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 Cox proportional hazards model is a standard tool for modelling the effect of covariates on time to event in the presence of censoring. The appropriateness of this model is conditioned by the validity of the proportional hazards assumption. The assumption is explained in the thesis and methods for its testing are described in detail. The tests are implemented in R, including self-written version of the Lin- Zhang-Davidian test. Their application is illustrated on medical data. The ability of the tests to reveal the violation of the proportional hazards assumption is investigated in a simulation study. The results suggest that the highest power is attained by the newly implemented Lin-Zhang-Davidian test in most cases. In contrast, the weighted version of the Lin-Wei-Ying test was found to have inadequate size for low sample sizes.

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.

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.

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

Philosophiae Doctor - PhD / The HIV/AIDS pandemic has been a torment to the African developmental agenda, especially the Southern African Development Countries (SADC), for the past two decades. The disease and condition tends to affect the productive age groups. Children have also not been spared from the severe effects associated with the disease. The advent of antiretroviral treatment (ART) has brought a great relief to governments and patients in these regions. More people living with HIV/AIDS have experienced a boost in their survival prospects and hence their contribution to national developmental projects. Survival analysis methods are usually used in biostatistics, epidemiological modelling and clinical research to model time to event data. The most interesting aspect of this analysis comes when survival models are used to determine risk factors for the survival of patients undergoing some treatment or living with a certain disease condition. The purpose of this thesis was to determine prognostic risk factors for patients' survival whilst on ART. The study sought to highlight the risk factors that impact the survival time negatively at different survival time points. The study utilized a sample of paediatric and adult datasets from Namibia and Zimbabwe respectively. The paediatric dataset from Katutura hospital (Namibia) comprised of the adolescents and children on ART, whilst the adult dataset from Bulawayo hospital (Zimbabwe) comprised of those patients on ART in the 15 years and above age categories. All datasets used in this thesis were based on retrospective cohorts followed for some period of time. Different methods to reduce errors in parameter estimation were employed to the datasets. The proportional hazards, Bayesian proportional hazards and the censored quantile regression models were utilized in this study. The results from the proportional hazards model show that most of the variables considered were not signifcant overall. The Bayesian proportional hazards model shows us that all the considered factors had different risk profiles at the different quartiles of the survival times. This highlights that by using the proportional hazards models, we only get a fixed constant effect of the risk factors, yet in reality, the effect of risk factors differs at different survival time points. This picture was strongly highlighted by the censored quantile regression model which indicated that some variables were significant in the early periods of initiation whilst they did not significantly affect survival time at any other points in the survival time distribution. The censored quantile regression models clearly demonstrate that there are significant insights gained on the dynamics of how different prognostic risk factors affect patient survival time across the survival time distribution compared to when we use proportional hazards and Bayesian propotional hazards models. However, the advantages of using the proportional hazards framework, due to the estimation of hazard rates as well as it's application in the competing risk framework are still unassailable. The hazard rate estimation under the censored quantile regression framework is an area that is still under development and the computational aspects are yet to be incorporated into the mainstream statistical softwares. This study concludes that, with the current literature and computational support, using both model frameworks to ascertain the dynamic effects of different prognostic risk factors for survival in people living with HIV/AIDS and on ART would give the researchers more insights. These insights will then help public health policy makers to draft relevant targeted policies aimed at improving these patients' survival time on treatment.

Maintenance of medical equipment plays an important role in ensuring the healthcare quality so that the care can be conducted with minimal risk. Preventive maintenance is performed to maintain the equipment in satisfactory operating condition, while corrective maintenance is made when there is an unpredicted maintenance requirement. This study aims to determine what effect preventive maintenance has on corrective maintenance. A correlation analysis, regression analysis and survival analysis are performed on work-order data from 2000-2021. The results obtained indicate that increasing the number of preventive maintenances made to medical equipment will decrease the number of corrective maintenances required for the medical equipment.

Accurate prediction of mortality is an important component of forest growth and yield prediction systems, yet mortality remains one of the least understood components of the system. Whole-stand and individual-tree mortality models were developed for loblolly pine plantations throughout its geographic range in the United States. The model for predicting stand mortality were developed using stand characteristics and biophysical variables. The models were constructed using two modeling approaches. In the first approach, mortality functions for directly predicting tree number reduction were developed using algebraic difference equation method. In the second approach, a two-step modeling strategy was used where a model predicting the probability of tree death occurring over a period was developed in the first step and a function that estimates the reduction in tree number was developed in the second step. Individual-tree mortality models were developed using multilevel logistic regression and survival analysis techniques. Multilevel data structure inherent in permanent sample plots data i.e. measurement occasions nested within trees (e.g., repeated measurements) and trees nested within plots, is often ignored in modeling tree mortality in forestry applications. Multilevel mixed-effects logistic regression takes into account the full hierarchical structure of the data. Multilevel mixed-effects models gave better predictions than the fixed effects model; however, the model fits and predictions were further improved by taking into account the full hierarchical structure of the data. Semiparametric proportional hazards regression was also used to develop model for individual-tree mortality. Shared frailty model, mixed model extension of Cox proportional hazards model, was used to account for unobserved heterogeneity not explained by the observed covariates in the Cox model. / Ph. D.

Survival analysis is an effective tool for conservation studies, since it measure the risk of an event that is important for the survival of populations and preservation of biodiversity. In this thesis three different models for survival analysis are used to estimate the age at breeding between two genetically different populations of brown trout. These populations are an evolutionary enigma, since they apparently coexist in direct competition with each other, which according to ecological theory should not happen. Thus it is of interest if differences between them can be identified. The data consists of brown trouts and has been collected over 20 years. The models are the Cox Proportional Hazards model, the Complementary Log-Log Link model and the Log Logistic Accelerated Failure-Time model. The Cox model were estimated in three different ways due to the nonproportional hazards in the estimates of time to breeding, which gave different interpretations of the same model. All of the models agree that the population B breed at younger ages than the population A, which suggests that the two populations have different reproductive strategies.