One of the major goals in large-scale genomic studies is to identify genes with a prognostic impact on time-to-event outcomes, providing insight into the disease's process. With the rapid developments in high-throughput genomic technologies in the past two decades, the scientific community is able to monitor the expression levels of thousands of genes and proteins resulting in enormous data sets where the number of genomic variables (covariates) is far greater than the number of subjects. It is also typical for such data sets to have a high proportion of censored observations. Methods based on univariate Cox regression are often used to select genes related to survival outcome. However, the Cox model assumes proportional hazards (PH), which is unlikely to hold for each gene. When applied to genes exhibiting some form of non-proportional hazards (NPH), these methods could lead to an under- or over-estimation of the effects. In this thesis, we develop methods that will directly address t / Statistics

One of the most common measures of clinical outcomes is the survival time. Accurately linking cancer molecular profiling with survival outcome advances clinical management of cancer. However, existing survival analysis relies intensively on statistical evidence from a single level of data, without paying much attention to the integration of interacting multi-level data and the underlying biology. Advances in genomic techniques provide unprecedented power of characterizing the cancer tissue in a more complete manner than before, opening the opportunity of designing biologically informed and integrative approaches for survival analysis. Many cancer tissues have been profiled for gene expression levels and genomic variants (such as copy number alterations, sequence mutations, DNA methylation, and histone modification). However, it is not clear how to integrate the gene expression and genetic variants to achieve a better prediction and understanding of the cancer survival. To address this challenge, we propose two approaches for data integration in order to both biologically and statistically boost the features selection process for proper detection of the true predictive players of survival. The first approach is data-driven yet biologically informed. Consistent with the biological hierarchy from DNA to RNA, we prioritize each survival-relevant feature with two separate scores, predictive and mechanistic. With mRNA expression levels in concern, predictive features are those mRNAs whose variation in expression levels are associated with the survival outcome, and mechanistic features are those mRNAs whose variation in expression levels are associated with genomic variants (copy number alterations (CNAs) in this study). Further, we propose simultaneously integrating information from both the predictive model and the mechanistic model through our new approach GEMPS (Gene Expression as a Mediator for Predicting Survival). Applied on two cancer types (ovarian and glioblastoma multiforme), our method achieved better prediction power than peer methods. Gene set enrichment analysis confirms that the genes utilized for the final survival analysis are biologically important and relevant. The second approach is a generic mathematical framework to biologically regularize the Cox's proportional hazards model that is widely used in survival analysis. We propose a penalty function that both links the mechanistic model to the clinical model and reflects the biological downstream regulatory effect of the genomic variants on the mRNA expression levels of the target genes. Fast and efficient optimization principles like the coordinate descent and majorization-minimization are adopted in the inference process of the coefficients of the Cox model predictors. Through this model, we develop the regulator-target gene relationship to a new one: regulator-target-outcome relationship of a disease. Assessed via a simulation study and analysis of two real cancer data sets, the proposed method showed better performance in terms of selecting the true predictors and achieving better survival prediction. The proposed method gives insightful and meaningful interpretability to the selected model due to the biological linking of the mechanistic model and the clinical model. Other important forms of clinical outcomes are monitoring angiogenesis (formation of new blood vessels necessary for tumor to nourish itself and sustain its existence) and assessing therapeutic response. This can be done through dynamic imaging, in which a series of images at different time instances are acquired for a specific tumor site after injection of a contrast agent. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a noninvasive tool to examine tumor vasculature patterns based on accumulation and washout of the contrast agent. DCE-MRI gives indication about tumor vasculature permeability, which in turn indicates the tumor angiogenic activity. Observing this activity over time can reflect the tumor drug responsiveness and efficacy of the treatment plan. However, due to the limited resolution of the imaging scanners, a partial-volume effect (PVE) problem occurs, which is the result of signals from two or more tissues combining together to produce a single image concentration value within a pixel, with the effect of inaccurate estimation to the values of the pharmacokinetic parameters. A multi-tissue compartmental modeling (CM) technique supported by convex analysis of mixtures is used to mitigate the PVE by clustering pixels and constructing a simplex whose vertices are of a single compartment type. CAM uses the identified pure-volume pixels to estimate the kinetics of the tissues under investigation. We propose an enhanced version of CAM-CM to identify pure-volume pixels more accurately. This includes the consideration of the neighborhood effect on each pixel and the use of a barycentric coordinate system to identify more pure-volume pixels and to test those identified by CAM-CM. Tested on simulated DCE-MRI data, the enhanced CAM-CM achieved better performance in terms of accuracy and reproducibility. / Ph. D.

