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Prevalence is a valuable epidemiological measure about the burden of disease in a community for planning health services; however, true prevalence is typically underestimated and there exists no reliable method of confirming the estimate of this prevalence in question. This thesis studies imprecise priors for the development of a statistical reasoning framework regarding this epidemiological decision making problem. The concept of imprecise probabilities introduced by Walley (1991) is adopted for the construction of this inferential framework in order to model prior ignorance and quantify the degree of imprecision associated with the inferential process. The study is restricted to the standard and zero-truncated Poisson sampling models that give an exponential family with a canonical log-link function because of the mechanism involved with the estimation of population size. A three-parameter exponential family of posteriors which includes the normal and log-gamma as limiting cases is introduced by applying normal priors on the canonical parameter of the Poisson sampling models. The canonical parameters simplify dealing with families of priors as Bayesian updating corresponds to a translation of the family in the canonical hyperparameter space. The canonical link function creates a linear relationship between regression coefficients of explanatory variables and the canonical parameters of the sampling distribution. Thus, normal priors on the regression coefficients induce normal priors on the canonical parameters leading to a higher-dimensional exponential family of posteriors whose limiting cases are again normal or log-gamma. All of these implementations are synthesized to build the ipeglim package (Lee, 2013) that provides a convenient method for characterizing imprecise probabilities and visualizing their translation, soft-linearity, and focusing behaviours. A characterization strategy for imprecise priors is introduced for instances when there exists a state of complete ignorance. The learning process of an individual intentional unit, the agreement process between several intentional units, and situations concerning prior-data conflict are graphically illustrated. Finally, the methodology is applied for re-analyzing the data collected from the epidemiological disease surveillance of three specific cases – Cholera epidemic (Dahiya, 1973), Down’s syndrome (Zelterman, 1988), and the female users of methamphetamine and heroin (B ̈ ohning, 2009).

Optimal experimental designs for generalized linear models have received increasing attention in recent years. Yet, most of the current research focuses on binary data models especially the one-variable first-order logistic regression model. This research extends this topic to count data models. The primary goal of this research is to develop efficient and robust experimental designs for the Poisson regression model in toxicity studies. D-optimal designs for both the one-toxicant second-order model and the two-toxicant interaction model are developed and their dependence upon the model parameters is investigated. Application of the D-optimal designs is very limited due to the fact that these optimal designs, in terms of ED levels, depend upon the unknown parameters. Thus, some practical designs like equally spaced designs and conditional D-optimal designs, which, in terms of ED levels, are independent of the parameters, are studied. It turns out that these practical designs are quite efficient when the design space is restricted. Designs found in terms of ED levels like D-optimal designs are not robust to parameters misspecification. To deal with this problem, sequential designs are proposed for Poisson regression models. Both fully sequential designs and two-stage designs are studied and they are found to be efficient and robust to parameter misspecification. For experiments that involve two or more toxicants, restrictions on the survival proportion lead to restricted design regions dependent on the unknown parameters. It is found that sequential designs perform very well under such restrictions. In most of this research, the log link is assumed to be the true link function for the model. However, in some applications, more than one link functions fit the data very well. To help identify the link function that generates the data, experimental designs for discrimination between two competing link functions are investigated. T-optimal designs for discrimination between the log link and other link functions such as the square root link and the identity link are developed. To relax the dependence of T-optimal designs on the model truth, sequential designs are studied, which are found to converge to T-optimal designs for large experiments. / Ph. D.

Using historical data from the past two seasons of the National Hockey League, three different prediction models based on Poisson regression are developed. The aim is to determine whether taking into account the recent form of a team as well as data from how they have previously performed against their opponent can help make better predictions of how many goals they will score against this opponent and thereby calculate the likelihood of each outcome. The three models are evaluated using different measures, for example comparing the odds yielded by the models against the odds of bookmakers. Different ways to account for recent form are discussed. The paper concludes that using recent form and head-to-head data will indeed improve predictions.

