Introdução: As técnicas mais comumente empregadas em análise de sobrevida que utilizam dados censurados são o estimador produto limite de Kaplan-Meier (KM) e o modelo de riscos proporcionais de Cox. Estas técnicas têm como suposição que a causa da perda de seguimento seja independente do tempo de sobrevida. Objetivo: O presente estudo visa a analisar o efeito das perdas de seguimento nestas duas técnicas. Material e Métodos: O estudo foi realizado utilizando-se o banco de dados dos pacientes cadastrados no Registro Hospitalar do Hospital do Câncer de São Paulo em 1994. Foram elaborados 28 bancos de dados simulando perdas informativas e não informativas. A perda informativa foi simulada transformando os óbitos em vivos, na proporção de 5 a 50%. A perda não informativa foi simulada através do sorteio de 5 a 50% do total do banco. O estimador de Kaplan-Meier (KM) foi utilizado para estimar a sobrevida acumulada no primeiro, terceiro e quinto ano de seguimento, e o modelo de riscos proporcionais de Cox para estimar as hazard ratio (HR). Todas as estimativas obtidas no KM e as HR's foram comparadas com os resultados do banco de dados original. Resultados: Houve maior proporção de perda nos pacientes com maior escolaridade, admitidos por convênio e particular e os menos graves (estádio I ou II). Quanto maior a proporção de perda informativa, maior a diferença alcançada nas estimativas realizadas pelo KM, verificando-se que a perda de seguimento superior a 15% acarretou diferenças superiores a 20% nas estimativas da probabilidade de sobrevida. As HR's foram menos afetadas, e proporções superiores a 20% de perda de seguimento acarretaram variações de cerca de 10% nas estimativas. Quando as perdas foram não informativas não houve diferenças significativas nas estimativas pelo KM e nas HR's em relação ao banco original. Conclusões: É importante avaliar se as perdas ocorridas em estudos de coorte são informativas ou não, pois se forem podem acarretar distorções principalmente nas estimativas feitas pelo método de KM. / Introduction: The Kaplan Meier product limit estimator (KM) and the Cox proportional hazard (HR) model are the most used tools in survival analysis. These two methods have the key assumption that censoring must be independent from the survival time. Objective: To analyze the consequences of loss to follow up in these two methods. Methods: The study has utilized the data of the Cancer Registry of the patients of Hospital do Cancer in São Paulo of 1994. The informative censure was simulated transforming the death by 5 to 50% into alive. Besides 5 to 50% was spared at random simulating the non-informative censoring. The survival probability and was calculated to the first, third and fifth year of follow –up. All the estimated probabilities and HR’s were compared with the results of the original data. Results: Patients with greater scholars, lower stages and admitted by health plans or private had more losses to follow up. The maximum proportion of accepted loss to follow –up is 10% to 15% when using the KM estimator, and the HR are less affected by the loss to follow-up and one can afford having 20% of it. When the losses were non informative there were no differences between the original probabilities. Conclusions: The possibility of over or under estimated probability must be analyzed in the presence of the losses to follow- up when using the KM and HR in survival analyses.

