entre os diferentes locais de amostragem, generalizando o primeiro modelo no qual consideramos a permanência dos animais em um mesmo local. Neste caso, tornou-se possível estimar o tamanho da área de vida (movimentação) da espécie além de predizer locais com maiores abundâncias de animais. Em ambos modelos, propomos uma abordagem bayesiana para o processo inferencial e derivamos algoritmos de simples implementação computacional, a partir do uso de técnicas de dados aumentados. As propriedades frequentistas dos estimadores bayesianos foram avaliadas por meio de estudos de simulação e, por fim, estas propostas de modelagem foram aplicadas a três conjuntos de dados reais de aracnídeos. / In this thesis we propose two spatial capture-recapture models for estimation of population abundance in the open population. The proposed statistical models conform to data obtained through individual tag capture-recapture sampling performed in different areas within the habitat, taking into account the rates of births and deaths during the study period and the geographical locations of the catches. In the first model, we propose a hierarchical modeling for local population sizes in order to obtain the predictive distribution of population abundance for regions not visited by sampling. In this step, a structure for zero-inflated data was adopted to accommodate situations when sampling is performed in areas without the presence of the species. The second proposed model takes into account the movement of the animals among the different sampling areas, generalizing the first model in which we consider the permanence of the animals in the same area. In this case, it became possible to estimate the size of the area of movement of the species and to predict areas with higher abundances of animals. In both models, we propose a Bayesian approach to the inferential process and derive algorithms from simple computational implementation, from the use of augmented data techniques. The frequentist properties of the Bayesian estimators were evaluated by simulation studies and, finally, these modeling proposals were applied to three real data sets of arachnids.