A Model for Liver Homeostasis Using Modified Mean-Reverting Ornstein–Uhlenbeck Process

Short of a liver biopsy, hepatic disease and drug-induced liver injury are diagnosed and classified from clinical findings, especially laboratory results. It was hypothesized that a healthy hepatic dynamic equilibrium might be modelled by an Ornstein–Uhlenbeck (OU) stochastic process, which might lead to more sensitive and specific diagnostic criteria. Using pooled data from healthy volunteers in pharmaceutical clinical trials, this model was applied using maximum likelihood (ML) methods. It was found that the exponent of the autocorrelation function was proportional to the square root of time rather than time itself, as predicted by the OU model. This finding suggests a stronger autocorrelation than expected and may have important implications regarding the use of laboratory testing in clinical diagnosis, in clinical trial design, and in monitoring drug safety. Besides rejecting the OU hypothesis for liver test homeostasis, this paper presents ML estimates for the multivariate Gaussian distribution for healthy adult males. This work forms the basis for a new approach to mathematical modelling to improve both the sensitivity and specificity of clinical measurements over time

Analysis of Models for Epidemiologic and Survival Data

Mortality statistics are useful tools for public-health statisticians, actuaries and policy makers to study health status of populations in communities and to make plans in health care systems. Several statistical models and methods of parameter estimation have been proposed. In this thesis, we review some benchmark mortality models and propose three alternative statistical models for both epidemiologic data and survival data. For epidemiologic data, we propose two statistical models, a Smoothed Segmented Lee-Carter model and a Smoothed Segmented Poisson Log-bilinear model. The models are modifications of the Lee-Carter (1992) model which combine an age segmented Lee-Carter parameterization with spline smoothed period effects within each age segment. With different period effects across age groups, the two models are fitted by maximizing respectively a penalized least squares criterion and a penalized Poisson likelihood. The new methods are applied to the 1971-2006 public-use mortality data sets released by the National Center for Health Statistics (NCHS). Mortality rates for three leading causes of death, heart diseases, cancer and accidents, are studied. For survival data, we propose a phase type model having features of mixtures, multiple stages or hits and a trapping state. Two parameter estimation techniques studied are a direct numerical method and an EM algorithm. Since phase type model parameters are known to be difficult to estimate, we study in detail the performance of our parameter estimation techniques by reference to the Fisher Information matrix. An alternative way to produce a Fisher Information matrix for an EM parameter estimation is also provided. The proposed model and the best available parameter estimation techniques are applied to a large SEER 1992-2002 breast cancer dataset

Stochastic Dynamic Models for Functional Data.

Functional data arise frequently in many fields of biomedical research as sequential observations over time. The observations are generated by an unknown dynamic mechanism. This dynamic process has an unspecified mean function, and the observations can be considered as arising from this mean function plus noise. In this dissertation, we treat this unknown function as a realization or sample path of a stochastic process, using a stochastic dynamic model (SDM). This will enable us to study dynamics of the underlying process, including how the stochastic process and its derivatives evolve over time, both within the observation time (through estimation and inference) and afterwards(through forecasting). We first introduce a new modeling strategy to estimate a smooth function for time series functional data. The proposed models and methods are illustrated on prostate specific antigen (PSA) data, where we use a Gaussian process to model the rate function of PSA and achieve more precise forecasting. We then extend the models to multi-subject functional data and consider the effect of covariates on the rate functions. We finally propose a time-varying stochastic position model, which can approximate the breakpoints in the function. The discretized model is applied to array comparative genomic hybridization (CGH) data analysis. The estimation and inference are conducted using MCMC algorithms with Euler approximation and data augmentation. Simulations and real data analysis demonstrate that our methods outperform several alternative approaches.Ph.D.BiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78804/1/bzhu_1.pd