In Sweden, there has been an long term effort to allow as heavy traffic as possible, provided thatthe road network can handle it. This is because heavy traffic offers a competitive advantage withsocio-economic gains. In July 2018, the Swedish Transport Administration made 12 percent ofthe Swedish road network avaliable for the new maximum vehicle weight of 74 tonnes, basedon a legislative change from 2017. It is known that heavy traffic has a negative effect on thedegradation of the road, but it prevails divided opinions on whether 74 tonnes have a greaterimpact on the degradation rate compared to previous maximum gross weights of 64 tonnes.The 74 tonne vehicles have the same allowed axle load, which means more axles per vehicle. Some argue that an increased total load and more axles affect the degradation associated withtime-dependent material properties, while others argue that 74 tonnes mean fewer heavy vehiclesoverall, and thus should have a positive impact on the road’s lifespan. The construction companySkanska therefore requests a statistical analysis that enables to nuance the effects that heavytraffic has on the Swedish state road network. Since there is very limited data on the effect of 74 tonne traffic, this Master thesis instead focuseson modeling heavy traffic in general in order to be able to draw conclusions on which variablesare significant for a road’s lifetime. The method used is survival analysis where the lifetimeof the road is defined as the time between two maintenance treatments. The model selectedis the semi-parametric ’Cox Proportional Hazard Model’. The model is fitted with data froman open source database called LTPP (Long Term Pavement Performance) which is providedby the National Road and Transport Research Institute (VTI). The result of the modeling ispresented with hazard ratios, which is the relative risk that a road will require maintance atthe next time stamp compared to a reference category. The covariates that turned out to besignificant for a road’s lifetime and thus are included in the model are; lane width, undergroundtype, speed limit, asphalt layer thickness, bearing layer thickness and proportion of heavy traffic. Survival curves estimated by the model are also presented. In addition, a sensitivity analysis ismade by exploring survival curves estimated for different scenarios, with different combinationsof covariate levels.The results is then compared with previous studies on the subject. The most interesting finding isa case study from Finland since Finland allow 76 tonne vehicles since 2013. In the comparison,the model’s significant variables are confirmed, but the significance of precipitation and thenumber of axes for a roads lifetime is also highlighted

