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.

Orientador: Djalma de Carvalho Moreira Filho / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Ciências Médicas / Made available in DSpace on 2018-08-26T22:55:22Z (GMT). No. of bitstreams: 1 Ferraz_RosemeiredeOlanda_D.pdf: 2711370 bytes, checksum: b4966f4c4ea3b88daffa54c0576bd307 (MD5) Previous issue date: 2015 / Resumo: O objetivo deste estudo é identificar os fatores associados ao tempo de sobrevida do câncer de mama, como idade, estadiamento e extensão do tumor, utilizando modelos de riscos proporcionais de Cox e de riscos competitivos de Fine-Gray. E também propor um modelo de regressão paramétrico para ajustar o tempo de sobrevida na presença dos riscos competitivos. É um estudo de coorte retrospectivo de base-populacional referente a 524 mulheres diagnosticadas com câncer de mama no período de 1993 a 1995, acompanhadas até 2011, residentes no município de Campinas/SP. Um ponto de corte para a variável contínua da idade foi escolhido utilizando-se modelos de Cox. Nos ajustes de modelos simples e múltiplo de Fine-Gray e de Cox, a idade não foi significativa quando o óbito por câncer de mama foi o evento de interesse. As curvas de sobrevivências estimadas por Kaplan-Meier evidenciaram diferenças expressivas nas probabilidades comparando-se os óbitos por câncer de mama e por riscos competitivos. As curvas de sobrevida por câncer de mama não apresentaram diferenças significativas quando comparadas as categorias de idades, segundo teste de log rank. Os modelos de Fine-Gray e Cox identificaram praticamente as mesmas covariáveis influenciando no tempo de sobrevida para ambos eventos de interesse, óbitos por câncer de mama e óbitos por riscos competitivos. Foram comparados os modelos exponencial, de Weibull e lognormal com o modelo gama generalizada e conclui-se que o modelo de regressão de Weibull foi o mais adequado para ajustar o tempo de sobrevida na presença dos riscos competitivos, conforme resultados dos testes de razões de verossimilhanças / Abstract: The aim of this study is to identify associated factors to time failure survival of breast cancer such as age, stage and extent of the tumor using Cox's proportional hazards and Fine-Gray competing risks models. It is a retrospective cohort study of population-based concerning to 524 women diagnosed with breast cancer in the period 1993-1995, followed until 2011, living in the city of Campinas, São Paulo State, Brazil. The cutoff age variable has been defined using Cox models. In the settings of simple and multiple models of Fine-Gray and Cox age was not significant when the death from breast cancer was the outcome of interest. The survival curves estimated by Kaplan-Meier showed significant differences in the odds comparing the deaths from breast cancer and competing risks. The survival curves for breast cancer showed no significant differences when comparing age groups, according to the logrank test. The Fine-Gray and Cox models identified the same covariates influencing the survival time for both events of interest: deaths from breast cancer and deaths from competing risks. The exponential, Weibull and lognormal regression models were compared with generalized gamma model and it is concluded that the Weibull regression model was the most appropriate to adjust the survival time in the presence of competing risks, according to results of the ratio likelihood tests / Doutorado / Epidemiologia / Doutora em Saúde Coletiva

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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.

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.

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.

Introdução: Os múltiplos e interativos efeitos protetores do aleitamento materno exclusivo (AME) na saúde e sobrevivência infantil justificam as recomendações universais para promover sua prática. Poucos são os estudos que avaliam a tendência do padrão do AME entre países. Objetivo: Analisar a mudança temporal do AME em cinco países da América Latina e Caribe (ALC) comparando dados das décadas de 1990 e 2000. Métodos: A dissertação é composta por um manuscrito, que avaliou dados de crianças de 0 a 6 meses incluídas nas amostras das pesquisas Demographic Health Survey conduzidas em Brasil, Colômbia, Haiti, Peru e República Dominicana. Foram estimadas as prevalências do AME e suas taxas anuais de variação ponderada, segundo país e ano de inquérito. A duração do AME foi estimada usando a análise de sobrevida de Kaplan-Meier, considerando a idade atual da criança como o tempo de sobrevida e o AME como variável binária, referente à situação da prática no momento da entrevista. As curvas de sobrevivência foram construídas por país, em cada década, e a comparação entre elas usou o teste log-rank. A mediana do tempo de amamentação foi calculada para cada variável independente e a relação entre essas variáveis e o desmame até os seis meses foi analisada pela técnica de regressão de Cox com modelo múltiplo. Resultados: A prevalência de AME aumentou em quatro dos cinco países estudados, com incremento ao ano mais marcante na Colômbia (11 por cento ) e no Haiti (17 por cento ). A duração mediana apresentou duas tendências de evolução: aumento com equidade na Colômbia e no Haiti, e estagnação com distribuição desigual entre os subgrupos populacionais da última década no Brasil, Peru e República Dominicana. No modelo múltiplo de regressão, variáveis de demografia e do perfil de uso dos serviços de saúde associaram-se à duração do AME. A residência em área rural foi a variável reiteradamente associada, de forma negativa no Brasil (HR=1,68; IC 95 por cento :1,06-2,67) e na Colômbia (HR=1,39; IC 95 por cento :1,03-1,87), enquanto que positivamente no Peru (HR=0,40; IC 95 por cento :0,19-0,83). Conclusão: O balanço da tendência do AME na ALC é positivo, embora não uniforme ao longo das duas décadas analisadas. Os achados sinalizam a necessidade de intervenções para a promoção do AME que levem em consideração a localização geográfica das famílias e a qualidade prestada nos serviços de saúde / Introduction: Multiple and interactive protective effects of exclusive breastfeeding (EBF) in health and child survival justify recommendations for promoting universal practice. There are few studies that assess the tendency of the pattern of EBF between countries. Objective: To analyze the temporal change of the AME in five countries in Latin America and Caribbean (LAC) comparing data from 1990 and 2000 decades. Methods: The dissertation consists of a manuscript, which evaluated data from children aged 0 to 6 months in the samples of the Demographic Health Survey conducted research in Brazil, Colombia, Haiti, Peru and the Dominican Republic. Were estimated the prevalence of exclusive breastfeeding and its weighted annual rates of change, according to country and survey year. The duration of EBF was estimated using survival analysis Kaplan-Meier method, considering the current age of the child as the survival time and EBF as binary variable, concerning the state of practice at the time of the interview. The survival curves were constructed for each country, in every decade, and the comparison between them used the log-rank test. The median duration of breastfeeding was calculated for each independent variable and the relationship between these variables and weaning at six months was analyzed using Cox regression model. Results: The prevalence of EBF increased in four of the five countries studied, increasing the most remarkable years in Colombia (II per cent ) and Haiti (17 per cent ). The median duration of evolution showed two trends: growth with equity in Colombia and Haiti, and stagnation with unequal distribution among the population subgroups of the last decade in Brazil, Peru and the Dominican Republic. In the multiple model of regression variables and the demographic profile of use of health services were associated with duration of EBF. The residence in a rural area was the variable consistently associated negatively in Brazil (HR = 1.68, CI 95 per cent : 1,06-2,67) and Colombia (HR = 1.39, CI 95 per cent : 1,03-1,87), while positively in Peru (HR = 0.40, CI 95 per cent : 0,19-0,83). Conclusion: The balance of the trend of EBF in LAC is positive, though not uniform throughout the two decades analyzed. The findings suggest the need for interventions for the promotion of exclusive breastfeeding taking into account the geographical location of families and provided quality health services

O modelo semiparamétrico de Cox é frequentemente utilizado na modelagem de dados de sobrevivência, pois é um modelo muito flexível e permite avaliar o efeito das covariáveis sobre a taxa de falha. Uma das principais vantagens é a fácil interpretação, de modo que a razão de riscos de dois indivíduos não varia ao longo do tempo. No entanto, em algumas situações a proporcionalidade dos riscos para uma dada covariável pode não ser válida e, este caso, uma abordagem que não dependa de tal suposição é necessária. Nesta tese, propomos um modelo tipo Cox em que o efeito da covariável e a função de risco basal são representadas via bases de Fourier e ondaletas de Haar clássicas e deformadas. Propomos também um procedimento de predição da função de sobrevivência para um paciente específico. Estudos de simulações e aplicações a dados reais sugerem que nosso método pode ser uma ferramenta valiosa em situações práticas em que o efeito da covariável é dependente do tempo. Por meio destes estudos, fazemos comparações entre as duas abordagens propostas, e comparações com outra já conhecida na literatura, onde verificamos resultados satisfatórios. / The semiparametric Cox model is often considered when modeling survival data. It is very flexible, allowing for the evaluation of covariates effects. One of its main advantages is the easy of interpretation, as long as the rate of the hazards for two individuals does not vary over time. However, this proportionality of the hazards may not be true in some practical situations and, in this case, an approach not relying on such assumption is needed. In this thesis we propose a Cox-type model that allows for time-varying covariate effects, for which the baseline hazard is based on Fourier series and wavelets on a time-frequency representation. We derive a prediction method for the survival of future patients with any specific set of covariates. Simulations and an application to a real data set suggest that our method may be a valuable tool to model data in practical situations where covariate effects vary over time. Through these studies, we make comparisons between the two approaches proposed here and comparisons with other already known in the literature, where we verify satisfactory results.