A Simple Modeling Framework For Prediction In The Human Glucose-Insulin System

In this paper, we build a new, simple, and interpretable mathematical model to describe the human glucose-insulin system. Our ultimate goal is the robust control of the blood glucose (BG) level of individuals to a desired healthy range, by means of adjusting the amount of nutrition and/or external insulin appropriately. By constructing a simple yet flexible model class, with interpretable parameters, this general model can be specialized to work in different settings, such as type 2 diabetes mellitus (T2DM) and intensive care unit (ICU); different choices of appropriate model functions describing uptake of nutrition and removal of glucose differentiate between the models. In both cases, the available data is sparse and collected in clinical settings, major factors that have constrained our model choice to the simple form adopted. The model has the form of a linear stochastic differential equation (SDE) to describe the evolution of the BG level. The model includes a term quantifying glucose removal from the bloodstream through the regulation system of the human body, and another two terms representing the effect of nutrition and externally delivered insulin. The parameters entering the equation must be learned in a patient-specific fashion, leading to personalized models. We present numerical results on patient-specific parameter estimation and future BG level forecasting in T2DM and ICU settings. The resulting model leads to the prediction of the BG level as an expected value accompanied by a band around this value which accounts for uncertainties in the prediction. Such predictions, then, have the potential for use as part of control systems which are robust to model imperfections and noisy data. Finally, a comparison of the predictive capability of the model with two different models specifically built for T2DM and ICU contexts is also performed.Comment: 47 pages, 9 figures, 7 table

