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Alzheimer's Disease (AD) affects nearly 5.4 million Americans as of 2016 and is the most common form of dementia. The disease is characterized by the presence of neurofibrillary tangles and amyloid plaques [1]. The amount of plaques are measured by Braak stage, post-mortem. It is known that AD is positively associated with hypercholesterolemia [16]. As statins are the most widely used cholesterol-lowering drug, there may be associations between statin use and AD. We hypothesize that those who use statins, specifically lipophilic statins, are more likely to have a low Braak stage in post-mortem analysis. In order to address this hypothesis, we wished to fit a regression model for ordinal outcomes (e.g., high, moderate, or low Braak stage) using data collected from the National Alzheimer's Coordinating Center (NACC) autopsy cohort. As the outcomes were matched on the length of follow-up, a conditional likelihood-based method is often used to estimate the regression coefficients. However, it can be challenging to solve the conditional-likelihood based estimating equation numerically, especially when there are many matching strata. Given that the likelihood of a conditional logistic regression model is equivalent to the partial likelihood from a stratified Cox proportional hazard model, the existing R function for a Cox model, coxph( ), can be used for estimation of a conditional logistic regression model. We would like to investigate whether this strategy could be extended to a regression model for ordinal outcomes. More specifically, our aims are to (1) demonstrate the equivalence between the exact partial likelihood of a stratified discrete time Cox proportional hazards model and the likelihood of a conditional logistic regression model, (2) prove equivalence, or lack there-of, between the exact partial likelihood of a stratified discrete time Cox proportional hazards model and the conditional likelihood of models appropriate for multiple ordinal outcomes: an adjacent categories model, a continuation-ratio model, and a cumulative logit model, and (3) clarify how to set up stratified discrete time Cox proportional hazards model for multiple ordinal outcomes with matching using the existing coxph( ) R function and interpret the regression coefficient estimates that result. We verified this theoretical proof through simulation studies. We simulated data from the three models of interest: an adjacent categories model, a continuation-ratio model, and a cumulative logit model. We fit a Cox model using the existing coxph( ) R function to the simulated data produced by each model. We then compared the coefficient estimates obtained. Lastly, we fit a Cox model to the NACC dataset. We used Braak stage as the outcome variables, having three ordinal categories. We included predictors for age at death, sex, genotype, education, comorbidities, number of days having taken lipophilic statins, number of days having taken hydrophilic statins, and time to death. We matched cases to controls on the length of follow up. We have discussed all findings and their implications in detail.

為瞭解臺灣地區男女自殺死亡率的差異，本文採用Held and Riebler (2010)所建議的多元年齡-年代-世代模型，同時探討男女性自殺死亡率在年齡、年代及世代三種效應上的差異，我們同時使用非條件概似函數法（或稱對數線性模型法）及條件概似函數法（或稱多項式邏輯模型法）對台灣地區男女自殺死亡資料來配適模型。結果發現在假設世代效應與性別無關的前提下，年齡方面， 女性的自殺死亡率在10歲到24歲時顯著比男性高，在15到19歲這個年齡層差異達到最大，20歲之後差異開始變小，到了25至34歲，兩性則已無顯著差異，35歲之後男性的自殺死亡率開始顯著大於女性，並且隨著年齡增長兩性的差異越大，直到60歲之後差異才開始減小，到70歲時兩性無顯著差異。年代方面，男女的自殺死亡率在1959年到1973年間沒有顯著的差異，在1974到1988年女性的自殺死亡率顯著大於男性並於1979年到1983年來到最低點，也就是差異最大，之後差異開始變小，到了1989年時兩性已無顯著差異，從1994年開始男性的自殺死亡率反而開始顯著大於女性，而且隨著年代增加差異越大，並於2004到2008這個年代層差異達到最大。 / To understand the differences in suicide mortality between men and women in Taiwan, this study uses the Multivariate Age-Period-Cohort model proposed by Held and Riebler (2010), and explores the differences in suicide mortality between men and women on age, period and cohort effects adjusted for the other two. We use both unconditional likelihood function method (or log-linear model) and conditional likelihood function method (or multinomial logit model) to fit the model. Assuming that the cohort effect is independent of the gender, female suicide mortality in the age of 10 to 24 years old appears significantly higher than that of male, and the maximum age difference appears at the age of 15 to 19 years old. The difference is getting smaller after the age of 20, and gender difference is no longer significant between age of 25 to 34. After 35-year-old, male suicide death rate starts to exceed that of female, and the difference increases until the age of 60. After 60 years old, the difference starts to decrease till age of 70 at which there is no significant gender differences. There is no significant gender-specific suicide mortality difference between years 1959 and 1973. From 1974 to 1988 female suicide mortality rate is significantly greater than male. The difference reaches the peak in1979 to 1983. After that, the difference is getting smaller, and gender difference is no longer significant between 1989 and 1993. From 1994, suicide mortality for men begins to be significantly greater than women, and the difference increases with period. This difference reaches the maximum level in 2004 to 2008.

