Building trajectories through clinical data to model disease progression

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Clinical trials are typically conducted over a population within a defined time period in order to illuminate certain characteristics of a health issue or disease process. These cross-sectional studies provide a snapshot of these disease processes over a large number of people but do not allow us to model the temporal nature of disease, which is essential for modeling detailed prognostic predictions. Longitudinal studies, on the other hand, are used to explore how these processes develop over time in a number of people but can be expensive and time-consuming, and many studies only cover a relatively small window within the disease process. This thesis describes the application of intelligent data analysis techniques for extracting information from time series generated by different diseases. The aim of this thesis is to identify intermediate stages in a disease process and sub-categories of the disease exhibiting subtly different symptoms. It explores the use of a bootstrap technique that fits trajectories through the data generating “pseudo time-series”. It addresses issues including: how clinical variables interact as a disease progresses along the trajectories in the data; and how to automatically identify different disease states along these trajectories, as well as the transitions between them. The thesis documents how reliable time-series models can be created from large amounts of historical cross-sectional data and a novel relabling/latent variable approach has enabled the exploration of the temporal nature of disease progression. The proposed algorithms are tested extensively on simulated data and on three real clinical datasets. Finally, a study is carried out to explore whether we can “calibrate” pseudo time-series models with real longitudinal data in order to improve them. Plausible directions for future research are discussed at the end of the thesis

A matter of timing : A modelling-based investigation of the dynamic behaviour of reproductive hormones in girls and women

Hypothalamus-hypofyse-gonade aksen er en del av det kvinnelige endokrine systemet, og regulerer evnen til reproduksjon. Hormoner produsert og utskilt fra tre kjertler (hypotalamus, hypofysen, eggstokkene) påvirker hverandre via tilbakemeldingsinteraksjoner, som er nødvendige for å etablere en regelmessig menstruasjonssyklus hos kvinner. Matematiske modeller som forutsier utviklingen av slike hormonkonsentrasjoner og modning av eggstokkfollikler er nyttige verktøy for å forstå menstruasjonssyklusens dynamiske oppførsel. Slike modeller kan for eksempel hjelpe oss med å undersøke patologiske tilstander som endometriose og polycystisk ovariesyndrom. Videre kan de brukes til systematiske undersøkelser av effekten av medikamenter på det kvinnelige endokrine systemet. Derfor kan vi potensielt bruke slike menstruasjonsyklusmodeller som kliniske beslutningsstøttessystemer. Vi trenger modeller som forutsier hormonkonsentrasjoner sammen med modningen av eggstokkfollikler hos enkeltindivider gjennom påfølgende sykluser. Dette for å kunne simulere hormonelle behandlinger som stimulerer vekst av eggstokkfolliklene (eggstokkstimuleringsprotokoller). Her legger jeg fram et forslag til en matematisk menstruasjonsyklusmodell og viser modellens evne til å forutsi resultatet av eggstokkstimuleringsprotokoller. For å kalibrere denne typen modell trenges individuelle tidsseriedata. Innsamling av slike data er tidskrevende, og forutsetter høy grad av engasjement fra deltakerne i studien. Det er derfor viktig å finne brukbare datatyper som er mindre tid- og ressurskrevende å samle inn, og som likevel kan brukes til modellkalibrering. En type data som er enklere å samle inn er tversnittdata. I denne avhandlingen har jeg utviklet en prosedyre for å bruke tversnittpopulasjonsdata i modellens kalibreringsprosess, og viser hvordan en modell kalibrert med tversnittdata kan brukes til å forutsi individuelle resultater ved oppdatering av en del av modellens parametere. I tillegg til det vitenskapelige bidraget, håper jeg at avhandlingen min skaper oppmerksomhet rundt viktigheten av forskning på kvinners reproduktive helse, og at avhandlingen underbygger verdien av matematiske modeller i forskning på kvinnehelse.The hypothalamic-pituitary-gonadal axis (HPG axis), a part of the human endocrine system, regulates the female reproductive function. Feedback interactions between hormones secreted from the glands forming the HPG axis are essential for establishing a regular menstrual cycle. Mathematical models predicting the time evolution of hormone concentrations and the maturation of ovarian follicles are useful tools for understanding the dynamic behaviour of the menstrual cycle. Such models can, for example, help us to investigate pathological conditions, such as endometriosis or Polycystic Ovary Syndrome. Furthermore, they can be used to systematically study the effects of drugs on the endocrine system. In doing so, menstrual cycle models could potentially be integrated into clinical routines as clinical decision support systems. For the simulation-based investigation of hormonal treatments aiming to stimulate the growth of ovarian follicles (Controlled Ovarian Stimulation (COS)), we need models that predict hormone concentrations and the maturation of ovarian follicles in biological units throughout consecutive cycles. Here, I propose such a mechanistic menstrual cycle model. I also demonstrate its capability to predict the outcome of COS. Individual time series data is usually used to calibrate mechanistic models having clinical implications. Collecting these data, however, is time-consuming and requires a high commitment from study participants. Therefore, integrating different data sets into the model calibration process is of interest. One type of data that is often more feasible to collect than individual time series is cross-sectional data. As part of my thesis, I developed a workflow based on Bayesian updating to integrate cross-sectional data into the model calibration process. I demonstrate the workflow using a mechanistic model describing the time evolution of reproductive hormones during puberty in girls. Exemplary, I show that a model calibrated with cross-sectional data can be used to predict individual dynamics after updating a subset of model parameters. In addition to the scientific contributions of this thesis, I hope that it creates attention for the importance of research in the area of women's reproductive health and underpins the value of mathematical modelling for this field.Doktorgradsavhandlin