1D single-cell migration on microlanes and at interfaces

Cell migration is essential to maintaining the functionality of the human body, for example in immune response. Nonetheless, the ability of cells to move in the body also plays a major role in diseases, such as cancer metastasis. In order to be able to predict how cell migration is affected by environmental cues and to find drugs that allow controlling cell migration, we need a better understanding of the process and methods to quantitatively investigate this. In their natural environment, cells are exposed to many influences from their surrounding. In order to study cell migration independently of those cues or to specifically study certain effects, defined conditions are required in which cell movement can be analysed. With the help of microstructured surfaces, it is possible to get defined environments by controlling surface coatings. By the use of different coatings, which are cell adhesive or cell repellent, it is possible to confine the movement of cells to one-dimensional lanes. Applying scanning time-lapse microscopy, the movement of hundreds of individual cells can be observed in parallel. In this work, we find that the movement of breast cancer cells on lanes can be approximately described with a two-state model where phases of directed and random motion alternate. In addition, the ability of the cells to react to changes in the substrate can be investigated by incorporating barriers consisting of cell-repellent surface coatings. This results in characteristic measures that provide a detailed description of the cell behaviour on lanes and thus enables a multiparameter quantification of cell movement. The adhesion points of the cells to the substrate play an important role for transmission of forces and thus for the locomotion of cells. In order to investigate this factor in more detail, a new micropatterning method was developed that allows producing lanes with steps of changing adhesiveness. On these lanes, one and the same cell can be examined in environments with different adhesiveness. This made it possible to reproduce the existence of a maximum cell velocity for medium adhesiveness at the single-cell level. We show that the velocity of the cells changes twice at the steps–when the front and when back traverses. This, and the maximum in the velocity, can be explained by a simple phenomenological model in which the cell interacts with the substrate at only two points–at the front and the back–and with a coupling between front and back. Furthermore, we show that cells perform relative measurements of adhesiveness at the transitions and strikingly react almost exclusively to a reduction of adhesiveness. These findings are important for guiding cells by environmental cues and for their effects on cell velocity, but they also raise new questions, for instance about how the coupling of the front and back of the cell works at the molecular level. In addition, the multiparameter quantification of cell motility is applied to differentiate cell types and to study the effect of possible anti-migration drugs that could be used in cancer therapy. This method also proved useful for the investigation of the mode of action of micro RNA 200c on cell migration, a candidate for novel forms of gene therapy. In particular, the assay allows recording changes in migration behaviour in a time-resolved manner. Thus, certain points in time can be identified at which changes in the expression of involved proteins are expected. Corresponding correlation studies between gene expression and changes of the phenotype could help to elucidate complex regulatory networks and thus contribute to finding new effective approaches in cancer therapy.Zellmigration ist essentiell um die Funktionalität des menschlichen Körpers aufrecht zu erhalten, zum Beispiel für das Immunsystem. Aber auch bei Krankheiten, wie bei der Metastasierung von Krebs, spielt die Fähigkeit von Zellen sich im Körper Fortzubewegen eine große Rolle. Um das Verhalten von Zellen in Abhängigkeit von Umwelteinflüssen vorhersagen zu können und um Medikamente zu entwickeln, die eine Kontrolle der Zellmigration erlauben, brauchen wir ein besseres Verständnis des Prozesses und Methoden um dies quantitativ untersuchen zu können. In ihrer natürlichen Umgebung sind Zellen vielen Reizen aus ihrer Umgebung ausgesetzt. Um Zellmigration unabhängig davon untersuchen zu können oder um gezielt bestimmte Einflüsse zu studieren, benötigt man definierte Umgebungen in denen die Zellbewegung analysiert werden kann. Mit Hilfe von mikrostrukturierten Oberflächen ist es durch die Kontrolle der Oberflächenbeschichtung möglich definierte Modellsysteme zu schaffen. Durch die Verwendung von verschiedenen Beschichtungen, die es Zellen entweder erlauben daran zu haften oder zellabweisend sind, ist es möglich die Bewegung der Zellen auf eindimensionale Bahnen zu beschränken. Mittels Abrastern durch Zeitraffermikroskopie lässt sich so die Bewegung von hunderten einzelnen Zellen parallel beobachten. In dieser Arbeit wurde festgestellt, dass sich die Bewegung von Brustkrebszellen auf Bahnen näherungsweise mit einem Zweizustandsmodell beschreiben lässt. Dabei wechseln sich Phasen mit gerichteter und zufälliger Bewegung ab. Zusätzlich kann durch den Einbau von Barrieren, bestehend aus zellabweisender Oberflächenbeschichtung, die Fähigkeit der Zellen auf Änderungen im Substrat zu reagieren untersucht werden. Daraus resultieren charakteristische Messgrößen, die das Zellverhalten auf den Bahnen genau beschreiben und somit eine Multiparameterquantifizierung der Zellbewegung ermöglichen. Die Adhäsionspunkte der Zellen zum Substrat spielen eine große Rolle für die Kraftübertragung und damit für das Vorwärtskommen der Zellen. Um diesen Einflussfaktor genauer zu untersuchen, wurde eine neue Mikrostrukturierungsmethode entwickelt, die es erlaubt Bahnen mit sich stufenweise verändernder Adhäsivität herzustellen. Auf diesen Bahnen kann ein und dieselbe Zelle in Umgebungen mit unterschiedlicher Adhäsivität untersucht werden. Damit konnte die Existenz eines Maximums der Zellgeschwindigkeit für mittlere Adhäsivität auf Einzelzellebene reproduziert werden. Es zeigt sich, dass sich die Geschwindigkeit der Zellen an den Stufenübergängen sowohl beim Übergang der Zellvorder- als auch der Rückseite ändert. Dies, und das Maximum der Geschwindigkeit kann mit einem einfachen phänomenologischen Modell erklärt werden, bei dem die Zelle nur an zwei Punkten – hinten und vorne – mit dem Substrat inteagiert, wobei Vorder- und Rückseite gekoppelt sind. Weiterhin zeigt sich, dass Zellen an den Übergängen relative Messungen der Adhäsivität durchführen und vor allem auf eine Verringerung der Adhäsivität reagieren. Diese Erkenntnisse sind von Bedeutung für die Steuerung von Zellen durch Umgebungseinflüsse und deren Einfluss auf die Zellgeschwindigkeit, aber sie werfen auch neue Fragen auf, etwa über die Funktionsweise der Kopplung von Zellvorder- und Rückseite auf molekularer Ebene. Darüber hinaus findet die Multiparameterquantifizierung der Zellbewegung auf Bahnen Anwendung bei der Unterscheidung von verschiedenen Zelltypen und bei der Untersuchung der Wirkung von möglichen migrationshemmenden Medikamenten, die in der Krebstherapie eingesetzt werden könnten. Auch für die Untersuchung der Wirkungsweise von micro RNA 200c auf die Zellbewegung, eines Kandidaten für neuartige Formen der Gentherapie, erwies sich diese Methode als nützlich. Insbesondere ermöglicht sie Änderungen des Migrationsverhaltens auf den Bahnen zeitaufgelöst zu erfassen. Somit können bestimmte Zeitpunkte identifiziert werden, zu denen man Änderungen in der Expression beteiligter Proteine erwartet. Entsprechende Korrelationsstudien, zwischen Genexpression und Änderung des Phänotyps, könnten dabei helfen komplizierte regulatorische Netzwerke aufzuklären und so neue wirkungsvolle Ansätze für die Krebstherapie zu finden

