Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models

Penalization of the likelihood by Jeffreys' invariant prior, or by a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of models includes logistic regression, where the Jeffreys-prior penalty is known additionally to reduce the asymptotic bias of the maximum likelihood estimator; and also models with other commonly used link functions such as probit and log-log. Shrinkage towards equiprobability across observations, relative to the maximum likelihood estimator, is established theoretically and is studied through illustrative examples. Some implications of finiteness and shrinkage for inference are discussed, particularly when inference is based on Wald-type procedures. A widely applicable procedure is developed for computation of maximum penalized likelihood estimates, by using repeated maximum likelihood fits with iteratively adjusted binomial responses and totals. These theoretical results and methods underpin the increasingly widespread use of reduced-bias and similarly penalized binomial regression models in many applied fields

Informative g-Priors for Logistic Regression

Eliciting information from experts for use in constructing prior distributions for logistic regression coefficients can be challenging. The task is especially difficult when the model contains many predictor variables, because the expert is asked to provide summary information about the probability of “success” for many subgroups of the population. Often, however, experts are confident only in their assessment of the population as a whole. This paper is about incorporating such overall information easily into a logistic regression data analysis using g-priors. We present a version of the g-prior such that the prior distribution on the overall population logistic regression probabilities of success can be set to match a beta distribution. A simple data augmentation formulation allows implementation in standard statistical software packages.Keywords: Generalized linear model, Prior elicitation, Binomial regressio

Performance measures in dose-finding experiments

In the first phase of pharmaceutical development, and assuming that the probability of positive response increases with dose, the main statistical goal is to estimate a percentile of the dose–response function for a given target Г. We compare the Maximum Likelihood and centred isotonic regression estimators of the target dose and we discuss several performance criteria to assess inferential precision, the amount of toxicity exposure and the trade-off between them for a set of some exemplary adaptive designs. We compare these designs using graphical tools. Several scenarios are considered using simulation, including the use of several start-up rules, the change of slope of the dose-toxicity function at the target dose and also different theoretical models, as logistic, normal or skew-normal distribution functions.Fernando Plo and Jose Moler acknowledge the financial support received from the projects Ministerio de Economía y Competitividad (MTM2014‐53340‐P) and Secretaría de Estado de Investigación, Desarrollo e Innovación (MTM2016‐77015‐R)

Penalized Regression Methods for Modelling Rare Events Data with Application to Occupational Injury Study

Occupational injuries are a serious public health concern for workers around the world. Among all occupational injuries reported to the Workers' Compensation Board of Saskatchewan (WCB-SK) from 2007-2016, 177 (0.06%) out of 280,704 injury claims were fatal. Although work-related injuries are relatively rare, they have tremendous impact on the workers, their family, as well as a company's overall productivity, hiring/training costs, and insurance premiums. To help inform prevention of fatal claims, this study identified factors that increase the probability of fatal injury claims in Saskatchewan. WCB Saskatchewan's administrative occupational injury claims data from 2007-2016 was used to extract fatal and non-fatal occupational events. Potential covariates included worker characteristics (age, gender, occupation) and incident characteristics (source of injury, cause of injury, part of body). Given the fatality being rare in this study, conventional logistic regression including multiple categorical covariates with over 40 parameters yielded biased parameter estimates. Penalized logistic regression methods, such as bias-correction method, i.e. Firth's method as well as the model selection methods, i.e., lasso and elastic net were compared to identify an optimal modelling strategy for calculating the odds ratio (OR) and 95% confidence intervals (CI) for probability of a WCB claim being fatal (vs. non-fatal). Based on the best-fitting model, i.e., Firth's logistic regression of the selected variables under the elastic net method, odds of a claim being fatal was 5.5 (95% CI: 2.77,12.46) times higher among men than women and was 6.59 (95% CI: 3.59,12.20) times higher for seniors aged 65-85 as compared with those who are aged 14-24. Odds of a claim being fatal among those who work in primary industry is 2.85 (95% CI: 1.07,9.39) higher than those working in social sciences. The odds of injury being fatal for machinery sources is 51 (95% CI: 10.38,505.38) times higher than chemical products as the source. Men workers are at higher risk of a claim being fatal (vs non-fatal). With respect to age, result of analysis showed that the middle-aged workers are at a lower risk, and the young workers are at a higher risk than middle aged workers. The risk of a claim being fatal increased sharply as age increased from 45 to 85. Primary industry sector and machinery have a disproportionate share of fatal claims. This knowledge can improve workplace safety by learning from past incidents, identifying significant risk factors, and implementing targeted prevention strategies. Through development of effective interventions, we hope to prevent fatal injuries in Saskatchewan

Model selection methods and their application in genome-wide association studies

Ph.DDOCTOR OF PHILOSOPH

Prothetische Rehabilitation von Kopf-Hals-Tumorpatienten mit Hilfe von enossalen Astra-Tech-Implantaten

