Neste trabalho são apresentados dois modelos de sobrevivência com fração de cura e efeitos aleatórios, um baseado no modelo de Chen-Ibrahim-Sinha para fração de cura e o outro, no modelo de mistura. São estudadas abordagens clássica e bayesiana. Na inferência clássica são utilizados estimadores REML. Para a bayesiana foi utilizado Metropolis-Hastings. Estudos de simulação são feitos para avaliar a acurácia das estimativas dos parâmetros e seus respectivos desvios-padrão. O uso dos modelos é ilustrado com uma análise de dados de câncer na orofaringe. / In this work, it is shown two survival models with long term survivors and random effects, one based on Chen-Ibrahim-Sinha model for models with surviving fraction and the other, on mixture model. We present bayesian and classical approaches. In the first one, we use Metropolis-Hastings. For the second one, we use the REML estimators. A simulation study is done to evaluate the accuracy of the applied techniques for the estimatives and their standard deviations. An example on orofaringe cancer is used to illustrate the models considered in the study.

La modélisation des effets centre dans le cadre des données de survie repose souvent sur l'utilisation de modèles de Cox à effets mixtes. Tester un effet centre revient alors à tester à zéro la variance de l'effet aléatoire correspondant. La distribution sous l'hypothèse nulle des statistiques des tests paramétriques usuels n'est alors pas toujours connue. Les procédures de permutation ont été proposées comme alternative, pour les modèles linéaires généralisés mixtes.L'objectif est de développer, pour l'analyse des effets centre dans un modèle de survie de Cox à effets mixtes, une procédure de test de permutation pour les effets aléatoires.La première partie du travail présente la procédure de permutation développée pour le test d'un unique effet centre sur le risque de base, avec une application à la recherche d'un effet centre dans un essai clinique chez des patients atteints de leucémie myéloïde aiguë. La seconde partie porte sur l'extension de la procédure au test d'effets aléatoires multiples afin d’étudier à la fois des effets centre sur le risque de base et sur l'effet de variables, avec des illustrations sur deux cohortes de patients atteints de leucémie aiguë. Dans une troisième partie, les méthodes proposées sont appliquées à une cohorte multicentrique de patients en réanimation atteints d'hémopathies malignes, pour étudier les facteurs déterminant les effets centre sur la mortalité hospitalière. Les procédures de permutation proposées constituent une approche robuste et d'implémentation relativement aisée pour le test, en routine, d'effets aléatoires, donc un outil adapté pour l'analyse d'effets centre en épidémiologie clinique, afin de comprendre leur origine. / Centre effects modelling within the framework of survival data often relies on the estimation of Cox mixed effects models. Testing for a centre effect consists in testing to zero the variance component of the corresponding random effect. In this framework, the identification of the null distribution of usual tests statistics is not always straightforward. Permutation procedures have been proposed as an alternative, for generalised linear mixed models.The objective was to develop a permutation test procedure for random effects in a Cox mixed effects model, for the test of centre effects.We first developed and evaluated permutation procedures for the test of a single centre effect on the baseline risk. The test was used to investigate a centre effect in a clinical trial of induction chemotherapy for patients with acute myeloid leukaemia.The second part consisted in extending the procedure for the test of multiple random effects, in survival models. The aim was to be able to examine both center effects on the baseline risk and centre effects on the effect of covariates. The procedure was illustrated on two cohorts of acute leukaemia patients. In a third part, the permutation approach was applied to a cohort of critically ill patients with hematologic malignancies, to investigate centre effects on the hospital mortality.The proposed permutation procedures appear to be robust approaches, easily implemented for the test of random centre effect in routine practice. They are an appropriate tool for the analysis of centre effects in clinical epidemiology, with the purpose of understanding their sources.

Sedan 2010 kan en friskola överklaga kommunens beslut om skolpeng ifall den anser att lika villkor inte har uppnåtts. Reformen har lett till att tusentals konflikter mellan friskolor och kommuner har tagits till domstol. I denna studie kartläggs och beskrivs de konflikter som rör kompensation till friskolor för kommunala underskott. Därtill prövas hypoteser om samband mellan politisk ideologi, kommunstorlek, nivå på skolpeng respektive andel friskolor och konflikt genom regressioner av paneldata.Resultaten visar substantiella samband mellan vänsterstyre, en hög andel friskolor respektive kommunstorlek och ökad sannolikhet för konflikt. Därtill visar kartläggningen att Sveriges största friskolekoncern är överrepresenterad i konflikterna. Det indikerar att reformen – vars syfte var att stärka friskolornas roll i bidragsprocessen – i första hand stärkt stora aktörer.