Made available in DSpace on 2016-06-02T20:04:51Z (GMT). No. of bitstreams: 1 4032.pdf: 1016886 bytes, checksum: 6e1eb83f197a88332f8951b054c1f01a (MD5) Previous issue date: 2011-11-18 / Financiadora de Estudos e Projetos / The capture-recapture process, largely used in the estimation of the number of elements of animal population, is also applied to other branches of knowledge like Epidemiology, Linguistics, Software reliability, Ecology, among others. One of the _rst applications of this method was done by Laplace in 1783, with aim at estimate the number of inhabitants of France. Later, Carl G. J. Petersen in 1889 and Lincoln in 1930 applied the same estimator in the context of animal populations. This estimator has being known in literature as _Lincoln-Petersen_ estimator. In the mid-twentieth century several researchers dedicated themselves to the formulation of statistical models appropriated for the estimation of population size, which caused a substantial increase in the amount of theoretical and applied works on the subject. The capture-recapture models are constructed under certain assumptions relating to the population, the sampling procedure and the experimental conditions. The main assumption that distinguishes models concerns the change in the number of individuals in the population during the period of the experiment. Models that allow for births, deaths or migration are called open population models, while models that does not allow for these events to occur are called closed population models. In this work, the goal is to characterize likelihood functions obtained by applying methods of elimination of nuissance parameters in the case of closed population models. Based on these likelihood functions, we discuss methods for point and interval estimation of the population size. The estimation methods are illustrated on a real data-set and their frequentist properties are analised via Monte Carlo simulation. / O processo de captura-recaptura, amplamente utilizado na estimação do número de elementos de uma população de animais, é também aplicado a outras áreas do conhecimento como Epidemiologia, Linguística, Con_abilidade de Software, Ecologia, entre outras. Uma das primeiras aplicações deste método foi feita por Laplace em 1783, com o objetivo de estimar o número de habitantes da França. Posteriormente, Carl G. J. Petersen em 1889 e Lincoln em 1930 utilizaram o mesmo estimador no contexto de popula ções de animais. Este estimador _cou conhecido na literatura como o estimador de _Lincoln-Petersen_. Em meados do século XX muitos pesquisadores se dedicaram à formula ção de modelos estatísticos adequados à estimação do tamanho populacional, o que causou um aumento substancial da quantidade de trabalhos teóricos e aplicados sobre o tema. Os modelos de captura-recaptura são construídos sob certas hipóteses relativas à população, ao processo de amostragem e às condições experimentais. A principal hipótese que diferencia os modelos diz respeito à mudança do número de indivíduos da popula- ção durante o período do experimento. Os modelos que permitem que haja nascimentos, mortes ou migração são chamados de modelos para população aberta, enquanto que os modelos em que tais eventos não são permitidos são chamados de modelos para popula- ção fechada. Neste trabalho, o objetivo é caracterizar o comportamento de funções de verossimilhança obtidas por meio da utilização de métodos de eliminação de parâmetros perturbadores, no caso de modelos para população fechada. Baseado nestas funções de verossimilhança, discutimos métodos de estimação pontual e intervalar para o tamanho populacional. Os métodos de estimação são ilustrados através de um conjunto de dados reais e suas propriedades frequentistas são analisadas via simulação de Monte Carlo.