Em análise de sobrevivência estuda-se o tempo até a ocorrência de um determinado evento de interesse e na literatura, a abordagem mais usual é a paramétrica, em que os dados seguem uma distribuição de probabilidade. Diversas distribuições conhecidas são utilizadas para acomodar dados de tempos de falha, porém, grande parte destas distribuições não é capaz de acomodar funções de risco não monótonas. Kumaraswamy (1980) propôs uma nova distribuição de probabilidade e, baseada nela, mais recentemente Cordeiro e de Castro (2011) propuseram uma nova família de distribuições generalizadas, a Kumaraswamy generalizada (Kum-G). Esta distribuição além de ser flexível, contém distribuições com funções de risco unimodal e em forma de banheira. O objetivo deste trabalho é apresentar a família de distribuições Kum-Ge seus casos particulares para analisar dados de tempo de vida dos indivíduos em risco, considerando que uma parcela da população nunca apresentará o evento de interesse, além de considerarmos que covariáveis influenciem na função de sobrevivência e na proporção de curados da população. Algumas propriedades destes modelos serão abordadas, bem como métodos adequa- dos de estimação, tanto na abordagem clássica quanto na bayesiana. Por fim, são apresentadas aplicações de tais modelos a conjuntos de dados existentes na literatura. / In survival analysis is studied the time until the occurrence of a particular event of interest and in the literature, the most common approach is parametric, that the data follow a probability distribution. Various known distributions are used to accommodate failure times data, however, most of these distributions is not able to accommodate non monotonous hazard functions. Kumaraswamy (1980) proposed a new probability distribution and, based on it, most recently Cordeiro e de Castro (2011) proposed a new family of generalized distributions, Kumaraswamy generalized (Kum-G). This distribution besides being flexible, has distributions with unimodal and tub form of hazard functions. The objective of this paper is to present the family of Kum-G distributions and their particular cases to analyze lifetime data of individuals at risk, considering that part of the population never present the event of interest, and considering that covariates influencing in the survival function and the cured proportion of the population. Some properties of these models will be discussed as well as appropriate estimation methods, in the classical and Bayesian approaches. Finally, applications of such models are presented to data sets existingin the literature.

Resumo: A seleção baseada em características reprodutivas tem sido muito empregada em programas de melhoramento genético de suíno. Assim, objetivaram-se avaliar os efeitos ambientais e genéticos que influenciam o intervalo desmame-cio (IDC) e verificar sua influência no número de nascidos total (TL), nascidos vivos (NV) e mortos (NM) em fêmeas suínas. Para análise dos efeitos ambientais, utilizaram-se 8.104 dados da 1ª a 6ª ordem de parição, e, para as estimativas dos parâmetros genéticos, apenas as informações do 1º ao 3º IDC, o que resultou em 6.548 observações, que foram analisadas pelo método REML, utilizando-se modelos uni e multicaracterística. Para este último, considerou-se cada IDC (1º, 2º e 3º) como uma característica distinta. Avaliaram-se, também, as correlações genéticas entre o IDC, TL, NM e idade ao primeiro parto (IPP). Para os fatores ambientais, o modelo incluiu como efeitos fixos rebanho, linhagem, ano (AP) e estação (EP) de parto, e as covariáveis idade da porca ao parto (IDPP), TL e duração da lactação (DL). A DL, na forma linear, e a IDPP, na forma quadrática, influenciaram o IDC. Rebanho, AP e EP foram fontes de variação significativas, enquanto TL e linhagem não o foram. Não foi observada influência do IDC sobre TL, NV, nem sobre NM. A herdabilidade estimada para o IDC pelo modelo de repetibilidade foi baixa. As correlações genéticas entre os IDC (1º, 2º e 3º) foram de moderada a baixa magnitude, evidenciando que o modelo multicaracterística é mais indicado para as estimativas de parâmetro genético nessa população. As correlações genéticas entre IDC, TL e NM, assim como IDC e IPP foram favoráveis à seleção. / Abstract: Selection for reproductive traits has been largely used in swine breeding programs. The aims of this study were to evaluate environmental and genetic effects that affect the weaning-to-estrus interval (WEI) in sows and to assess their influence on litter size (LS), number of live born (LP) and dead born piglets (DP). Data consisting of 8,104 WEI from the 1st to 6th farrowing recorded in two herds were used for environmental analysis, but for estimating the genetic parameters only data from the 1st to 3rd farrowing were used, totalling 6,548 records. Genetic analysis was performed using the REML method with single and multitrait models, where each WEI was considered as a different trait. Genetic correlations among WEI, LS, DP and age at first farrowing (AFF) were also estimated using a multitrait model. For the environmental analysis, the model included as fixed effects the herd, line, and year (YF) and season (SF) of farrowing, and as covariates the sow's age at farrowing (SAF), LS, and lactation length (LL). The effects were linear for LL and quadratic for SAF. The herd, YF and SF were important sources of variation, whereas LS and line were not significant. There were no effects of WEI on the litter traits (LS, LP and DP). The heritability estimated for WEI was low, and genetic correlations among its different intervals were of moderate to low magnitude, evidencing that a multitrait model was more indicated for estimating the genetic parameters for this trait in this population. The genetic correlations between WEI and LS, DP and AFF would be favourable in a selection. / Orientador: Jeffrey Frederico Lui / Coorientadora: Lúcia Galvão de Albuquerque / Banca: Humberto Tonhati / Banca: Joslaine Noely dos Santos Gonçalves Cyrillo / Mestre