[EN] The global objective of the present thesis was to study the functional longevity defined as length of productive life (LPL) in five Spanish specialized lines of rabbit (A, V, H and LP). Chapter 3, aimed to check the genetic heterogeneity for longevity between the five lines estimating the additive variance and the corresponding effective heritabilities. As well as to test the genetic importance of time-dependent factors such as positive palpation order (OPP), physiological status (PS) and number of kits born alive (NBA) on the genetics of longevity. This point has been assessed using four different Cox proportional hazard models; the first one (Model 1) included all the previous factors in addition to the year-season effect, the inbreeding coefficient effect and finally the animal effect as random factor. The remaining three models were the same as Model 1 but excluding OPP (Model 2), or PS (Model 3), or NBA (Model 4). The complete data set comprised 15,670 does with records 35.6 % having censoring data, and the full pedigree file involved 19,405 animals. The heritability estimates for longevity in the five lines were low and ranged from 0.02±0.01 to 0.14±0.09, and consequently, it is not recommended to include this trait as selection criteria in rabbit breeding programs. Despite of the large variation of the heritability estimates, the corresponding HPD95% always overlapped and consequently the hypothesis of all lines having the same heritability cannot be discarded. Comparing the additive variance estimates of the four models, it was observed that by correcting for PS 51, 39, 38, 83 and 75% of the additive variance in lines A, V, H, LP and R, respectively, was removed. The risk of death or culling decreases as OPP advanced. Non-pregnant-non-lactating females are those under the higher risk. The does which had zero NBA had the highest risk, apart for this special figure (zero NBA) the risk decreased as NBA increased. Chapter 4 intended to estimate the genetic and environmental correlations between longevity and two prolificacy traits (number of kits born alive (NBA) and number of kits alive at weaning (NW)). Furthermore, to estimate the genetic and environmental correlations between longevity and the percentage of days that the doe spent in the different physiological statuses with respect to its entire productive life. The complete pedigree file comprised 19,405 animals. The datasets included records on 15,670 does which had 58,329 kindlings and 57,927 weanings. In general the genetic correlations between NBA and NW, and the hazard were low to very low, and the only line for which it can be said these genetic correlation to be different from zero was the LP line. Regarding the correlations between longevity and the percentage of days the doe spent in each physiological status, there were evidences of non-negligible genetic correlations between the two traits. Chapter 5 purposed to compare the five lines at their foundation and at fixed time periods during their selection programs. The first comparison was done at the origin of the lines, involving the complete data set, and using a genetic model (CM) including the additive values of the animals, so the effect of selection was considered. For the second comparison the same model as the first comparison was used, but excluding the additive effects from the model of analysis (IM), and involving only the data corresponding to each period, so the differences between the lines included the additive values of the animals. The lines V, H and LP showed at foundation a substantial superiority over line A. The line R had higher risk of death or culling with relevant differences when compared to V, H and LP lines. The maximum relative risks were observed between the lines LP and R (0.239), and between LP and A (0.317). For the comparisons at fixed times, the pattern of the differences between the A line and the others was similar to those observed at foundation. / [ES] El objetivo global de la presente tesis fue estudiar la longevidad funcional en cinco líneas españolas de conejos (A, V, H y LP), el carácter se definió como la longitud de la vida productiva. En el Capítulo 3, dirigido a comprobar la heterogeneidad genética de la longevidad entre las 5 líneas, se estimaron las varianzas aditivas y sus correspondientes heredabilidades efectivas. Y además se evaluó la importancia del orden de la palpación positiva (OPP), el estado fisiológico (PS) y el número de gazapos nacidos vivos (NBA) sobre el determinismo genético de la longevidad. Para ello se utilizaron 4 modelos de Cox de riesgos proporcionales; el primer modelo (Modelo 1) incluyó todos los factores anteriores, además del efecto del año-estación, el efecto de la consanguinidad y, finalmente, el valor aditivo de los animales como efecto aleatorio. Los otros tres modelos fueron igual que el Modelo 1 pero excluyendo OPP (Modelo 2), o PS (Modelo 3), o NBA (Modelo 4). Los datos de longevidad estaban referidos a 15,670 conejas y tuvieron una