Hierarchical entry of variables was carried out using significant variables (p < 0.20) in the univariate analysis (Figure 1). To identify the in- dependent effect of transplant explanatory vari- ables, Cox’s multivariate **model** of **proportional** risks was used (**hazard** ratio – HR). Firstly, **model** 1 was adjusted with the individual variables; then, the contextual variables of the dialysis unit were included in **model** 2; and lastly, the contextual variables of the patient’s city of residence. In this last adjusted **model** the random effect or fragility of the city’s HDI was included 27 . The inclusion of this random effect was carried out under the assumption that patients who reside in the same city are exposed to similar health care conditions and public policies. Gamma probability distri-

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Chapter 2 starts with an overview of the major project in which this thesis is included. The covariates and the response variable are also presented. Afterwards, we focus on theoretical issues about the survival analysis. More precisely, it describeds the basic **Cox** regression **model**. A brief review of the usual procedures to evaluate the **proportional** hazards assumption of the **Cox** regression **model** is provided. A summary of the most common residuals used in this context is also presented. The chapter ends with one of the newer areas of application of survival analysis: the use of the **Cox** regression **model** for describing multiple events per subject. It reviews three common models to accommodate the feature of the data sets: Andersen-Gill **model**, Wei-Lin-Weissfeld **model** and Prentice-Williams-Peterson **model**. In the present study, it applied the Prentice-Williams-Peterson **model** to describe mammogams’ dynamics. Therefore, it also provideds the **hazard** function and the partial likelihood function for modelling the delay between consecutive mammogams.

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variables, including tHcy, folate, vitamin B12, vitamin B6 and hs-CRP. Hence, geometric means with 95% confidence intervals (CIs) are given for these variables. Quantitative data were assessed using the Student’s t-test, or by ANOVA with Tukey’s post-hoc test when appropriate. Associations between qualitative variables were analyzed with the x 2 test. Correlations between quantitative variables were assessed using Pearson’s correlation test. Significant associations between tHcy levels and other continuous or categorical variables, were assessed by multiple regression models estimating R 2 and standardized b-coefficients. Categorical vari- ables were used after transformation into binary variables (i.e. for MTHFR 677CRT polymorphism we considered homozygosity versus non-homozygosity for the T allele). Hyperhomocysteinemia (HHcy) was defined by tHcy levels higher than the 90 th percentile of population’s distribution, i.e. $25.2 mmol/l. Survival was assessed by the Kaplan-Meier method (log-rank statistic) and **Cox** regression. Kaplan-Meier methods were used for survival plots. Multivariate **Cox** **proportional** hazards analyses were performed considering sex, age, other tHcy determinants (MTHFR genotype, B-vitamin levels, GFR), and all predictors of mortality at univariate analyses, including drug therapy at discharge. Final models were obtained by a backward stepwise logistic regression approach, with P = 0.10 as the critical value for entering/excluding variables in the **model**. **Hazard** ratios (HRs) and 95% CIs are reported with two-tailed probability values. A P value less than 0.05 was used to indicate statistical significance.

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A potential extension of the proposed shrinkage method is the development of covariate selection. This is clearly an important issue in microarrays in which the focus is to select genes that achieve good predictive power. If the gene selection is the main focus, we find the Lasso method offers an elegant solution since it gives an automatic way of selecting genes. In fact, the Lasso shows excellent performance when the signal is sparse, as shown in our simulation studies (Table 1). However, in the presence of a large number of informative genes (less sparse cases), the performance of the Lasso is less reliable since it tends to select only a few genes among them and often results in the null **model** with no prediction power (Table 2). A large number of informative genes are also encountered in the lymphoma data reported in Matsui [16], where the number of genes in the optimal set is t = 75 or 85. Matusi [16] suggests a gene filtering procedure that chooses the top t genes in terms of univariate **Cox** analyses, where t is the threshold that leads to the best predictive power in cross validation. Although this methodology is computationally simple, the top t genes are based on univariate significance only. Hence, it is interesting to extend the gene filtering approach to take into account the combined, multivariate predictive information of genes using the proposed shrinkage method. We will leave this problem to a future research topic.

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Biomarker associations with all-cause mortality in the Estonian Biobank were replicated in the FINRISK validation cohort. **Cox** regression models were evaluated during the first 5 y of follow-up in the FINRISK study in order to match the follow-up time in the Estonian Biobank cohort. The same set of adjustment factors was used as for the discovery cohort (see above). The incremental predictive value of the four circulating biomarkers was tested in the FINRISK validation cohort by comparing a risk prediction score composed of conventional risk factors (**Model** B) to a risk prediction score extended with the four biomarkers. The risk prediction scores for 5-y mortality in the FINRISK study were calculated based on the regression coefficients derived from the Estonian Biobank cohort in the age range 25–74 y (Table 2). Discrimination was assessed by C-statistics [17] and integrated discrimination improvement (IDI) accounting for censoring [18]. Net reclassification improvement (NRI) was assessed as a con- tinuous measure [18], and by assigning participants to one of four categories (,1.25%, 1.25%–2.5%, 2.5%–5%, .5%) according to their 5-y risk of death based on the reference **model** and the biomarker **model** [19]. IDI denotes the average increase in risk estimates for persons who died during follow-up plus the average decrease in risk estimates among persons who did not die [18]. In Figure 2. Identification of circulating biomarkers associated with the risk of all-cause mortality in the Estonian Biobank cohort. Candidate biomarkers were included in a stepwise manner into a multivariate **Cox** **model** for all-cause mortality adjusted for sex and using age as the time scale. Each biomarker is plotted against the negative log 10 of the corresponding p-value. Numbers indicate HR [95% confidence interval] per