The modern electronic financial market is composed of a large amount of actors. With the surge in algorithmic trading some of these actors collectively behave in increasingly complex ways. Historically, academic research related to financial markets has been focused on areas such as asset pricing, portfolio management and financial econometrics. However, the fragmentation of the financial market has given rise to a different set of problems, namely the order allocation problem, as well as smart order routers as a tool to comply with these. In this thesis we consider price discrepancies between order books, trading the same instruments, as a proxy for order routing opportunities. A survival analysis framework for these price differences is developed. Specifically, we consider the two widely used Kaplan-Meier and Cox Proportional Hazards models, as well as the somewhat less known Random Survival Forest model, in order to investigate whether such a framework is effective for predicting the survival times of price differences. The results show that the survival models outperform random models and fixed routing decisions significantly. Thus suggesting that such models could beneficially be incorporated into existing SOR environments. Furthermore, the implementation of order book parameters as covariates in the CPH and RSF models add additional performance. / Den moderna elektroniska marknaden består av ett stort antal aktörer som, till följd av ökningen av algoritmisk handel, beter sig alltmer komplext. Historiskt sett har akademisk forskning inom finans i huvudsak fokuserat på områden som prissättning av tillgångar, portföljförvaltning och finansiell ekonometri. Fragmentering av finansiella marknader har däremot gett upphov till nya sorters problem, däribland orderplaceringsproblemet. Följdaktligen har smart order routers utvecklats som ett verktyg för att tillmötesgå detta problem. I detta examensarbete studerar vi prisskillnader mellan orderböcker som tillhandhåller handel av samma instrument. Dessa prisskillnader representerar möjligheter för order routing. Vi utvecklar ett ramverk inom överlevnadsanalys för dessa prisskillnader. Specifikt används de välkända Kaplan-Meier- och Cox Proportional Hazards-modellerna samt den något mindre kända Random Survival Forest, för att utvärdera om ett sådant ramverk kan användas för att förutspå prisskillnadernas livstider. Våra resultat visar att dessa modeller överträffar slumpmässiga modeller samt deterministiska routingstrategier med stor marginal och antyder därmed att ett sådant ramverk kan integreras i SOR-system. Resultaten visar dessutom att användning av orderboksparametrar som variabler i CPH- och RSF-modellerna ökar prestandan.

Diante da importância do sistema financeiro para a economia de um país, faz-se necessária sua constante fiscalização. Nesse sentido, a identificação de problemas existentes no cenário bancário apresenta-se fundamental, visto que as crises bancárias ocorridas mundialmente ao longo da história mostraram que a falta de credibilidade bancária e a instabilidade do sistema financeiro geram enormes custos financeiros e sociais. Os modelos de previsão de insolvência bancária são capazes de identificar a condição financeira de um banco devido ao valor correspondente da sua probabilidade de insolvência. Dessa forma, o presente trabalho teve como objetivo identificar os principais indicadores característicos da insolvência de bancos privados no Brasil. Para isso, foi utilizada a técnica de análise de sobrevivência em uma amostra de 70 bancos privados no Brasil, sendo 33 bancos insolventes e 37 bancos solventes. Foi possível identificar os principais indicadores financeiros que apresentaram-se significativos para explicar a insolvência de bancos privados no Brasil e analisar a relação existente entre estes indicador e esta probabilidade. O resultado deste trabalho permitiu a realização de importantes constatações para explicar o fenômeno da insolvência de bancos privados no Brasil, bem como, permitiu constatar alguns aspectos característicos de bancos em momentos anteriores à sua insolvência. / The financial system is very important to the economy of a country, than its supervision is necessary. Accordingly, the identification of problems in the banking scenario is fundamental, since the banking crisis occurring worldwide throughout history have shown that and instability of the financial system generates huge financial and social costs. The banking failure prediction models are able to identify the financial condition of a bank based on the value of its probability of insolvency. Thus, this study aimed to identify the main financial ratios that can explain the insolvency of private banks in Brazil. For this, it was used the survival analysis to analize a sample of 70 private banks in Brazil, with 33 solvent banks and 37 insolvent banks. It was possible to identify the key financial indicators that were significantly to explain the bankruptcy of private banks in Brazil and it was possible to examine the relationship between these financial ratios and the probability of bank failure. The result of this work has enabled the achievement of important findings to explain the phenomenon of the bankruptcy of private banks in Brazil, and has seen some characteristic of banks in times prior to its insolvency.