Likelihood-based marginalized models using random effects have become popular for analyzing longitudinal categorical data. These models permit direct interpretation of marginal mean parameters and characterize the serial dependence of longitudinal outcomes using random effects [12,22]. In this paper, we propose model that expands the use of previous models to accommodate longitudinal nominal data. Random effects using a new covariance matrix with a Kronecker product composition are used to explain serial and categorical dependence. The Quasi-Newton algorithm is developed for estimation. These proposed methods are illustrated with a real data set and compared with other standard methods.

In traditional meta-analysis, a random-effects model is used to deal with heterogeneity and the random-effect is assumed to be normally distributed. However, this can be problematic in the presence of outliers. One solution involves using a heavy tailed distribution for the random-effect to more adequately model the excess variation due to the outliers. Failure to consider an alternative approach to the standard in the presence of unusual or outlying points can lead to inaccurate inference. A heavy tailed distribution is favoured because it has the ability to down-weight outlying studies appropriately, therefore the removal of a study does not need to be considered. In this thesis, the performance of the t-distribution and a finite mixture model are assessed as alternatives to the normal distribution through a comprehensive simulation study. The parameters varied are the average mean of the non-outlier studies, the number of studies, the proportion of outliers, the heterogeneity and the outlier shift distance from the average mean. The performance of the distributions is measured using bias, mean squared error, coverage probability, coverage width, Type I error and power. The methods are also compared through an empirical study of meta-analyses from The Cochrane Library (2008). The simulation showed that the performance of the alternative distributions is better than the normal distribution for a number of scenarios, particularly for extreme outliers and high heterogeneity. Generally, the mixture model performed quite well. The empirical study reveals that both alternative distributions are able to reduce the influence of the outlying studies on the overall mean estimate and thus produce more conservative p-values than the normal distribution. It is recommended that a practitioner consider the use of an alternative random-effects distribution in the presence of outliers because they are more likely to provide robust results. / Thesis / Master of Science (MSc)

Meta-analyses are conducted to synthesize the quantitative results of related studies. The random-effects meta-analysis model is based on the assumption that a distribution of true effects exists in the population. This distribution is often assumed to be normal with a mean and variance. The population variance, also called heterogeneity, can be estimated numerous ways. Accurate estimation of heterogeneity is necessary as a description of the distribution and for determining weights applied in the estimation of the summary effect when using inverse-variance weighting. To evaluate a wide range of estimators, we compared 16 estimators (Bayesian and non-Bayesian) of heterogeneity with regard to bias and mean square error over conditions based on reviews of educational and psychological meta-analyses. Three simulation conditions were varied: (a) sample size per meta-analysis, (b) true heterogeneity, and (c) sample size per effect size within each meta-analysis. Confidence or highest density intervals can be calculated for heterogeneity. The heterogeneity estimators that performed best over the widest range of conditions were paired with heterogeneity interval estimators. Interval estimators were evaluated based on coverage probability, interval width, and coverage of the estimated value. The combination of the Paule Manel estimator and Q-Profile interval method is recommended when synthesizing standardized mean difference effect sizes.

Reliability measures have been well studied over many years, beginning with an entire chapter devoted to intraclass correlation in the first edition of Fisher (1925). Such measures have been thoroughly studied for two factor models. This dissertation, motivated by a medical research problem, extends point and confidence interval estimation of both intraclass correlation coefficient and interater reliability coefficient to models containing three crossed random factors -- subjects, raters and occasions. The intraclass correlation coefficient is used when decision is made on an absolute basis with rater's scores, while the interater reliability coefficient is defined for decisions made on a relative basis. The estimation is conducted using both ANOVA and MCMC methods. The results from the two methods are compared. The MCMC method is preferred for analyses of small data sets when ICC values are high. Besides, the bias of estimator of intraclass correlation coefficient in one-way random effects model is evaluated. / Statistics

Thesis advisor: Geoffrey Sanzenbacher / Despite growing importance in the global economy, many of the countriees with large natural resource economies are among the poorest. In this paper, I first construct a theoretical model that provides a framework for the harm of natural resources on corruption levels and governance. Then, I construct what I call the Resource Volatility Index. This measures both a country's level of dependence on a category of resources and the price volatility of these resources themselves. Finally, I use Correlated Random Effects models to show that both average and year-varying levels of this index can explain the level of corruption and the quality of governance in a given country. The nagative impacts I find on both variables confirms previous economic theory on governments funded by natural resources. / Thesis (BA) — Boston College, 2024. / Submitted to: Boston College. Morrissey School of Arts and Sciences. / Discipline: Economics. / Discipline: Scholar of the College.

