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

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.

Many breast cancer diagnoses and second cancers are associated with BRCA gene mutations. Early detection of cancer is necessary to improve health outcomes, particularly with second cancers. Little is known about the influence of risk factors on time to diagnosis of second primary cancers after diagnosis with BRCA-related breast cancer. The purpose of this cohort study was to examine the risk of diagnosis of second primary cancers among women diagnosed with breast cancer after adjusting for BRCA status, age, and ethnicity. The study was guided by the empirical evidence supporting the mechanism of action in the mutation of BRCA leading to the development of cancer. Composite endpoint was used to define second primary cancer occurrences, and Kaplan-Meier survival curves were used to compare the median time-to-event among comparison groups and BRCA gene mutation status. Cox proportional hazards was used to examine the relationships between age at diagnosis, ethnicity, BRCA gene mutation status, and diagnosis of a second primary cancer. The overall median time to event for diagnosis of second primary cancers was 14 years. The hazard ratios for BRCA2 = 1.47, 95% CI [1.03 - 2.11], White = 1.511, 95% CI [1.18 - 1.94], and American Indian/Hawaiian = 1.424, 95% CI [1.12 -1.81] showing positive significant associations between BRCA2 mutation status and risk of diagnosis of second primary colorectal, endometrial, cervical, kidney, thyroid, and bladder cancers. Data on risk factors for development of second cancers would allow for identification of appropriate and timely screening procedures, determining the best course of action for prevention and treatment, and improving quality of life among breast cancer survivors.

Darbo metu buvo išnagrinėta įvairių faktorių (kovariančių) įtaka reumatoidiniu artritu sergančio 531 ligonio mirtingumui. Buvo taikomas vienas iš regresinių išgyvenamumo modelių – Cox’o modelis. Iš minėtos 531 ligonio imties mirę buvo 32 ligoniai. Iš pradžių buvo tiriama ligonių imtis laiko nuo ligos pradžios aspektu. Šiuo atveju prognozuojantys veiksniai buvo amžius, kada liga buvo diagnozuota (AMZDGN), lytis (LYTKOD), gydymas Metotreksatu (GYD_MTX) ir gydymas Azatriopinu/Imuranu (AZA_IMUR). Vėliau, tiriant ligonių mirtingumą kaip amžiaus funkciją, nustatyti svarbiausi lemiantys veiksniai buvo šie: ligonių lytis (LYTKOD) ir gydymas Azatriopinu/Imuranu (AZA_IMUR). Gauti rezultatai, t.y. ligonių išgyvenamumą lemiančios kovariantės (veiksniai), beveik visiškai sutampa su gydytojų nurodytais. Tai dar kartą patvirtina matematinių statistinių modelių, šiuo atveju nagrinėjamo Cox‘o modelio, taikymo realiame gyvenime, svarbą. Kitai duomenų imčiai, t.y. vėžiu sergančių ligonių duomenų aibei, buvo taikomas Persikertančių mirimų intensyvumų (SCE) modelis, t.y. tikrinama Cox‘o modelio adekvatumo duomenims hipotezė. Hipotezė buvo atmesta, nes minėtiems duomenims Cox‘o modelis negalioja. Pagrindinis darbo rezultatas yra šis: gautas kriterijus Cox‘o modelio adekvatumui tikrinti, naudojant nupjautus iš kairės ir cenzūruotus iš dešinės duomenis, sudarytos programos kriterijui realizuoti. Reumatoidinio artrito ligonių duomenų aibei, t.y. nupjautiems iš kairės ir cenzūruotiems iš dešinės... [toliau žr. visą tekstą] / In this work the Cox proportional hazards model was applied to investigate the influence of various factors (covariates) to mortality of rheumatoid arthritis patients of Vilnius. In the first case, the sample of 531 patients was analysed. Analysing survival of patients of the sample as function of time from the beginnig of the disease, the prognostic factors were LYTKOD (the sex of patients), AMZDGN (patients‘ age, when the rheumatoid arthritis was diagnosed), GYD_MTX (treatment with metotrexat) and AZA_IMUR (treatment with Azatriopin/Imuran). When survival was analysed as function of age then the prognostic factor were LYTKOD (the sex of patients) and AZA_IMUR (treatment with Azatriopin/Imuran). The results are almost identical to those, which doctors suggested. This fact confirms the importance of using mathematical statistical models to solve the problems of the real life. In this case, the importance of using the Cox model. On the other hand, Simple cross-effects (SCE) model was aplied for the sample of canser patients. In the case of this model the hypothesis of Cox model fiting for canser patients‘ data was rejected. The most important result of this work is that the criterion of Cox model fitting to left truncated and right censored data was constructed. Also a program of SAS for the criterion was created. The the hypothesis of Cox model fiting for the rheumatoid arthritis patients wasn‘t rejected, because Cox model fit for these data.

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