<p>A general time-to-event data analysis known as event history analysis is considered. The focus is on the analysis of time-to-event data using Cox's regression model when the time to the event may be measured from different origins giving several observable time scales and when longitudinal measurements are involved. For the multiple time scales problem, procedures to choose a basic time scale in Cox's regression model are proposed. The connections between piecewise constant hazards, time-dependent covariates and time-dependent strata in the dual time scales are discussed. For the longitudinal measurements problem, four methods known in the literature together with two proposed methods are compared. All quantitative comparisons are performed by means of simulations. Applications to the analysis of infant mortality, morbidity, and growth are provided.</p>

A general time-to-event data analysis known as event history analysis is considered. The focus is on the analysis of time-to-event data using Cox's regression model when the time to the event may be measured from different origins giving several observable time scales and when longitudinal measurements are involved. For the multiple time scales problem, procedures to choose a basic time scale in Cox's regression model are proposed. The connections between piecewise constant hazards, time-dependent covariates and time-dependent strata in the dual time scales are discussed. For the longitudinal measurements problem, four methods known in the literature together with two proposed methods are compared. All quantitative comparisons are performed by means of simulations. Applications to the analysis of infant mortality, morbidity, and growth are provided.

La variabilité des concentrations plasmatiques mesurées lors d’une anesthésie générale avec le propofol est directement reliée à une variabilité inter-animale, sa pharmacocinétique. L’objectif de cette étude est de caractériser la pharmacocinétique du propofol et de rechercher les effets des caractéristiques démographiques sur la variation des paramètres pharmacocinétiques. Les chiens (n=44) ayant participé à cette étude ont été anesthésiés au propofol à 6 mois (n=29), 12 (n=21) mois et/ou 24 mois (n=35). L’anesthésie a été induite avec du propofol (en moyenne 5 mg) et maintenue avec une perfusion (débit initial de 360 mg/kg/h). Des ajustements de perfusion ainsi que des bolus supplémentaires seront administrés si le comportement de l’animal l’exige. Une randomisation stratifiée des sexes aux deux groupes de prémédication, le premier recevant de l’acépropmazine (0,05 mg/kg en I.M.) et le deuxième une association d’acépromazine (0.05 mg/kg IM) et de butorphanol (0.1mg/kg IM). Des échantillons sanguins ont été prélevés de t=0 jusqu'à t=300 minutes ou plus. Au total 1339 prélèvements ont été analysés. Un modèle mamillaire à 3 compartiments décrit de manière adéquate nos données. Les valeurs moyennes de CLt V1, CL2, V2, CL3 and V3 sont respectivement égales à 0.65 L/min (SD=0.24), 2.6 L (SD=2.04), 2.24 L/min (1.43), 9.6 L (SD=7.49), 0.42 L/min (SD=0.199), 46.4 L (SD=40.6). Les paramètres pharmacocinétiques obtenus ont révélé une grande variabilité interindividuelle, en particulier CL2, V1, V2 et V3 .Le poids est une co-variable significative pour CLt et V2. L’âge est une co-variable significative pour CL3 et V3. L’ajout de la parenté pour V2 et V3 au modèle a amélioré la qualité de l’ajustement du modèle. Les paramètres V1 et CL2 sont indépendants des facteurs physiologiques étudiés. / The variability of plasma concentrations measured during general anesthesia with propofol is directly related to inter-animal variability of its pharmacokinetics. The objective of this study was to characterize the pharmacokinetics of propofol and to investigate the effects of demographic variables on the pharmacokinetic parameters. Dogs (n = 44) that participated in this study were anesthetized with propofol at 6 months (n = 29), 12 (n = 21) and/or 24 months (n = 35). Anesthesia was induced with propofol (average dose of 5 mg) and maintained with an infusion (initial rate of 360 mg/kg/h). Infusion adjustment and bolus doses were performed if required by the behavior of the animal . A stratified randomization of both sexes on two premedications groups [acepropmazine (0.05 mg /kg I.M) or Acepropmazine (0.05 mg /kg I.M) and butorphanol (0.1 mg /kg IM)]. Blood samples were collected from t = 0 to t = 300 minutes or more. A total of 1339 samples were analyzed. A 3-compartment mamillary model showed good predictive performances. The average values of CLt V1, CL2, V2, CL3 and V3 were 0.65 L/min (SD=0.24), 2.6 L (SD=2.04), 2.24 L/min (1.43), 9.6 L (SD=7.49), 0.42 L/min (SD=0.199), 46.4 L (SD=40.6) respectively. The pharmacokinetic parameters obtained showed a large inter-individual variability, in particular CL2, V1, V2 and V3. Adding to the model the covariates weight to CLt and V2, age to CL3 and V3, and kinship to V2 and V3 to the model to improved the performance and the quality of adjustment. Therefore, V1 and CL2 are constant parameters in this population.