Escalonamento com controle de overdose (EWOC-PH, escalation with overdose control proporcional hazards) é um método bayesiano com controle de overdose que estima a dose máxima tolerada (MTD, maximum tolerated dose) assumindo que o tempo que um paciente leva para apresentar toxicidade segue o modelo de riscos proporcionais. Neste trabalho analisamos quais são as consequências em adotarmos um método que se baseia no modelo de riscos proporcionais quando o tempo até toxicidade segue o modelo de chances de sobrevivência proporcionais. A fim de buscar responder se teríamos uma superestimativa ou uma subestimativa da MTD foram feitas simulações em que consideramos dados de chances de sobrevivência proporcionais e aplicação do método EWOC-PH para analisarmos a MTD. Como uma extensão do método EWOC-PH, propomos o método EWOC-POS que assume que os tempos seguem o modelo de chances de sobrevivência proporcionais. / Escalation with overdose control proportional hazards is a Bayesian method with overdose control that estimates the maximum tolerated dose (MTD) assuming that the time a patient takes to show toxicity follows the proportional hazards model. In this work, we analyse the consequences of adopting a method based on the proportional hazard model when the time until toxicity follows the proportional survival model. In order to seek to answer if we would have an overestimate or an underestimate of MTD, simulations were performed in which we considered proportional odds survival data and application of the EWOC-PH method. As an extension of the EWOC-PH method, we propose the EWOC-POS method which assumes that time until toxicity follows the proportional odds survival model.

Diante da importância do sistema financeiro para a economia de um país, faz-se necessária sua constante fiscalização. Nesse sentido, a identificação de problemas existentes no cenário bancário apresenta-se fundamental, visto que as crises bancárias ocorridas mundialmente ao longo da história mostraram que a falta de credibilidade bancária e a instabilidade do sistema financeiro geram enormes custos financeiros e sociais. Os modelos de previsão de insolvência bancária são capazes de identificar a condição financeira de um banco devido ao valor correspondente da sua probabilidade de insolvência. Dessa forma, o presente trabalho teve como objetivo identificar os principais indicadores característicos da insolvência de bancos privados no Brasil. Para isso, foi utilizada a técnica de análise de sobrevivência em uma amostra de 70 bancos privados no Brasil, sendo 33 bancos insolventes e 37 bancos solventes. Foi possível identificar os principais indicadores financeiros que apresentaram-se significativos para explicar a insolvência de bancos privados no Brasil e analisar a relação existente entre estes indicador e esta probabilidade. O resultado deste trabalho permitiu a realização de importantes constatações para explicar o fenômeno da insolvência de bancos privados no Brasil, bem como, permitiu constatar alguns aspectos característicos de bancos em momentos anteriores à sua insolvência. / The financial system is very important to the economy of a country, than its supervision is necessary. Accordingly, the identification of problems in the banking scenario is fundamental, since the banking crisis occurring worldwide throughout history have shown that and instability of the financial system generates huge financial and social costs. The banking failure prediction models are able to identify the financial condition of a bank based on the value of its probability of insolvency. Thus, this study aimed to identify the main financial ratios that can explain the insolvency of private banks in Brazil. For this, it was used the survival analysis to analize a sample of 70 private banks in Brazil, with 33 solvent banks and 37 insolvent banks. It was possible to identify the key financial indicators that were significantly to explain the bankruptcy of private banks in Brazil and it was possible to examine the relationship between these financial ratios and the probability of bank failure. The result of this work has enabled the achievement of important findings to explain the phenomenon of the bankruptcy of private banks in Brazil, and has seen some characteristic of banks in times prior to its insolvency.

<p>This thesis consists of four papers about the assumption of proportional hazards for the Cox model in survival analysis. </p><p>The <b>first paper </b>compares the hazard ratio estimated from the Cox model to an exact calculation of the geometric average of the hazard ratio when the underlying assumption of proportional hazards is false, i.e. when the hazards are not proportional. The estimates are evaluated in a simulation study.</p><p>The <b>second paper</b> describes and compares six of the most common numerical procedures to check the assumption of proportional hazards for the Cox model. The tests are evaluated in a simulation study.</p><p>Six graphical procedures to check the same assumption of proportional hazards for the Cox model are described and compared in the <b>third paper</b>. A criterion for rejection is derived for each procedure, to make it possible to compare the results of the different methods. The procedures are evaluated in a simulation study.</p><p>In the <b>fourth paper </b>the effects of covariate measurement error on testing the assumption of proportional hazards is investigated. Three of the most common numerical procedures to check the assumption of proportional hazards for the Cox model are evaluated in a simulation study. </p>