tasa de censura de 35.6%. La genealogía completa involucró a 19,405 animales. Las estimas de heredabilidad efectiva para la longevidad en las 5 líneas fueron bajas y variaron de 0.02±0.01 a 0.14±0.09. A pesar de la gran variación de las estimas puntuales de heredabilidad, los correspondientes intervalos HPD95% siempre se solaparon y por lo tanto la hipótesis de que todas las líneas tengan la misma heredabilidad no pudo descartase. Se observó que la exclusión de PS incrementó la varianza aditiva aproximadamente, en un 51, 39, 38, 83 y 75% en las líneas A, V, H, LP y R, respectivamente. El riesgo de muerte o eliminación disminuía a medida que avanzaba el OPP, observándose el riesgo más alto durante los primeros dos partos, partos en los que las conejas todavía están creciendo lo que sería un factor de riesgo importante. El nivel No-Gestante-No-Lactante de PS tuvo el mayor riesgo. Este nivel se interpreta como indicador de baja fertilidad y/o problemas de salud de la coneja. Las conejas que tenían cero NBA tuvieron el mayor riesgo de muerte o eliminación, aunque para el resto de niveles de NBA se apreció una disminución del riesgo a medida que aumenta la prolificidad. En el capítulo 4, se estimaron las correlaciones genéticas y ambientales entre la longevidad y dos caracteres de prolificidad [número de gazapos nacidos vivos (NBA) y el número de destetados (NW)]. El fichero de datos incluyó 58,329 partos y 57,927 destetes. También se estimaron las correlaciones entre longevidad y el porcentaje de días que la coneja pasó en los diferentes estados fisiológicos con respecto a la totalidad de su vida productiva. La única línea para la que se puede decir que la correlación genética entre NBA o NW y el riesgo fue significativamente diferente de cero fue la línea LP. Hubo evidencias de correlaciones genéticas no despreciables entre la longevidad y el porcentaje de días que la hembra pasó en cada estado fisiológico los dos caracteres. En el capítulo 5 se compararon las longevidades medias de las 5 líneas en su fundación y en períodos de tiempo determinados. La comparación de las líneas en el origen, utilizó todos los datos y un modelo genético (CM) que incluía los valores aditivos de los animales. Para la comparación en tiempos fijos se utilizó el mismo modelo, pero excluyendo los efectos aditivos del modelo de análisis (IM), utilizando sólo los datos correspondientes a cada período, por lo que las diferencias entre las líneas incluían los cambios debidos a la selección. Las líneas V, H y LP mostraron una superioridad sustancial sobre las líneas A y R. Los riesgos relativos máximos se observaron entre las líneas LP y R (0.239), y entre LP y A (0.317). Con respecto a las comparaciones en tiempos fijos, el patrón de las diferencias entre la línea de A y las otras líneas fue similar a los observados en la fundación. / [CAT] L'objectiu global de la present tesi va ser estudiar la longevitat funcional en cinc línies espanyoles de conills (A, V, H i LP), el caràcter es va definir com la longitud de la vida productiva. Al Capítol 3, dirigit a comprovar l'heterogeneïtat genètica de la longevitat entre les 5 línies, es van estimar les variàncies additives i les seues corresponents heretabilitats efectives. A més a més, es va avaluar la importància de factors dependents del temps, com l'orde de la palpació positiva (OPP) , l'estat fisiològic (PS) i el nombre de llorigons nascuts vius (NBA) sobre el determinisme genètic de la longevitat. Per a això es van utilitzar 4 models de Cox de riscos proporcionals; el primer model (Model 1) va incloure tots els factors anteriorment assenyalats, a més de l'efecte de l'any-estació, l'efecte de la consanguinitat i, finalment, el valor additiu dels animals com a efecte aleatori. Els altres tres models van ser igual que el Model 1 però excloent l'OPP (Model 2) , o PS (Model 3) , o NBA (Model 4) . Les dades de longevitat estaven referides a 15,670 conilles i van tindre una taxa de censura de 35.6%. La genealogia completa va involucrar a 19,405 animals. Les estimes d'heretabilitat efectiva (Model 1) per a la longevitat en les 5 línies van ser baixes i van variar de 0.02±0.01 a 0.14±0.09. A pesar de la gran variació de les estimes puntuals d'heretabilitat, els corresponents intervals HPD95% sempre es van solapar i per tant la hipòtesi que totes les línies tinguen la mateixa heretabilitat no va poder descartar-se. Es va observar que l'exclusió de PS va incrementar la variància additiva, aproximadament, en un 51, 39, 38, 83 i 75% en les línies A, V, H, LP i R, respectivament. El risc de mort o eliminació disminuïa a mesura que avançava l'OPP, observant-se el risc més alt durant els primers dos parts, en què les conilles encara estan creixent el que seria un factor de risc important. El nivell No-Gestant-No-Lactant de PS va tindre el major risc en comparació amb els altres nivells. Les conilles que tenien zero NBA van tindre el major risc de mort o eliminació, encara que per a la resta de nivells de NBA es va apreciar una disminució