In this thesis, ties and time-varying covariates in survival analysis are investigated. There are two types of ties: ties between event times (Type 1 ties) and ties between event times and the time that discrete time-varying covariates change or "jump"(Type 2 ties). The Cox proportional hazards model is one of the most important regression models for survival analysis. Methods for including Type 1 ties and time-varying covariates in the Cox proportional hazards model are well established in previous studies, but Type 2 ties have been ignored in the literature. This thesis discusses the effect of Type 2 ties on Cox's partial likelihood, the current default method to treat Type 2 ties in statistical packages SAS and R (called Fail before Jump in this thesis), and proposes alternative methods (Random and Equally Weighted) for Type 2 ties. A simulation study as well as an analysis of data sets from real research both suggest that both Random and Equally Weighted methods perform better than the other two methods. Also the effect of the percentages of Type 1 and Type 2 ties on these methods for handling both types of ties is discussed. / NSERC

Doctor of Philosophy(PhD) / This thesis employs survival analysis framework (Allison, 1984) and the Cox’s hazard model (Cox, 1972) to estimate the probability that a credit rating survives in its current grade at a certain forecast horizon. The Cox’s hazard model resolves some significant drawbacks of the conventional estimation approaches. It allows a rigorous testing of non-Markovian behaviours and time heterogeneity in rating dynamics. It accounts for the changes in risk factors over time, and features the time structure of probability survival estimates. The thesis estimates three stratified Cox’s hazard models, including a proportional hazard model, and two dynamic hazard models which account for the changes in macro-economic conditions, and the passage of survival time over rating durations. The estimation of these stratified Cox’s hazard models for downgrades and upgrades offers improved understanding of the impact of rating history in a static and a dynamic estimation framework. The thesis overcomes the computational challenges involved in forming dynamic probability estimates when the standard proportionality assumption of Cox’s model does not hold and when the data sample includes multiple strata. It is found that the probability of rating migrations is a function of rating history and that rating history is more important than the current rating in determining the probability of a rating change. Switching from a static estimation framework to a dynamic estimation framework does not alter the effect of rating history on the rating migration hazard. It is also found that rating history and the current rating interact with time. As the rating duration extends, the main effects of rating history and current rating variables decay. Accounting for this decay has a substantial impact on the risk of rating transitions. Downgrades are more affected by rating history and time interactions than upgrades. To evaluate the predictive performance of rating history, the Brier score (Brier, 1950) and its covariance decomposition (Yates, 1982) were employed. Tests of forecast accuracy suggest that rating history has some predictive power for future rating changes. The findings suggest that an accurate forecast framework is more likely to be constructed if non-Markovian behaviours and time heterogeneity are incorporated into credit risk models.