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Meanwhile, for the last few decades, the maintenance actions for systems have become more and more complex. For the operation of complex system as a multi-component system, it is not any more enough to **model** the system as a single-component system. Meanwhile, it is not anymore enough to just pay attention to just one single important sub-system without concern for the whole system. Take the generating unit for example, it can be important and cost-efficient to deal with maintenance policy for the whole unit instead of independent subcomponents. One reason is that the systems consist of many components which depend on each other with dependences. For the multi-component system, there may exist three kinds of dependences among the components: stochastic, structure, economic dependences [10]. Interactions between components complicate the modelling and optimization of maintenance. Meanwhile, interactions also offer the opportunity to group maintenance which may save costs. As a result, it follows that maintenance optimization is a big challenge and it is not surprising that many scholars have studied the maintenance optimization problems for multi-component systems [10-12]. In this research, more attentions would be paid to the multi-component system with economic dependence among the components [12]. Economic dependence means that performing maintenance on several subsystems jointly costs less money and/or time than on each subsystem separately [13]. Therefore, there often exist potential cost savings by implementing an opportunistic maintenance policy [11, 14, 15]. Opportunistic maintenance basically refers to the

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melhor nos pacientes com ES (o padrão histológico de PINE fibrótica) e expressão de **COX**-2 > 2,25% (mediana da sobrevida: 70,75 meses) do que naqueles com FPI (o padrão histológico de PIU) e expressão de **COX**-2 < 2,25% (mediana da sobrevida: 46,32 meses; Figura 2). Portanto, codificamos o padrão histológico de PINE fibrótica como uma única variável dummy com valor = 1 e o padrão histológico de PIU com valor = 2. Os resultados da análise multivariada baseada no modelo de regressão de riscos proporcionais de **Cox** são apresentados na Tabela 3. Após termos controlado a idade, os resultados dos testes de função pulmonar, o padrão histológico de PIU e o padrão histológico de PINE fibrótica, constatamos que apenas duas variáveis se associaram de maneira significativa ao tempo de sobrevida: o padrão histológico de PINE fibrótica e **COX**-2 em septos alveolares (p = 0,02). Uma vez que essas duas variáveis foram contabilizadas, nenhuma das demais se relacionou à sobrevida. A análise multivariada revelou baixo risco de morte para pacientes jovens com VEF 1 /CVF baixa, padrão histológico de PINE fibrótica e **COX**-2 de alto grau em septos alveolares.

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The outline for this paper is as follows. Section 1 introduced the work. Section 2 describes the main assumptions underlying the mortgage valuation **model** and presents the stochastic processes followed by corresponding variables, the general partial differential equation and the corresponding options held by the borrower. It develops the commercial mortgage valuation **model** and presents its quasi-closed form solution. Some of the **model** limitations are identified. In section 3, the formulae derived during the course of the work are verified and validated via graphical and numerical analysis. Finally, the conclusion is presented, including suggestions for future developments.

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was identified mainly along the tidal inlet **hazard** area and within the human-occupied portion of the beach, where overwash is expected to occur within 5 years of return period. The developed method considers the main overwash driving forces and proved to identify hazardous areas previously observed in the area. Occasional differences between modelled and observed overwash areas can be attributable to equipment errors, morphology interpreta- tion subjectivity and maladjustments in runup parameterisation. Nevertheless, the method proved to be effective in reproducing the overall Ancão peninsula vulnerability and can be widely applied. Therefore, it is a simple and potentially important tool for coastal management that enables mitigation strategies for occupied coasts and as- sessment of geological and ecological consequences in natural areas.

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performed for each data type (giving the required 50 realisations of the 1-in-10 000 yr event). The annual aggregate EP curves resulting from these **model** runs are shown in Fig. 5, with uncertainty bounds that represent the 5–95 % confidence intervals gen- erated by the financial module. Also plotted are the modelled losses of two observed historical floods (August 1986 and November 2002), produced by driving the hydraulic

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apresentou interação com a Tyr355, aminoácido importante para o metabolismo do substrato da **COX**-2, o ácido araquidônico. As outras interações feitas pelo composto, como as interações π, são importantes para fixação do ligante ao sítio ativo, embora não estejam diretamente ligadas com a sua seletividade. Os experimentos in vitro e in vivo permitiram confirmar os resultados dos experimentos in silico, uma vez que o ensaio imunoenzimático mostrou que este composto apresenta maior inibição da **COX**-2 em relação à **COX**-1. Ainda, a atividade do composto 5-OCH 3 foi avaliada em modelo de edema de pata induzido por