Die kaufunktionelle Rehabilitation bei Patienten mit Kopf-Hals-Karzinomen ist ein wichtiger Therapieschritt. Implantatgestützte Versorgungen weisen gegenüber konventionellen Prothesen zahlreiche spezifische Vorzüge auf und stellen mittlerweile in vielen Fällen das Mittel der Wahl dar. Klinische Studien bestätigen, dass eine Implantation auch nach Bestrahlung oder Knochentransplantation möglich ist, dass jedoch mit schlechteren Erfolgsquoten als bei gesunden Patienten gerechnet werden muss. Zur Untersuchung des Implantaterfolges und der Lebensqualität bei Kopf-Hals-Tumorpatienten wurde 2008 eine Studie in Zusammenarbeit mit der Firma ASTRA TECH (mittlerweile Dentsply Sirona) durch die Klinik und Poliklinik für Mund-, Kiefer- und Gesichtschirurgie des Universitätsklinikums Regensburg initiiert. Die vorliegende Dissertation stellt das Endergebnis dar. 52 Patienten wurden in die Studie eingeschlossen. Die Endauswertung erfolgte mit den 39 Patienten welche am Ende des Beobachtungszeitraums von 2 Jahren nachuntersucht werden konnten. Von diesen 39 Patienten wurden 29 bestrahlt. 234 Implantate wurden inseriert. Der Implantaterfolg wurde nach unterschiedlichen Kriterien ausgewertet und es wurden verschieden Faktoren hinsichtlich ihres Einflusses auf den Implantaterfolg untersucht. Die Evaluation der Lebensqualität erfolgte anhand der Fragebögen EORTC QLQ-C30, EORTC QLQ-H&N35, OHIP-G 14 und „Zufriedenheit mit dem Zahnersatz“. Da die Bewertung des Implantaterfolges in den unterschiedlichen Studien der Literatur nicht nach einem einheitlichen Standard durchgeführt wurde, ist ein Vergleich der berichteten Überlebens- und Erfolgsquoten mit den eigenen Ergebnissen nur bedingt möglich. In der vorliegenden Arbeit konnte gezeigt werden, dass sich die Erfolgsrate unter Hinzunahme zusätzlicher Bewertungskriterien verschlechtert. Bereits die Anwendung der für Tumorpatienten sehr strengen modifizierten Albrektsson-Kriterien führt gegenüber dem reinen Implantatüberleben nach 2 Jahren (92,31 %) zu einer deutlich schlechteren Erfolgsquote (78,63 %). Ursächlich ist hier vor allem ein marginaler Knochenabbau von mehr als 1,7 mm bei vielen Implantaten. Beim Heranziehen zusätzlicher parodontaler Parameter wie der Sondierungstiefe oder Blutungsindices verschlechtert sich die Erfolgsrate zusätzlich (70,35 %). Für die Parameter „Nikotinkonsum“, „Bestrahlungsdosis > 60 Gy“ und „Knochentransplantat“ wurde ein signifikanter negativer Einfluss auf den Implantaterfolg nachgewiesen. Den Patienten hilft die Implantatversorgung zurück in einen normalen Alltag zu finden. Die Verbesserung von ästhetischem Erscheinungsbild und Kaufunktion bringen vor allem im sozialen Bereich einen Benefit. Die Patienten fühlen sich wieder sicher in Zusammenhang mit ihren Zähnen und profitieren von einer erleichterten Nahrungsaufnahme, vor allem in Gesellschaft. Eine Steigerung der Lebensqualität durch den implantatgetragenen Zahnersatz konnte verzeichnet werden. Jedoch ist durch die Tumorerkrankung immer die Gefahr eines Rezidivs oder Zweitkarzinoms gegeben, was neben dem zunehmenden Alter der Patienten wieder zu einer schlechteren Bewertung der Lebensqualität führen kann

Quantitative determinants of prefabs: A corpus-based, experimental study of multiword units in the lexicon

In recent years many researchers have been rethinking the Words and Rules\u27 model of syntax (Pinker 1999), instead arguing that language processing relies on a large number of preassembled multiword units, or \u27prefabs\u27 (Bolinger 1976). A usage-based perspective predicts that linguistic units, including prefabs, arise via repeated use, and prefabs should thus be associated with the frequency with which words co-occur (Langacker 1987). Indeed, in several recent experiments, corpus analysis is found to be associated with behavioral measures for multiword sequences (Kapatsinski and Radicke 2009, Ellis and Simpson-Vlach 2009). This dissertation supplements such findings with two new psycholinguistic investigations of prefabs. Study 1 revisits a dictation experiment by Schmitt et al. (2004), in which participants are asked to listen to stretches of speech and repeat the input verbatim, after performing a distractor task intended to encourage reliance on prefabs. I describe the results of an updated experiment which demonstrates that participants are less likely to interrupt or partially alter high-frequency multiword sequences. Although the original study by Schmitt et al. (2004) reported null findings, the revised methodology suggests that frequency indeed plays a role in the creation of prefabs. Study 2 investigates the distribution of affix positioning errors (he go aheads) which give evidence that some multiword sequences (e.g., go ahead) are retrieved from memory as a unit. As part of this study, I describe a novel methodology which elicits the errors of interest in an experimental setting. Errors evincing holistic retrieval are induced more often among multiword sequences that are high in Mutual Dependency, a corpus measure that weighs a sequence\u27s frequency against the frequencies of its component words. Followup analyses indicate that sequence frequency is positively associated with affix errors, but only if component-word frequencies are included as variables in the model. In sum, the studies in this dissertation provide evidence that prefabricated, multiword units are associated with high frequency of a sequence, in addition to statistical measures that take component words\u27 frequency into account. These findings provide further support for a usage-based model of the lexicon, in which linguistic units are both gradient and changeable with experience

HIERARCHICAL MODELLING FOR INFECTIOUS DISEASES

Ph.DDOCTOR OF PHILOSOPH