Cette thèse aborde deux sujets peu traités dans la littérature concernant le théorie des valeurs extrêmes : celui des observations en présence de covariables et celui des mesures de dépendance pour des paires d'observations. Dans la première partie de cette thèse, nous avons considéré le cas où la variable d'intérêt est observée simultanément avec une covariable, pouvant être fixe ou aléatoire. Dans ce contexte, l'indice de queue dépend de la covariable et nous avons proposé des estimateurs de ce paramètre dont nous avons étudié les propriétés asymptotiques. Leurs comportements à distance finie ont été validés par simulations. Puis, dans la deuxième partie, nous nous sommes intéressés aux extrêmes multivariés et plus particulièrement à mesurer la dépendance entre les extrêmes. Dans une situation proche de l'indépendance asymptotique, il est très difficile de mesurer cette dépendance et de nouveaux modèles doivent être introduits. Dans ce contexte, nous avons adapté un outil de géostatistique, le madogramme, et nous avons étudié ses propriétés asymptotiques. Ses performances sur simulations et données réelles ont également été exhibées. Cette thèse offre de nombreuses perspectives, tant sur le plan pratique que théorique dont une liste non exhaustive est présentée en conclusion de la thèse. / This thesis presents a study of the extreme value theory and is focused on two subjects rarely analyzed: observations associated with covariates and dependence measures for pairs of observations.In the first part, we considered the case where the variable of interest is simultaneously recorded with a covariate which can be either fixed or random. The conditional tail index then depends on the covariate and we proposed several estimators with their asymptotic properties. Their behavior have been approved by simulations.In the second part, we were interested in multivariate extremes and more particularly in measuring the dependence between them. In a case of near asymptotic independence, we have to introduce new models in order to measure the dependence properly. In this context, we adapted a geostatistical tool, the madogram, and studied its asymptotic properties. We completed the study with simulations and real data of precipitations.

This thesis studies regression discontinuity designs with the use of additional covariates for estimation of the average treatment effect. We prove asymptotic normality of the covariate-adjusted estimator under sufficient regularity conditions. In the case of a high-dimensional setting with a large number of covariates depending on the number of observations, we discuss a Lasso-based selection approach as well as alternatives based on calculated correlation thresholds. We present simulation results on those alternative selection strategies.:1. Introduction 2. Preliminaries 3. Regression Discontinuity Designs 4. Setup and Notation 5. Computing the Bias 6. Asymptotic Behavior 7. Asymptotic Normality of the Estimator 8. Including Potentially Many Covariates 9. Simulations 10. Conclusion

To understand the modeling challenges and to examine the important factors considered in Malayan sun bear (Helarctos malayanus) distribution studies, we reviewed 33 peer-reviewed articles published from 2003-2023. These studies used 54 environmental or anthropogenic variable types to investigate the distribution, habitat preference, and home range composition of sun bears. Most variable types are human disturbance (n=4), climate (n=3), topography (n=1), vegetation (n=11), or other ecological factors (n=3). Nevertheless, a number of rarely used variables might also be useful to include in future evaluations (i.e., food abundance), and observational evidence suggests that predator occurrence could also be informative. Importantly, no studies tested the performance of model prediction by using other presence points of the species in a similar or adjacent biogeographical area. In Myanmar, where the bear’s distribution is not well-known, we set up three annual surveys using 120 camera-trap stations in a portion of the Htamanthi Wildlife Sanctuary (HWS) in northern Myanmar during 2016-17 to 2018-19 to identify factors influencing bear distribution. From a total effort of 15,315 trap nights, we obtained 47 independent photo events of sun bears at 16%, 13%, and 9% of the stations each year. We analyzed eight factors potentially influencing the bear distribution and found that the top three ranked models were a combination of elevation, NDVI (Normalized Difference Vegetation Index), distance to water, and slope. The presence of tigers (Panthera tigris) in the area was found to have a positive relation with mean sun bear occupancy. In this study, we tested the prediction performance of the single-season occupancy model with another dataset. We tested the prediction performance of the top six models in the PresenceAbsence Package and calculated the AUC (Area under receiver curved), TSS (True skill statistics), and Kappa scores. The AUC score ranged from 0.5 to 0.6, while the TSS score ranged from -0.001 to 0.28. None of the top six models’ predictions perfectly agreed with the sanctuary-wide survey data. The discrepancies may be due to the limited sample size, the temporal scale of the prediction, and the presence of other ecological factors (e.g., predators, competitors, or food availability) not accounted for in the habitat use prediction. To improve the prediction performance of occupancy models, we recommend that future sun bear surveys increase the number and size of sampling efforts and include ecological covariates such as potential predators when possible.