Bayesian Multilevel Analysis of Binary Time-Series Cross-Sectional Data in Political Economy

In this dissertation project, I propose a Bayesian generalized linear multilevel model with pth order autoregressive errors: GLMM-AR(p)) for modeling inter-temporal dependence, con-temporary correlation, and heterogeneity of unbalanced binary Time- Series Cross-Sectional data. The model includes two unnested sources of clustering in the unit- and time-dimensions for analyzing heterogeneities and contemporal corre- lation which are salient in the era of globalization. Group-level variations are further explained with unit- and time-specific characteristics. For handling dynamics in pol- itics and political economy, I apply the autoregressive error specification to analyze serial correlation which may not be fully captured by the selected covariates. Two applications on civil war and sovereign default demonstrate how the proposed model controls for multiple potential confounders. It also improves reliability of statistical inferences and helps forecasts by more efficiently using the information in data. The first application focuses on the causal relationship between ethnic minority rule and civil war onset. The GLMM-AR(p) model helps study those background factors which affect the relationship under investigation. The second applied study considers how regime duration affects sovereign default conditional on regime type by putting the national policy-making regarding repaying external debt into the international context. To model the heterogeneous vulnerability or sensitivity of the developing countries to global shocks, I extend the GLMM-AR(p) model to analyze time-specific unit-varying effects

Causal inference for continuous-time processes when covariates are observed only at discrete times

Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumptions that guarantee the consistency of discrete-time g-estimation. In more general cases, when those assumptions are violated, we propose a controlling-the-future method that performs at least as well as g-estimation in most scenarios and which provides consistent estimation in some cases where g-estimation is severely inconsistent. We apply the methods discussed in this paper to simulated data, as well as to a data set collected following a massive flood in Bangladesh, estimating the effect of diarrhea on children's height. Results from different methods are compared in both simulation and the real application.Comment: Published in at http://dx.doi.org/10.1214/10-AOS830 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adaptive Bayesian Learning with Action and State-Dependent Signal Variance

This manuscript presents an advanced framework for Bayesian learning by incorporating action and state-dependent signal variances into decision-making models. This framework is pivotal in understanding complex data-feedback loops and decision-making processes in various economic systems. Through a series of examples, we demonstrate the versatility of this approach in different contexts, ranging from simple Bayesian updating in stable environments to complex models involving social learning and state-dependent uncertainties. The paper uniquely contributes to the understanding of the nuanced interplay between data, actions, outcomes, and the inherent uncertainty in economic models