Lyme disease is the most significant vector-borne disease in the United States. Its southward advance over the last several decades has been quantified, and previous research has examined the potential role of climate change on the disease's expansion, but no research has considered the role of future land cover patterns upon its distribution. This research examines Lyme disease risk in the southeastern United States based on estimated land cover projections under four different Intergovernmental Panel on Climate Change Special Report Emissions Scenarios (IPCC-SRES) A1B, A2, B1, and B2. Results are aggregated to census tracts which are the basic unit of analysis for this study. This study applied previously established relationships between Lyme disease and land cover in Virginia to the projected land cover layers under each scenario. The study area, the southeastern United States, was defined from Level III Ecoregions that are present in Virginia and extend throughout the Southeast. Projected land cover data for each scenario were obtained from the USGS. The projected land cover datasets are compatible with the National Land Cover Dataset (NLCD) categories and had seventeen land cover categories. The raster datasets were reclassified to four broad land cover types: Water, Developed, Forest, and Herbaceous areas and the relationship between certain landscape configurations were analyzed using FRAGSTATS 4.2. Significant variables established in previous research were used to develop a spatial Poisson regression model to project Lyme disease incidence for each decade to the year 2100. Results indicated that potential land cover suitability for Lyme disease transmission will increase under two scenarios (A1B and A2) while potential land cover suitability for Lyme disease transmission was predicted to decrease under the other two scenarios (B1 and B2). Total area under the highest category of potential land cover suitability Lyme disease transmission was calculated for each year under each scenario. The A2 scenario experiences the most rapid acceleration of potential land cover suitability for Lyme disease transmission, with an average increase of 16,163.95 km² per decade, while the A1B scenario was projected to show an average increase of 3,458.47 km² per decade. Conversely, the B1 scenario showed an average decrease of 595.7 km² per decade and the B2 scenario showed the largest decrease of potential land cover suitability for Lyme disease transmission with an average decrease of 2,006.83 km² per decade. This study examined the potential spatial distribution of potential land cover suitability for Lyme disease transmission in the southeastern United States under four different future land cover scenarios. The results indicate geographic regions of the study area that are at greatest risk of potential land cover suitability for Lyme disease transmission under four different predictive scenarios developed by the IPCC. The A1B and A2 land cover projections are predicted to have an overall increase in areas where the Lyme disease transmission cycle will be enhanced by 2100 and the scenarios have a primary focus on economic development. Economic concerns outweigh environmental concerns for the A1B scenario, in addition to a high standard of living. The A2 scenario describes rapid population growth which results in high rates of land cover conversion to developed land; in addition, this scenario describes a reduction of environmental protection. The B1 and B2 land cover projections are predicted to have an overall decrease in areas of high Lyme disease transmission by 2100 and these scenarios have a central focus on environmental sustainability. The B1 scenario is characterized by a high environmental awareness which results in lower demand for forest products. A common theme for the B1 scenario is restoration and forest protection. Finally, the B2 scenario is described as improving local and regional environmental value which results in a high demand for biofuels and repossession of degraded lands, and an overall increase of forest cover. This study was the first to predict potential land cover suitability for Lyme disease risk and geographic distribution using projected land cover in the southeastern United States, and the results of this research can aid in the reduction of Lyme disease as it continues to expand in the south. / Master of Science

A main objective of Departments of Transportation is to improve the safety of the roadways over which they have jurisdiction. Safety projects, such as cable barriers and raised medians, are utilized to reduce both crash frequency and crash severity. The efficacy of these projects must be evaluated in order to use resources in the best way possible. Five models are proposed for the evaluation of traffic projects: (1) a Bayesian Poisson regression model; (2) a hierarchical Poisson regression model building on model (1) by adding hyperpriors; (3) a similar model correcting for overdispersion; (4) a dynamic linear model; and (5) a traditional before-after study model. Evaluation of these models is discussed using various metrics including DIC. Using the models selected for analysis, it was determined that cable barriers are quite effective at reducing severe crashes and cross-median crashes on Utah highways. Raised medians are also largely effective at reducing severe crashes. The results of before and after analyses are highly valuable to Departments of Transportation in identifying effective projects and in determining which roadway segments will benefit most from their implementation.

It is estimated that one third of the world's population is infected with tuberculosis. Though once thought a "dead" disease, tuberculosis is very much alive. The rise of drug resistant strains of tuberculosis, and TB-HIV coinfection have made tuberculosis an even greater worldwide threat. While HIV, poverty, and public health infrastructure are historically assumed to affect the burden of tuberculosis, recent research has been done to implicate smoking in this list. This analysis involves combining data from multiple sources in order determine if smoking is a statistically significant factor in predicting the number of incident tuberculosis cases in a country. Quasi-Poisson generalized linear models and negative binomial regression will be used to analyze the effect of smoking, as well as the other factors, on tuberculosis incidence. This work will enhance tuberculosis control efforts by helping to identify new hypotheses that can be tested in future studies. One of the main hypotheses is whether or not smoking increases the number of tuberculosis cases above and beyond the effects of other factors that are known to influence tuberculosis incidence. These known factors include TB-HIV coinfection, poverty and public health infrastructure represented by treatment outcomes.