This thesis consists of four papers about the assumption of proportional hazards for the Cox model in survival analysis. The <b>first paper </b>compares the hazard ratio estimated from the Cox model to an exact calculation of the geometric average of the hazard ratio when the underlying assumption of proportional hazards is false, i.e. when the hazards are not proportional. The estimates are evaluated in a simulation study. The <b>second paper</b> describes and compares six of the most common numerical procedures to check the assumption of proportional hazards for the Cox model. The tests are evaluated in a simulation study. Six graphical procedures to check the same assumption of proportional hazards for the Cox model are described and compared in the <b>third paper</b>. A criterion for rejection is derived for each procedure, to make it possible to compare the results of the different methods. The procedures are evaluated in a simulation study. In the <b>fourth paper </b>the effects of covariate measurement error on testing the assumption of proportional hazards is investigated. Three of the most common numerical procedures to check the assumption of proportional hazards for the Cox model are evaluated in a simulation study.

The objectives of this study were to measure injuries and impairments directly observed from gags Mycteroperca microlepis caught and released within a large-scale recreational fishery, develop methods that may be used to rapidly assess the condition of reef fish discards, and estimate the total portion of discards in the fishery that suffer latent mortality. Fishery observers were placed on for-hire charter and headboat vessels operating in the Gulf of Mexico from June 2009 through December 2012 to directly observe reef fishes as they were caught by recreational anglers fishing with hook-and-line gear. Fish that were not retained by anglers were inspected and marked with conventional tags prior to release. Fish were released in multiple regions over a large geographic area throughout the year and over multiple years. The majority of recaptured fish were reported by recreational and commercial fishers, and fishing effort fluctuated both spatially and temporally over the course of this study in response to changes in recreational harvest restrictions and the Deepwater Horizon oil spill. Therefore, it could not be assumed that encounter probabilities were equal for all individual tagged fish in the population. Fish size and capture depth when fish were initially caught-and-released also varied among individuals in the study and potentially influenced recapture reporting probabilities. The Cox proportional hazards regression model was used to control for potential covariates on both the occurrence and timing of recapture reporting events so that relative survival among fish released in various conditions could be compared. A total of 3,954 gags were observed in this study, and the majority (77.26%) were released in good condition (condition category 1), defined as fish that immediately submerged without assistance from venting and had not suffered internal injuries from embedded hooks or visible damage to the gills. However, compared to gags caught in shallower depths, a greater proportion of gags caught and released from depths deeper than 30 meters were in fair or poor condition. Relative survival was significantly reduced (alpha (underline)<(/underline)0.05) for gags released in fair and poor condition after controlling for variable mark-recapture reporting rates for different sized discards among regions and across months and years when individual fish were initially captured, tagged and released. Gags released within the recreational fishery in fair and poor condition were 66.4% (95% C.I. 46.9 to 94.0%) and 50.6% (26.2 to 97.8%) as likely to be recaptured, respectively, as gags released in good condition. Overall discard mortality was calculated for gags released in all condition categories at ten meter depth intervals. There was a significant linear increase in estimated mortality from less than 15% (range of uncertainty, 0.1-25.2%) in shallow depths up to 30 meters, to 35.6% (5.6-55.7%) at depths greater than 70 meters (p < 0.001, R2 = 0.917). This analysis demonstrated the utility of the proportional hazards regression model for controlling for potential covariates on both the occurrence and timing of recapture events in a large-scale mark-recapture study and for detecting significant differences in the relative survival of fish released in various conditions measured under highly variable conditions within a large-scale fishery.