del risc a mesura que augmentà la prolificitat. Al Capítol 4, es van estimar les correlacions genètiques i ambientals entre la longevitat i dos caràcters de prolificitat [nombre de llorigons nascuts vius (NBA) i el nombre de deslletats (NW)]. El fitxer de dades va incloure 58,329 parts i 57,927 deslletaments. L'única línia per a la que es pot dir que la correlació genètica entre NBA o NW i el risc va ser significativament diferent de zero va ser la línia LP. Evidències de correlacions genètiques no menyspreables entre longevitat i els percentatge de dies que la femella va passar en cada estat fisiològic. Al Capítol 5 es compararen les longevitats mitges de les 5 línies en la seua fundació i en períodes de temps determinats. Per a la comparació de les línies a l'origen, es van utilitzar totes les dades i un model genètic (CM) que incloïa els valors additius dels animals, per la qual cosa es va considerar l'efecte de la selecció a partir de la fundació. En la comparació en temps fixos se va utilitzar el mateix model que en l'anterior, però excloent els efectes additius del model d'anàlisi (IM), utilitzant només les dades corresponents a cada període, per la qual cosa les diferències entre les línies incloïen els canvis deguts a la selecció. Les línies V, H i LP van mostrar una superioritat substancial sobre les línies A i R. Els riscos relatius màxims es van observar entre les línies LP i R (0.239), i entre LP i A (0.317). Respecte a les comparacions en temps fixos, el patró de les diferències entre la línia de A i les altres línies va ser semblant als observats en la fundació. / El Nagar, AGF. (2015). Genetic analysis of longevity in specialized lines of rabbits [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/52390 / TESIS

過去國內之抵押貸款提前清償與逾期還款之相關研究，在實證研究上最主要利用邏輯斯迴歸或是比例轉機模型( Proportional hazard model )分析影響一般住宅抵押貸款人提前清償與逾期還款之因素，並估計一般住宅抵押貸款人提前清償之機率。本文選擇採用研究抵押貸款時，國內未曾使用之卜瓦松迴歸( Poisson regression model )來估計比例轉機模型假設下影響提前清償與違約變數之參數，以研究影響抵押貸款借款人之提前償還與違約因素。 本研究結合比例轉機模型與卜瓦松迴歸模型，目的在結合兩模型之優點，在處理時間相依之共變數效率提高，並且在處理多重時間尺度的方程式較偏最大概似估計法直接，以得到較佳的研究成果。另外，過去國內提前清償與違約之文獻中並未加入利率走勢之變數，本研究加入再融資利率對31∼90天期商業本票利率之比率與再融資利率波動性兩變數，以考慮利率走勢對貸款者提前清償及違約行為之影響。 模型中的解釋變數包括地區、季節、抵押貸款年齡、貸款成數、貸款人年齡、性別、婚姻狀況、教育程度、職業、屋齡、房屋坪數、所得、貸款金額、月付額對薪資比、再融資利率/31∼90天期商業本票利率、再融資利率波動性等十六項。實證結果在提前清償部份，顯著正向之變數有貸款年齡、屋齡、房屋坪數、所得、月付額與薪資比，顯著負向之變數包括季節、再融資利率對31∼90天期商業本票利率之比率、貸款金額。在違約部份，顯著正向之變數包括貸款年齡、貸款成數、年齡、所得、月付額與薪資比、再融資利率對31∼90天期商業本票利率之比率；顯著負向之變數包括季節、教育程度及貸款金額。

Selection of signi?cant genes via expression patterns is important in a microarray problem. Owing to small sample size and large number of variables (genes), the selection process can be unstable. This research proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables in a regression setting and use a Bayesian mixture prior to perform the variable selection. Due to the binary nature of the data, the posterior distributions of the parameters are not in explicit form, and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the posterior distributions. The Bayesian model is ?exible enough to identify the signi?cant genes as well as to perform future predictions. The method is applied to cancer classi?cation via cDNA microarrays. In particular, the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify the set of signi?cant genes to classify BRCA1 and others. Microarray data can also be applied to survival models. We address the issue of how to reduce the dimension in building model by selecting signi?cant genes as well as assessing the estimated survival curves. Additionally, we consider the wellknown Weibull regression and semiparametric proportional hazards (PH) models for survival analysis. With microarray data, we need to consider the case where the number of covariates p exceeds the number of samples n. Speci?cally, for a given vector of response values, which are times to event (death or censored times) and p gene expressions (covariates), we address the issue of how to reduce the dimension by selecting the responsible genes, which are controlling the survival time. This approach enables us to estimate the survival curve when n << p. In our approach, rather than ?xing the number of selected genes, we will assign a prior distribution to this number. The approach creates additional ?exibility by allowing the imposition of constraints, such as bounding the dimension via a prior, which in e?ect works as a penalty. To implement our methodology, we use a Markov Chain Monte Carlo (MCMC) method. We demonstrate the use of the methodology with (a) di?use large B??cell lymphoma (DLBCL) complementary DNA (cDNA) data and (b) Breast Carcinoma data. Lastly, we propose a mixture of Dirichlet process models using discrete wavelet transform for a curve clustering. In order to characterize these time??course gene expresssions, we consider them as trajectory functions of time and gene??speci?c parameters and obtain their wavelet coe?cients by a discrete wavelet transform. We then build cluster curves using a mixture of Dirichlet process priors.

Selection of signi?cant genes via expression patterns is important in a microarray problem. Owing to small sample size and large number of variables (genes), the selection process can be unstable. This research proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables in a regression setting and use a Bayesian mixture prior to perform the variable selection. Due to the binary nature of the data, the posterior distributions of the parameters are not in explicit form, and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the posterior distributions. The Bayesian model is ?exible enough to identify the signi?cant genes as well as to perform future predictions. The method is applied to cancer classi?cation via cDNA microarrays. In particular, the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify the set of signi?cant genes to classify BRCA1 and others. Microarray data can also be applied to survival models. We address the issue of how to reduce the dimension in building model by selecting signi?cant genes as well as assessing the estimated survival curves. Additionally, we consider the wellknown Weibull regression and semiparametric proportional hazards (PH) models for survival analysis. With microarray data, we need to consider the case where the number of covariates p exceeds the number of samples n. Speci?cally, for a given vector of response values, which are times to event (death or censored times) and p gene expressions (covariates), we address the issue of how to reduce the dimension by selecting the responsible genes, which are controlling the survival time. This approach enables us to estimate the survival curve when n << p. In our approach, rather than ?xing the number of selected genes, we will assign a prior distribution to this number. The approach creates additional ?exibility by allowing the imposition of constraints, such as bounding the dimension via a prior, which in e?ect works as a penalty. To implement our methodology, we use a Markov Chain Monte Carlo (MCMC) method. We demonstrate the use of the methodology with (a) di?use large B??cell lymphoma (DLBCL) complementary DNA (cDNA) data and (b) Breast Carcinoma data. Lastly, we propose a mixture of Dirichlet process models using discrete wavelet transform for a curve clustering. In order to characterize these time??course gene expresssions, we consider them as trajectory functions of time and gene??speci?c parameters and obtain their wavelet coe?cients by a discrete wavelet transform. We then build cluster curves using a mixture of Dirichlet process priors.

The input collected from warranty claims data links customer feedback with product quality. Results from warranty claim analysis can potentially improve product quality, customer relationships and positively affect business. However working on warranty claims data holds many challenges that requires a significant share of time devoted to data cleaning and data processing. The purpose of warranty claims analysis is to get the comprehensive overview of the reliability, costs and quality of household appliances produced by ASKO. While there are different ways to approach this problem, we will focus on non-parametric and semi-parametric methods, by using Kaplan-Meier estimators and Cox proportional hazard model respectively. These kinds of models are time dependent and therefore used for prediction of household appliance reliability. Even though non-parametric models are quite informative they cannot handle additional characteristics about observable product hence the semi-parametric Cox proportional hazard model was proposed. Apart from the reliability analysis, we will also predict warranty costs with probit model and observe inequality in household appliances part failures as a part of quality control analysis. Described methods were selected due to the fact that the warranty claims analysis will be practiced in future by ASKO’s quality department and therefore straight forward methods with very informative results are needed.