Controlling mitochondrial dynamics: population genetics and networks

Mitochondria form an essential component of nearly all eukaryotic cells, are implicated in numerous diseases and may play important roles in ageing. Mitochondrial populations are dynamic, controlled and heterogeneous, with different types -- both mutant and wildtype -- potentially coexisting in single cells. This thesis will study the dynamics of both mitochondria and their genetic material (mtDNA) to improve our understanding of the role of these dynamics in pathology and ageing. This study suggests, as well as critically evaluates, reasons for the existence of complex continuous mitochondrial networks using coarse-grained mathematical models, underlining a nonlinear relation between functionality and network structure. Understanding the link between morphology and function is important as disruption of the former is directly implicated in cellular dysfunction. We perform experiments in which we measure the influence of mitochondrial fusion and division events on integrated mitochondrial membrane potential, an indicator of functionality, and find evidence for its conservation. The cellular homeostatic control acting on a mitochondrial population is poorly understood; to address this, we study the influence of general feedback control strategies on mutant and wildtype mtDNA dynamics. We introduce a simple linear control mechanism that captures a wide variety of biologically observed dynamics, and study optimal parameterisations through the construction of an energy-based mitochondrial cost function. Not only cellular control, but also gene-therapeutic control of mtDNA is studied, allowing us to investigate optimal treatment strategies to reduce mutant loads. The cellular proportion of mutant mtDNA molecules, known as heteroplasmy, is crucial in mitochondrial disease and we study the influence of cellular mtDNA exchange on heteroplasmy dynamics and mutant expansion during ageing. We find that this exchange of genetic material can induce preferential mutant expansion during ageing (even in the face of selection against mutants) through a stochastically driven increase in cellular mean heteroplasmy levels.Open Acces

Examining current practice for the analysis and reporting of harm outcomes in phase II and III pharmacology trials: exploring methods to facilitate improved detection of adverse drug reactions

Introduction Randomised controlled trials (RCTs) provide data to help establish the harm-profile of drugs but evidence suggests that this data is underutilised and analysis practices are suboptimal. Aims To develop and assess methods for the analysis and presentation of harm outcomes in phase II/III drug trials that can facilitate the detection of adverse drug reactions (ADRs) and enable communication of informative harm-profiles.Methods A systematic review looked at current practice for collection, analysis and reporting of harm outcomes and a scoping review to identify statistical methods proposed for their analysis was undertaken. A survey of clinical trial statisticians measured awareness of methods for the analysis of harm outcomes, barriers to their use and opinions on solutions to improve practice. Alternative strategies for analysis and presentation of harm outcomes were explored. Results The review of current practice confirmed that data on harm outcomes is not being fully utilised, providing evidence of inappropriate and inconsistent practices. The scoping review revealed a broad range of methods for the analysis of both prespecified and emerging harms. The survey confirmed sub-optimal practices and while there was a moderate level of awareness of alternative approaches, use was limited. Guidance and training on more appropriate methods was unanimously supported. Recommendation were devised via consensus to encourage trialists to use visualisations for analysing and reporting harm outcomes. Of the evaluated methods for the analysis of emerging harms none were appropriate in trials ≤5000 participants with some utility in specific scenarios, recommendations for use are provided. Conclusion Clinical trial statisticians agree that there is a need to improve how we analyse and report harm outcomes in RCTs. Efforts to date have focused on prespecified harm outcomes, with little thought given to emerging harms. Several solutions for immediate adoption are proposed but there remains the need for an easy to implement, objective, signal detection approach. