Global spread of infectious disease threatens the well-being of human, domestic, and wildlife health. A proper understanding of global distribution of these diseases is an important part of disease management and policy making. However, data are subject to complexities by heterogeneity across host classes and space-time epidemic processes [Waller et al., 1997, Hosseini et al., 2006]. The use of frequentist methods in Biostatistics and epidemiology are common and are therefore extensively utilized in answering varied research questions. In this thesis, we proposed the Hierarchical Bayesian approach to study the spatial and the spatio-temporal pattern of tuberculosis in Kenya [Knorr-Held et al., 1998, Knorr-Held, 1999, L opez-Qu lez and Munoz, 2009, Waller et al., 1997, Julian Besag, 1991]. Space and time interaction of risk (ψ[ij]) is an important factor considered in this thesis. The Markov Chain Monte Carlo (MCMC) method via WinBUGS and R packages were used for simulations [Ntzoufras, 2011, Congdon, 2010, David et al., 1995, Gimenez et al., 2009, Brian, 2003], and the Deviance Information Criterion (DIC), proposed by [Spiegelhalter et al., 2002], used for models comparison and selection. Variation in TB risk is observed among Kenya counties and clustering among counties with high TB relative risk (RR). HIV prevalence is identified as the dominant determinant of TB. We found clustering and heterogeneity of risk among high rate counties and the overall TB risk is slightly decreasing from 2002-2009. Interaction of TB relative risk in space and time is found to be increasing among rural counties that share boundaries with urban counties with high TB risk. This is as a result of the ability of models to borrow strength from neighbouring counties, such that near by counties have similar risk. Although the approaches are less than ideal, we hope that our formulations provide a useful stepping stone in the development of spatial and spatio-temporal methodology for the statistical analysis of risk from TB in Kenya. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

Orientador: Luiz Koodi Hotta / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T12:49:57Z (GMT). No. of bitstreams: 1 MercadoLondono_SergioLuis_M.pdf: 1311356 bytes, checksum: 23c15e842c02af3c1dc7de3a2a46a5df (MD5) Previous issue date: 2014 / Resumo: Uma das quantidades mais importante definida na epidemiologia é o número de reprodução basal, ou básico, associado com a pandemia e denotado por $R_0$. Ele proporciona uma medida da intensidade das intervenções necessárias para o controle da epidemia. Ao mesmo tempo, os modelos epidemiológicos compartimentais SIR, SEIR, tanto no enfoque enfoque determinístico quanto no estocástico, têm sido de grande ajuda para a compreensão dos mecanismos de transmissão de doenças infecciosas em todo o mundo. Esta dissertação apresenta alguns métodos para estimar esta quantidade através da utilização dos modelos epidemiológicos compartimentais. São considerados os quatro métodos apresentados por Chowell et al. (Mathematical Biosciences, 2007, v. 208, p. 571-589). O primeiro método é baseado na taxa de crescimento (inicial) exponencial da epidemia. Dada a taxa de crescimento exponencial e o modelo subjacente temos uma estimativa de $R_{0}$. No caso dos métodos 2 e 3 o processo de estimação do $R_0$ baseia-se nos modelos compartimentais, modelos SIR e SEIR no método 2, e em um modelo SEIR estendido no método 3. O método 4 utiliza uma abordagem bayesiana do modelo SIR estocástico. O objetivo da dissertação é estudar as propriedades dos estimadores baseados nos métodos 1, 2 e 4. Através de simulações são estimados os vícios, os erros quadráticos médios, as cobertura e as larguras dos intervalos de confiança. Os métodos são estudados quando os verdadeiros processos geradores de dados são os modelos SIR ou SEIR estocásticos. Inicialmente foram estudados os métodos, como apresentados por Chowell et al. (2007), e depois apresentadas modificações para melhorar o desempenho dos estimadores. A dissertação está organizada da seguinte forma: o Capítulo 2 consiste na apresentação dos modelos compartimentais, SIR e SEIR para análise das doenças infecciosas; tanto na abordagem determinística quanto estocástica. Este capítulo apresenta também o número de reprodução basal. O Capítulo 3 apresenta os quatro métodos de estimação apresentados em Chowell et al. (2007) para estimação do número de reprodução basal. O Capítulo 4 apresenta uma comparação de três dos quatro métodos através de simulação, quando o processo gerador de dados é um modelo SIR ou SEIR estocásticos. Neste capítulo também são apresentadas as modificações dos métodos. A conclusão final e as sugestões de trabalhos futuros são apresentadas no Capítulo 5 / Abstract: The basic reproduction number, usually denoted by $R_0$, is one of the most important quantities defined in epidemiology and is associated with the potential of an infectious disease to spread through a population. It provides a measure of the intensity needed to control the epidemic interventions. At the same time, the compartmental epidemiological models SIR and SEIR , both in the deterministic and in the stochastic approach, have been very helpful for understanding the mechanisms of infectious diseases transmission. This paper considers the four methods presented by Chowell et al. (Mathematical Biosciences, 2007, v. 208, p. 571-589) to estimate $R_0$. All methods are based on compartmental epidemiological models. The first method is based on the epidemic (initial) exponential growth rate. Given an estimate of the exponential growth rate and an underlying compartmental model we have an estimate of $R_{0}$. The second method is based on fitting SIR or SEIR compartmental models, and the third method in fitting an extended SEIR model. The fourth method uses a Bayesian approach to a stochastic SIR model. The aim of this work is to study the properties of estimators based on methods 1, 2 and 4. The bias, the mean squared errors, the coverage and the widths of the confidence intervals are estimated through simulation. The methods are studied when the true data generating processes are the stochastic SIR or SEIR models. Initially the methods, as presented by Chowell et al. (2007), were studied and then presented modifications to improve the performance of the estimators. The dissertation is organized as follows: Chapter 2 consists of the presentation of compartmental SIR and SEIR models, the deterministic and stochastic approaches for analysis of infectious diseases. This chapter also presents the basic reproduction number. Chapter 3 explains the four estimation methods presented in Chowell et al. (2007) to estimate the basic reproduction number. Chapter 4 discusses and compares three of the four methods by simulation when the data generating process is a SIR or SEIR model. In this chapter the modifications of the methods are also considered. The final conclusion and suggestions for future work are presented in Chapter 5 / Mestrado / Estatistica / Mestre em Estatística

The prevalence and the incidence are two primary epidemiological parameters in infectious disease modelling. The incidence is also closely related to the force of infection or the hazard of infection in survival analysis terms. The two measures carry the same information about a disease because they measure the rate at which new infections occur. The disease prevalence gives the proportion of infected individuals in the population at a given time, while the incidence is the rate of new infections. The thesis discusses methods for estimating HIV prevalence, incidence rates and the force of infection, against age and time, using cross-sectional seroprevalence data for pregnant women attending antenatal clinics. The data was collected on women aged 12 to 47 in rural KwaZulu-Natal for each of the years 2001 to 2006. The generalized linear model for binomial response is used extensively. First the logistic regression model is used to estimate annual HIV prevalence by age. It was found that the estimated prevalence for each year increases with age, to peaks of between 36% and 57% in the mid to late twenties, before declining steadily toward the forties. Fitted prevalence for 2001 is lower than for the other years across all ages. Several models for estimating the force of infection are discussed and applied. The fitted force of infection rises with age to a peak of 0.074 at age 15, and then decreases toward higher ages. The force of infection measures the potential risk of infection per individual per unit time. A proportional hazards model of the age to infection is applied to the data, and shows that additional variables such as partner’s age and the number of previous pregnancies do have a significant effect on the infection hazard. Studies for estimating incidence from multiple prevalence surveys are reviewed. The relative inclusion rate (RIR), accounting for the fact that the probability of inclusion in a prevalence sample depends on the individual’s HIV status, and its role in incidence estimation is discussed as a possible future approach of extending the current work. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

Orientador: Bianca Morelli Rodolfo Calsavara / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-26T15:10:31Z (GMT). No. of bitstreams: 1 SalesFilho_Nazime_M.pdf: 36937949 bytes, checksum: 4ceff2992bbc8648a89104715aac602e (MD5) Previous issue date: 2015 / Resumo: Neste trabalho será analisado um modelo matemático que descreve a propagação da dengue. Tal modelo é dado por um sistema de equações diferenciais ordinárias não lineares sujeitas a condições iniciais, que descreve duas populações: a de mosquitos e a humana. A população de mosquitos é dividida em duas subpopulações: fase aquática, incluindo os ovos, larvas e pupas, e fase alada, que é subdividida em mosquitos suscetíveis e infectados. A população humana é dividida em subpopulações de suscetíveis, infectados e removidos. No modelo citado é assumido que a população de mosquito e a população humana atingiram homogeneidade espacial, isto é, não há movimentação destas populações influenciando na disseminação da doença. O principal interesse neste trabalho é analisar qualitativamente o comportamento das populações em torno dos pontos de equilíbrio do sistema. Para este fim, além do uso de ferramentas analíticas também foram realizadas simulações numéricas utilizando o software Maple. Dessa forma foi possível obter informações sobre a disseminação da dengue, sob algumas hipóteses, mesmo sem obtermos solução explícita do sistema / Abstract: In this work it will be analyzed a mathematical model describing propagation of dengue disease. This model is given by a system of nonlinear ordinary differential equations, subjected to initial conditions, involving two populations: one of mosquitos and another of humans. The mosquitos population is divided in two subpopulations: the aquatic phase, including eggs, larvae and pupae, and the winged phase, that is divided in susceptible and infected mosquitos. The human population is divided in subpopulations of susceptible, infected and removed. In the cited model it is assumed that the mosquito and human populations achieved spatial homogeneity, i.e., there is no movement of these populations affecting the disease dissemination. The main interest of this work is to analyze qualitatively the populations behavior around the equilibrium points of the system. To this end, in addition to the use of analytical tools, numerical simulations were performed by using Maple software. In this way, it was possible to obtain information about dengue dissemination, under some hypotheses, even without obtaining explicit solution for the system / Mestrado / Matematica Aplicada e Computacional / Mestre em Matemática Aplicada e Computacional

Unexpected findings that contradict well-established relationships between exposures and outcomes are often referred to as “paradoxes” in the epidemiologic literature. For example, the “birth weight paradox” refers to the observed protective association between smoking during pregnancy and infant mortality among low birth weight infants. A recent body of literature suggests that this and several other well-known epidemiologic paradoxes can be attributed to collider bias. Collider bias results from conditioning on a variable that is caused by the exposure or shares common cause with the exposure and is caused by the outcome or shares common causes with the outcome. Several recent epidemiology textbooks and methodological studies further suggest that collider bias is the graphical representation of selection bias, suggesting that these two biases are synonymous. This structural approach to bias is conceptually very useful for defining, describing, and identifying selection bias, but it introduces paradoxes of its own due to contradictory conclusions in the selection and collider bias methodologic literatures about their likely impact on study results in terms of magnitude, direction, and strata affected. Resolving these discrepancies is essential for our theoretical understanding of the relationship between selection and collider bias and has important practical implications for how we teach epidemiology, design studies, and evaluate and quantify the potential effects of bias on our results. For example, while patterns of collider bias coincide qualitatively with the birth weight paradox, the magnitude of collider bias would have to be substantial to reverse the sign of the association, contrary to prevailing beliefs that collider bias only minimally affects our results. To date, the plausibility of collider bias as an explanation for the birth weight paradox has not been empirically evaluated using data in which the paradox is observed.Taken together, these inconsistencies and contradictions suggest that our understanding of selection bias and collider bias remains incomplete. The overarching goal of this dissertation was to advance the theoretical and quantitative understanding of the impact of collider bias on study results to clarify the relationship between selection and collider bias. I began by systematically reviewing the methodologic literature on selection and collider bias. I found that selection bias and collider bias are increasingly treated as synonyms, but that conclusions about the magnitude and direction of selection and collider bias, the stratum affected, and the conditions under which the effects of each type of bias were evaluated are highly inconsistent. This suggested that divergent findings about the impact of selection and collider bias might be resolved by considering the impact of collider bias under a broader set of circumstances. I used microsimulations grounded in the sufficient component cause model to examine collider bias not under the null; interrogate why multiplicative interaction appeared central to the impact of collider bias; and clarify which stratum or strata are affected by collider bias. I identified clear patterns for the magnitude, direction, and strata affected by collider bias and successfully reconciled discrepancies with the selection bias literature. This work also enabled me to interrogate both the causal mechanisms and mathematical principles that underlie collider bias, which revealed how collider bias leads to non-exchangeability and when stratifying on a collider results in bias. Finally, I applied this deeper understanding of the mechanisms underlying collider bias to empirically evaluate the plausibility of collider bias as an explanation for the birth weight paradox. Using microsimulations parameterized with 2015 National Center for Health Statistics Cohort Linked Birth-Infant Mortality, I identified scenarios that successfully reproduced the paradox and all observed relationships between smoking during pregnancy, infant mortality, and low birth weight. These findings strengthen the evidence for the role of collider bias in producing the paradox and shed light on the potential magnitude of unmeasured confounding and direct effects of smoking and low birth weight on infant mortality that may be required for the observed magnitude of the paradox to arise. This work clarifies that almost all selection bias is collider bias; that the effects of collider bias vary in magnitude and direction; that selecting on a collider always leads to bias, but this bias may not occur in the stratum that coincides with our analytical sample; and that collider bias may resolve the birth weight paradox, but is unlikely to explain all epidemiologic paradoxes.

Leung Siu-Ngan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 72-74). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Structure and Contents of Data Sets --- p.6 / Chapter 2 --- Estimation of Prevalence of Mentally Disorders --- p.10 / Chapter 2.1 --- Likelihood Function Approach --- p.10 / Chapter 2.2 --- Maximum Likelihood Estimation via EM Algorithm --- p.13 / Chapter 2.3 --- The SEM Algorithm --- p.16 / Chapter 3 --- Estimation of Lifetime Comorbidity --- p.24 / Chapter 3.1 --- What is Comorbidity? --- p.24 / Chapter 3.2 --- Likelihood Function Approach --- p.25 / Chapter 3.2.1 --- Likelihood Function Model --- p.27 / Chapter 3.2.2 --- Maximum Likelihood Estimation via EM Algorithm --- p.28 / Chapter 3.2.3 --- Odds Ratio --- p.31 / Chapter 4 --- Logistic Regression --- p.35 / Chapter 4.1 --- Imputation Method of Missing Values --- p.35 / Chapter 4.1.1 --- Hot Deck Imputation --- p.35 / Chapter 4.1.2 --- A logistic Regression Imputation Model for Dichotomous Response --- p.40 / Chapter 4.2 --- Combining Results from Different Imputed Data Sets --- p.47 / Chapter 4.3 --- Itemization on Screening --- p.60 / Chapter 4.3.1 --- Methods of Weighting on the Screening Questions --- p.61 / Chapter 4.3.2 --- Statistical Analysis --- p.62 / Chapter 5 --- Conclusion and Discussion --- p.68 / Appendix: SRQ Questionnaire --- p.69 / Bibliography --- p.72

Indiana University-Purdue University Indianapolis (IUPUI) / Phytoestrogens that abound in soy products, legumes, and chickpeas can induce biologic responses in animals and humans due to structural similarity to 17β-estradiol. Although experimental studies suggest that phytoestrogen intake may alter the risk of cancer and cardiovascular disease, few epidemiologic studies have investigated this research question. This dissertation investigated the associations of intake of total and individual phytoestrogens and their urinary biomarkers with these chronic conditions using data previously collected from two US national cohort studies (NHANES and PLCO). Utilizing NHANES data with urinary phytoestrogen concentrations and follow-up mortality, Cox proportional hazards regression (HR; 95% CI) were performed to evaluate the association between total cancer, cardiovascular disease, and all-cause mortality and urinary phytoestrogens. After adjustment for confounders, it was found that higher concentrations of lignans were associated with a reduced risk of death from cardiovascular disease (0.48; 0.24-0.97), whereas higher concentrations of isoflavones (2.14; 1.03-4.47) and daidzein (2.05; 1.02-4.11) were associated with an increased risk. A reduction in all-cause mortality was observed for elevated concentrations of lignans (0.65; 0.43-0.96) and enterolactone (0.65; 0.44-0.97). Utilizing PLCO data and dietary phytoestrogens, Cox proportional hazards regression examined the associations between dietary phytoestrogens and the risk of prostate cancer incidence. After adjustment for confounders, a positive association was found between dietary intake of isoflavones (1.58; 1.11-2.24), genistein (1.42; 1.02-1.98), daidzein (1.62; 1.13-2.32), and glycitein (1.53; 1.09-2.15) and the risk of advanced prostate cancer. Conversely, an inverse association existed between dietary intake of genistein and the risk of non-advanced prostate cancer (0.88; 0.78-0.99) and total prostate cancer (0.90; 0.81-1.00). C-reactive protein (CRP) concentration levels rise in response to inflammation and higher levels are a risk factor for some cancers and cardiovascular disease reported in epidemiologic studies. Logistic regression performed on NHANES data evaluated the association between CRP and urinary phytoestrogen concentrations. Higher concentrations of total and individual phytoestrogens were associated with lower concentrations of CRP. In summary, dietary intake of some phytoestrogens significantly modulates prostate cancer risk and cardiovascular disease mortality. It is possible that these associations may be in part mediated through the influence of phytoestrogen intake on circulating levels of C-reactive protein.