Deterministic and probabilistic-based model updating of aging steel bridges

Numerical modeling is a very useful tool in different fields of bridge engineering, such as load-carrying capacity assessment or structural health monitoring. Developing a reliable computational model that accurately represents the actual bridge mechanical behavior entails advanced FEM-based modeling complemented by a comprehensive experimental campaign that provides the necessary supporting information and allows validating simulation outcomes. This paper proposes a unified approach aimed at the experimental characterization and FE model updating of aging steel bridges. It first involves the realization of an extensive experimental campaign aimed at the bridge's geometrical, material, and dynamic behavior characterization. Then, a model calibration framework is developed, where deterministic (optimization) and probabilistic (Bayesian inference) approaches are employed, and techniques such as global variance-based sensitivity analysis and Kriging-based surrogate modeling are further implemented in order to enhance the identification process and reduce the overall computational burden. The methodology has been validated in a historical riveted steel bridge in O Barqueiro, north of Galicia, Spain. The results show a good agreement in the identified model parameter values and a noticeable correlation between numerical and experimental modal properties, with an average relative error in frequencies of 0.34% and 0.44% for the deterministic and probabilistic approaches and an average MAC (Modal Assurance Criterion) ratio of 0.96.Fundación BBVAAgencia Estatal de Investigación | Ref. PRE2019-087331Universidade de Vigo/CISU

A Bayesian Synthesis Approach to Data Fusion Using Augmented Data-Dependent Priors

abstract: The process of combining data is one in which information from disjoint datasets sharing at least a number of common variables is merged. This process is commonly referred to as data fusion, with the main objective of creating a new dataset permitting more flexible analyses than the separate analysis of each individual dataset. Many data fusion methods have been proposed in the literature, although most utilize the frequentist framework. This dissertation investigates a new approach called Bayesian Synthesis in which information obtained from one dataset acts as priors for the next analysis. This process continues sequentially until a single posterior distribution is created using all available data. These informative augmented data-dependent priors provide an extra source of information that may aid in the accuracy of estimation. To examine the performance of the proposed Bayesian Synthesis approach, first, results of simulated data with known population values under a variety of conditions were examined. Next, these results were compared to those from the traditional maximum likelihood approach to data fusion, as well as the data fusion approach analyzed via Bayes. The assessment of parameter recovery based on the proposed Bayesian Synthesis approach was evaluated using four criteria to reflect measures of raw bias, relative bias, accuracy, and efficiency. Subsequently, empirical analyses with real data were conducted. For this purpose, the fusion of real data from five longitudinal studies of mathematics ability varying in their assessment of ability and in the timing of measurement occasions was used. Results from the Bayesian Synthesis and data fusion approaches with combined data using Bayesian and maximum likelihood estimation methods were reported. The results illustrate that Bayesian Synthesis with data driven priors is a highly effective approach, provided that the sample sizes for the fused data are large enough to provide unbiased estimates. Bayesian Synthesis provides another beneficial approach to data fusion that can effectively be used to enhance the validity of conclusions obtained from the merging of data from different studies.Dissertation/ThesisDoctoral Dissertation Psychology 201

The pore geometry of pharmaceutical coatings: statistical modelling, characterization methods and transport prediction

This thesis contains new methods for bridging the gap between the pore geometry of porous materials and experimentally measured functional properties. The focus has been on diffusive transport in pharmaceutical coatings used in controlled drug delivery systems, but the methods are general and can be applied to other porous materials and functional properties. Relatively large datasets are needed to train realistic models connecting the pore geometry and diffusive transport properties of porous materials. 3-D statistical pore models based on microscopy images of the coating material were in this thesis used to generate large sets of pore structures, in which diffusive transport was computed numerically. Characterization measures capturing important features of the pore geometry were developed and used as predictors of diffusive transport rates in multiplicative regression models. The characterization measures have been implemented in a freely available software, MIST.In Paper I, a Gaussian random field based pore model was developed and fitted to microscopy images of the coating material. Due to the large size of the data, the model was formulated using a Gaussian Markov random field approximation, which allows for efficient inference. A new method for solving linear equations with Kronecker matrices which reduced the complexity of the model fitting algorithm considerably was developed. The pore model was found to fit the microscopy images well. In Paper II, characterization measures that have been shown to provide good regression models for diffusive transport rates were developed further and implemented. Multiplicative regression models were fitted to pore structures from the model from Paper I, and the new methods were shown to give improved results. In Papers III and V characterization measures that capture a type of bottleneck effect which was observed in another set of microscopy images of the coating material (Papers III and IV), but which is not captured by existing methods, were invented. Pore structures with this type of bottleneck were generated using 3-D statistical pore models, and the new type of bottleneck was found to be an important determinant of diffusive transport rates when the regression models were fitted to simple pore structures (Paper V)