Natural history models for breast cancer describe the unobservable disease progression. These models can either be fitted using likelihood-based estimation to data on individual tumour characteristics, or calibrated to fit statistics at a population level. Likelihood-based inference using individual level data has the advantage of ensuring model parameter identifiability. However, the likelihood function can be computationally heavy to evaluate or even intractable. In this thesis likelihood-free estimation using Approximate Bayesian Computation (ABC) will be explored. The main objective is to investigate whether ABC can be used to fit models to data collected in the presence of mammography screening. As a background, a literature review of ABC is provided. As a first step an ABC-MCMC algorithm is constructed for two simple models both describing populations in absence of mammography screening, but assuming different functional forms of tumour growth. The algorithm is evaluated for these models in a simulation study using synthetic data, and compared with results obtained using likelihood-based inference. Later, it is investigated whether ABC can be used for the models in presence of screening. The findings of this thesis indicate that ABC is not directly applicable to these models. However, by including a sub-model for tumour onset and assuming that all individuals in the population have the same screening attendance it was possible to develop an ABC-MCMC algorithm that carefully takes individual level data into consideration in the estimation procedure. Finally, the algorithm was tested in a simple simulation study using synthetic data. Future research is still needed to evaluate the statistical properties of the algorithm (using extended simulation) and to test it on observational data where previous estimates are available for reference. / Natural history models för bröstcancer är statistiska modeller som beskriver det dolda sjukdomsförloppet. Dessa modeller brukar antingen anpassas till data på individnivå med likelihood-baserade metoder, eller kalibreras mot statistik för hela populationen. Fördelen med att använda data på individnivå är att identifierbarhet hos modellparametrarna kan garanteras. För dessa modeller händer det dock att det är beräkningsintensivt eller rent utav omöjligt att evaluera likelihood-funktionen. Huvudsyftet med denna uppsats är att utforska huruvida metoden Approximate Bayesian Computation (ABC), som används för skattning av statistiska modeller där likelihood-funktionen inte är tillgänglig, kan implementeras för en modell som beskriver bröstcancer hos individer som genomgår mammografiscreening. Som en del av bakgrunden presenteras en sammanfattning av modern ABC-forskning. Metoden består av två delar. I den första delen implementeras en ABC-MCMC algoritm för två enklare modeller. Båda dessa modeller beskriver tumörtillväxten hos individer som ej genomgår mammografiscreening, men modellerna antar olika typer av tumörtillväxt. Algoritmen testades i en simulationsstudie med syntetisk data genom att jämföra resultaten med motsvarande från likelihood-baserade metoder. I den andra delen av metoden undersöks huruvida ABC är kompatibelt med modeller för bröstcancer hos individer som genomgår screening. Genom att lägga till en modell för uppkomst av tumörer och göra det förenklande antagandet att alla individer i populationen genomgår screening vid samma ålder, kunde en ABC-MCMC algoritm utvecklas med hänsyn till data på individnivå. Algoritmen testades sedan i en simulationsstudie nyttjande syntetisk data. Framtida studier behövs för att undersöka algoritmens statistiska egenskaper (genom upprepad simulering av flera dataset) och för att testa den mot observationell data där tidigare parameterskattningar finns tillgängliga.

Longitudinal data occur frequently in medical studies and covariates measured by error are typical features of such data. Generalized linear mixed models (GLMMs) are commonly used to analyse longitudinal data. It is typically assumed that the random effects covariance matrix is constant across the subject (and among subjects) in these models. In many situations, however, this correlation structure may differ among subjects and ignoring this heterogeneity can cause the biased estimates of model parameters. In this thesis, following Lee et al. (2012), we propose an approach to properly model the random effects covariance matrix based on covariates in the class of GLMMs where we also have covariates measured by error. The resulting parameters from this decomposition have a sensible interpretation and can easily be modelled without the concern of positive definiteness of the resulting estimator. The performance of the proposed approach is evaluated through simulation studies which show that the proposed method performs very well in terms biases and mean square errors as well as coverage rates. The proposed method is also analysed using a data from Manitoba Follow-up Study. / February 2017