Företag förväntas idag ta ett större samhällsansvar jämfört med tidigare och utvecklingen går hela tiden framåt. Kraven från intressenterna ökar och hållbarhetsredovisning används som ett verktyg för att presentera hur företag arbetar med ekonomiska-, miljömässiga- och sociala aspekter. Hållbarhetsredovisning ett viktigt instrument för att skapa legitimitet gentemot intressenter, långsiktig lönsamhet och idag en lagstiftad nödvändighet för en väsentlig del av svenska företag. Det kom en ny lagstiftning gällande hållbarhetsredovisning 2017, men många svenska företag har frivilligt hållbarhetsredovisat tidigare än så. Med denna studie vill vi undersöka om en VD:s observerbara egenskaper och företags karakteristika kan ha en påverkan på när svenska företag frivilligt implementerat hållbarhetsredovisning. Utifrån ett valt referensår (år 2000) har tiden till implementering och antalet redovisade hållbarhetssidor studerats för att kunna förklara hur viktigt företag anser det vara att arbeta med hållbart företagande och redovisa resultatet för sina intressenter. Studien syftar till att skapa förståelse kring om det finns specifika företags karakteristika och observerbara egenskaper hos företagets VD som har påverkat hur lång tid det tagit innan de undersökta företagen implementerade hållbarhetsredovisning, samt hur mycket hållbarhetsinformation som redovisades. För att besvara studiens syfte har vi använt en kvantitativ metod och samlat in data från 63 svenska företag inom 15 olika branscher. Företagens årsredovisningar har studerats och data har samlats in rörande en VD:s observerbara egenskaper och företags karakteristika. De observerbara egenskaper som studien har avsett att undersöka är: kön, ålder, tid på posten och utbildning. Sedan har även avkastning på eget kapital, antalet anställda, omsättning och branschtillhörighet studerats, vilket utgör företags karakteristika i studien. I studien har en Poisson-regression använts och vi har funnit många intressanta samband mellan de undersökta variablerna. Det tar i genomsnitt fem år snabbare för ett företag med en manlig VD att implementera hållbarhetsredovisning gentemot företag med en kvinnlig VD, samt att det tar längre tid att implementera hållbarhetsredovisning om företaget har en VD som suttit längre tid på posten. Även antalet eftergymnasiala utbildningsår har visat sig ha en positiv inverkan på implementeringstiden och ett företag med en VD som har en längre utbildning har börjat hållbarhetsredovisa tidigare. Antal eftergymnasiala utbildningsår har även ett positivt samband med mängden hållbarhetsinformation som redovisats under företagens implementeringsår.Företag med en högre omsättning implementerade hållbarhetsredovisning tidigare än företag med en lägre omsättning och företag med en högre omsättning redovisar även fler antalet sidor under implementeringsåret. Även branschtillhörighet har visat sig ha en påverkan på både implementeringsåret samt antalet redovisade sidor det specifika året. Sammanfattningsvis kan det fastställas att både specifika observerbara egenskaper hos en VD och vissa företags karakteristika har en påverkan på både implementeringsåret och antalet redovisade sidor. Detta ger en tydlig indikering på hur viktigt olika företag i olika branscher tycker det är att arbeta med hållbart företagande och redovisa sina handlingar gentemot företagets intressenter.

Cancer is a highly prevalent disease worldwide, claiming hundreds of lives each year. In the field of cancer research, it is customary to conduct surveys in which patients are asked to self-report and assess their symptoms and overall health. In such research, it is essential for patients to respond promptly to questionnaires to avoid recall bias and for a representative patient sample to respond to avoid biased sampling. This report aims to investigate the factors that impact response rate and response time using logistic regression and Poisson regression. The study focuses on a dataset of patients with colorectal cancer, with the response rate of patients with pancreatic cancer serving as a reference. By analyzing variables such as gender, age, place of residence, and the method of survey notification, the conclusion is that patients over the age of 80 who received their survey login codes on paper are the least responsive and underrepresented subgroup of the sample. In the analysis of the response time using Poisson regression, the conclusion is that the notification channel has the most significant impact on response rate. / Cancer är en mycket utbredd sjukdom världen över och kräver hundratals liv varje år. Inom cancerforskningen är det vanligt att genomföra undersökningar där patienter ombeds att självrapportera och bedöma sina symtom och övergripande hälsa. I sådana undersökningar är det avgörande att patienterna svarar snabbt på enkäter för att undvika minnesbias och för att få fram en representativ patientgrupp och undvika snedvriden urvalsprocess. Syftet med denna rapport är att undersöka faktorer som påverkar svarsfrekvensen och svarstiden genom att använda logistisk regression och Poisson-regression. Studien fokuserar på en dataset av patienter med tjocktarmscancer, där svarsfrekvensen hos patienter med bukspottkörtelcancer används som referens. Genom att analysera variabler som kön, ålder, bostadsort och metod för undersökningsmeddelande dras slutsatsen att patienter över 80 år som fick sina inloggningskoder på papper är den minst responsiva och mest underrepresenterade undergruppen av urvalet. I analysen av svarstiden med hjälp av Poisson-regression dras slutsatsen att undersökningskanalen har den största påverkan på svarsfrekvensen.

This is a thesis about the spatial distribution of willow warbler, nightingale, blackbird, robin and grey flycatcher in Svealand and Götaland, that is the southern third of Sweden. It explores the possibilities of using statistics to describe the distribution and variation of birds in a given region.The data was collected by observation of birds on sites called standard routes, with 25 kilometres between them. The standard routes are the points in a grid net placed upon the map of Sweden. The purpose of standard routes is to represent the birds in Sweden both geographic and biotopological.The thesis compare the results from kriging, variogram and four alternative poisson regressions. In the end I come up with the information provided by kriging and variogram and which poisson regression that bests estimates the population sizes of the birds at a given site with information about year, mean temperature from January to May and what kind of environment or habitat the site consist of.