Cox proportional hazard model is often used to estimate the effect of covariates on hazard for censored event times. In this thesis we study the semiparametric models of additive risk for censored data. In this model the hazard is given as a sum of unknown baseline hazard function and a product of covariates and coefficients. Further the general additive-multiplicative model is assumed. In this model the effect of a covariate can be either multiplicative, additive or both at the same time. We focuse on determining the effect of a covariate in the general model. This model can be used to test for the multiplicative or addtive effect of a covariate on the hazard.

This thesis surveys the method of extending Cox proportional hazard models (1972) and the general class of semiparametric model (2004) in the upgrades or downgrades of credit ratings by S&P. The two kinds of models can be used to modify the relationship of covariates to a recurrent event data of upgrades or downgrades. The benchmark credit-scoring model with a quintet of financial ratios which is inspired by the Z-Score model is employed. These financial ratios include measures of short-term liquidity, leverage, sales efficiency, historical profitability and productivity. The evidences of empirical results show that the financial ratios of historical profitability, leverage, and sales efficiency are significant factors on the rating transitions of upgrades. For the downgrades data setting, the financial ratios of short-term liquidity, productivity, and leverage are significant factors in the extending Cox models, whereas only the historical profitability is significant in the general class of semiparametric model. The empirical analysis of S&P credit ratings provide evidence supporting that the transitions of credit ratings are related to some determined financial ratios under these new econometrics methods.

In this thesis, we develop some inferential results for one-shot device testing data analysis. These extend and generalize existing methods in the literature. First, a competing-risk model is introduced for one-shot testing data under accelerated life-tests. One-shot devices are products which will be destroyed immediately after use. Therefore, we can observe only a binary status as data, success or failure, of such products instead of its lifetime. Many one-shot devices contain multiple components and failure of any one of them will lead to the failure of the device. Failed devices are inspected to identify the specific cause of failure. Since the exact lifetime is not observed, EM algorithm becomes a natural tool to obtain the maximum likelihood estimates of the model parameters. Here, we develop the EM algorithm for competing exponential and Weibull cases. Second, a semi-parametric approach is developed for simple one-shot device testing data. Semi-parametric estimation is a model that consists of parametric and non-parametric components. For this purpose, we only assume the hazards at different stress levels are proportional to each other, but no distributional assumption is made on the lifetimes. This provides a greater flexibility in model fitting and enables us to examine the relationship between the reliability of devices and the stress factors. Third, Bayesian inference is developed for one-shot device testing data under exponential distribution and Weibull distribution with non-constant shape parameters for competing risks. Bayesian framework provides statistical inference from another perspective. It assumes the model parameters to be random and then improves the inference by incorporating expert's experience as prior information. This method is shown to be very useful if we have limited failure observation wherein the maximum likelihood estimator may not exist. The thesis proceeds as follows. In Chapter 2, we assume the one-shot devices to have two components with lifetimes having exponential distributions with multiple stress factors. We then develop an EM algorithm for developing likelihood inference for the model parameters as well as some useful reliability characteristics. In Chapter 3, we generalize to the situation when lifetimes follow a Weibull distribution with non-constant shape parameters. In Chapter 4, we propose a semi-parametric model for simple one-shot device test data based on proportional hazards model and develop associated inferential results. In Chapter 5, we consider the competing risk model with exponential lifetimes and develop inference by adopting the Bayesian approach. In Chapter 6, we generalize these results on Bayesian inference to the situation when the lifetimes have a Weibull distribution. Finally, we provide some concluding remarks and indicate some future research directions in Chapter 7. / Thesis / Doctor of Philosophy (PhD)

<p>    </p> <p>The counting process is the fundamental of many real-world problems with event data. Poisson process, used as the background intensity of Hawkes process, is the most commonly used point process. The Hawkes process, a self-exciting point process fits to temporal event data, spatial-temporal event data, and event data with covariates. We study the Hawkes process that fits to heterogeneous drug overdose data via a novel semi-parametric approach. The counting process is also related to survival data based on the fact that they both study the occurrences of events over time. We fit a Cox model to temporal event data with a large corpus that is processed into high dimensional covariates. We study the significant features that influence the intensity of events. </p>