Incorporating unobserved heterogeneity and multiple event types in survival models : a Bayesian approach

This thesis covers theoretical and practical aspects of Bayesian inference and survival analysis, which is a powerful tool for the analysis of the time until a certain event of interest occurs. This dissertation focuses on non-standard models inspired by features of real datasets that are not accommodated by conventional models. Materials are divided in two parts. The first and more extended part relates to the development of flexible parametric lifetime distributions motivated by the presence of anomalous observations and other forms of unobserved heterogeneity. Chapter 2 presents the use of mixture families of lifetime distributions for this purpose. This idea can be interpreted as the introduction of an observation-specific random effect on the survival distribution. Two families generated via this mechanism are studied in Chapter 3. Covariates are introduced through an accelerated failure times representation, for which the interpretation of the regression coefficients is invariant to the distribution of the random effect. The Bayesian model is completed using reasonable (improper) priors that require a minimum input from practitioners. Under mild conditions, these priors induce a well-defined posterior distribution. In addition, the mixture structure is exploited in order to propose a novel method for outlier detection where anomalous observations are identified via the posterior distribution of the individual-specific random effects. The analysis is illustrated in Chapter 4 using three real medical applications. Chapter 5 comprises the second part of this thesis, which is motivated in the context of university outcomes. The aim of the study is to identify determinants of the length of stay at university and its associated academic outcome for undergraduate students of the Pontificia Universidad Católica de Chile. In this setting, survival times are defined as the time until the end of the enrollment period, which can relate to different reasons - graduation or dropout - that are driven by different processes. Hence, a competing risks model is employed for the analysis. Model uncertainty is handled through Bayesian model averaging, which leads to a better predictive performance than choosing a unique model. The output of this analysis does not account for all features of this complex dataset yet it provides a better understanding of the problem and a starting point for future research. Finally, Chapter 6 summarizes the main findings of this work and suggests future extensions

Líquenes epífitos: una herramienta para estudiar la continuidad ecológica en Isla Mocha, Chile

The purpose of this work was to study the ecological continuity Mocha Island National Reserve, through the knowledge of the richness and frequency of epiphytic lichens in 14 plots distributed at random within the reserve. The tree biomass and upper-stem volume were quantified for to establish correlations that may explain the distribution of epiphytic lichens. It proposes a new index of ecological continuity with cyanolichens (ICEC) for to establish the degree of alteration of this natural ecosystem. The total richness of lichenized fungi was 33 species, 3 of which are new records for Chile: Fissurina triticea; Pyrenula neglecta and Stick, subcaperata. A statistically significant relationship was founded between cyanolichens and upper-stem volume, which could indicate preference of this type of lichens by forest ecosystem with a large upper-stem volume. In basis of the ICEC proposed in this work, Mocha Island National Reserve is defined as an altered ecosystem

Periodic orbit bifurcations and scattering time delay fluctuations

We study fluctuations of the Wigner time delay for open (scattering) systems which exhibit mixed dynamics in the classical limit. It is shown that in the semiclassical limit the time delay fluctuations have a distribution that differs markedly from those which describe fully chaotic (or strongly disordered) systems: their moments have a power law dependence on a semiclassical parameter, with exponents that are rational fractions. These exponents are obtained from bifurcating periodic orbits trapped in the system. They are universal in situations where sufficiently long orbits contribute. We illustrate the influence of bifurcations on the time delay numerically using an open quantum map.Comment: 9 pages, 3 figures, contribution to QMC200

On the classical-quantum correspondence for the scattering dwell time

Using results from the theory of dynamical systems, we derive a general expression for the classical average scattering dwell time, tau_av. Remarkably, tau_av depends only on a ratio of phase space volumes. We further show that, for a wide class of systems, the average classical dwell time is not in correspondence with the energy average of the quantum Wigner time delay.Comment: 5 pages, 1 figur

Consideraciones sobre la hidrogeología de la cuenca del río Almanzora (SE peninsular)

15 páginas, 10 figuras.[ES] Se analizan las características hidrogeológicas de los distintos sistemas acuíferos presentes en la cuenca del río Almanzora, de gran importancia por su posición estratégica en una región con recursos muy limitados, dadas las adversas condiciones climáticas a las que está sometida. Se establece una subdivisión en base a sus características litológicas, estructurales y piezométricas. Se analizan las características geométricas de las diferentes unidades, los principales puntos de agua relacionados con las mismas, su evolución piezométrica y la evaluación de los recursos. También se exponen las características fisicoquímicas de las aguas estudiadas.[EN] The hydrogeological characteristics of the aquifer systems existing in the Almanzora River basin are analyzed. Those aquifers are very important due to the climatological conditions -semiarid region- where water is a basical resource. The systems are identified from the lithologicaL structural and piezometrical characteristics. The geometrical characteristics, the numer of wells and springs, the piezometric evolution and the resources evaluation are established in each hydrogeological unit. Finally, the physical-chemical characteristics of the water are also studied.Esta investigación se realizó en el marco del proyecto «Dinámica del geoecosistema de la cuenca del río Almanzora: evaluación de los procesos de desertificación» (ICONA-CSIC).Peer reviewe

Bayesian survival modelling of university outcomes

Dropouts and delayed graduations are critical issues in higher education systems world wide. A key task in this context is to identify risk factors associated with these events, providing potential targets for mitigating policies. For this, we employ a discrete time competing risks survival model, dealing simultaneously with university outcomes and its associated temporal component. We define survival times as the duration of the student's enrolment at university and possible outcomes as graduation or two types of dropout (voluntary and involuntary), exploring the information recorded at admission time (e.g. educational level of the parents) as potential predictors. Although similar strategies have been previously implemented, we extend the previous methods by handling covariate selection within a Bayesian variable selection framework, where model uncertainty is formally addressed through Bayesian model averaging. Our methodology is general; however, here we focus on undergraduate students enrolled in three selected degree programmes of the Pontificia Universidad Católica de Chile during the period 2000–2011. Our analysis reveals interesting insights, highlighting the main covariates that influence students’ risk of dropout and delayed graduation

Incorporating unobserved heterogeneity in Weibull survival models : a Bayesian approach

Outlying observations and other forms of unobserved heterogeneity can distort inference for survival datasets. The family of Rate Mixtures of Weibull distributions includes subject-level frailty terms as a solution to this issue. With a parametric mixing distribution assigned to the frailties, this family generates flexible hazard functions. Covariates are introduced via an Accelerated Failure Time specification for which the interpretation of the regression coefficients does not depend on the choice of mixing distribution. A weakly informative prior is proposed by combining the structure of the Jeffreys prior with a proper prior on some model parameters. This improper prior is shown to lead to a proper posterior distribution under easily satisfied conditions. By eliciting the proper component of the prior through the coefficient of variation of the survival times, prior information is matched for different mixing distributions. Posterior inference on subject-level frailty terms is exploited as a tool for outlier detection. Finally, the proposed methodology is illustrated using two real datasets, one concerning bone marrow transplants and another on cerebral palsy