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changes are not expected. Inspection of Table 5 indicates that 29 of the 32 thematic variables entered into the suscepti- bility models are not expected to change significantly in the considered period. However, land use types (three variables, BOSCO, SA, FRUTT) may change significantly in the pe- riod. In a representative portion of the Collazzone area, com- parison of land-use maps obtained form aerial photographs taken in 1941 (B in Table 1) and aerial photographs taken in 1999, revealed a reduction of about 65% of the forest cov- erage in the 57-year period, in favour chiefly of cultivated land. In the same period, agricultural practices have changed significantly, largely aided by new mechanical equipments. In the central Apennines, areas recently deforested for agri- cultural purposes are generally more prone to shallow land- slides. If this will be the case for the Collazzone area, some of the environmental variables considered in the susceptibil- ity **model** will change, possibly hampering the validity of the **model**, and new variables describing land use change should be considered to forecast the location of new slope failures.

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According to Merz et al. (2010), vulnerability is described as the result of the sum of exposure, susceptibility and capacity for response. Birkman et al. (2013) also deined this structure and highlighted the multidimensional, dynamic, complex and broad nature of the concept and components of vulnerability. This is evidenced by the intrinsic character of vulnerability in the composition of the community.Adger (2006) states that these components are translated into the skills of dealing with, recovering from, or resisting **hazard** situ ations, together with an understanding developed by the United Nations for what can be called resilience (UNISDR, 2009). Given this vast quantity of components, ranging from individuals to whole communities, Zhou et al. (2014) justify the lack of uniformity in deining the concept of vulnerability and the dificulty in establishing measurement methods in analyses of different scales.

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• It is obser ved that the proposed classification tree has an accuracy of more than 75% which is more significant than any default **model** consisting of all **hazard** or all non-**hazard** cases. Future research can be done in order to improve the accuracy level of the **model** by including other relevant predictor variables with the existing variables. On the other hand, the accuracy level is much higher (about 88%) in accident cases. On the other hand, this **model** has more prediction error in non- accident cases which is more than 30%. It may be because the **model** predicts the hazardous conditions based on the traffic performance indicators while the driver related characteristics for example, alertness and attention which cannot be observed so easily may have avoided the accidents from happening. To improve the accuracy in non-accident cases, fuzzy logic can be implemented in future research. It can be said that the classification **model** can predict accident cases more correctly than that of non-accident cases.

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Using Brazil, 2015 as the origin (Figs. 1A and 1C), the **model** appeared to crudely capture the risk of importation (AUC = 0.84 (95% CI [0.69–1.00])). Maximum likelihood estimate of the constant parameter k was 0.044 (95% CI [0.031–0.059]). Sensitivity and specificity were estimated at 77.5% (95% CI [64.6–90.4]) and 85.9% (95% CI [80.3–91.5]), respectively. Figure 2 shows the global distribution of the risk of importation. High risks of importation are identified in South America and the western part of European countries. Among the top 30 countries predicted at high risk of ZIKV importation in the end of 2016 (Fig. 3), 18 countries (60%) had already imported ZIKV before week 46.

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RESULTS: The total number of patients with and without a depressive disorder was 44,812. The incidence risk ratio (IRR) between these 2 cohorts indicated that depressive disorder patients had a higher risk of developing a subsequent vertebral fracture (IRR=1.41, 95% confidence interval [CI]=1.26–1.57, po0.001). In the multivariate analysis, the depressive disorder cohort showed a higher risk of vertebral fracture than the comparison cohort (adjusted **hazard** ratio=1.24, 95% CI=1.11–1.38, po0.001). Being older than 50 years, having a lower monthly income, and having hypertension, diabetes mellitus, cerebrovascular disease, chronic obstructive pulmonary disease, autoimmune disease, or osteoporosis were considered predictive factors for vertebral fracture in patients with depressive disorders.

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(PGE 2 ) production as an index of leukocyte **COX**-2 expression for bacterial endotoxins. Blain H et al. evaluated twenty-four healthy 21- to 25-year-old male volunteers performing analyses on whole blood submitting the materi- al to several concentrations of NSAIDs (in vitro) to deter- mine TXB 2 and PGE 2 levels.

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Table 2 shows mortality rates per 1000 person years and **hazard** ratios of mortality according to quartiles of sedentary time. In **model** 3 that included sociodemographic factors, lifestyle factors, multiple morbidities, mobility limitation, and MVPA, those in the highest quartile of sedentary hours had a 3.3 times increased risk of mortality compared to participants in lowest quartile (95% confidence interval (CI):1.59–6.69). The percent sedentary time was also strongly associated with mortality. Participants in the third quartile (**hazard** ratio (HR):4.05; 95%CI:1.55–10.60) and fourth quartile (HR:5.94; 95%CI:2.49–14.15) of percent sedentary

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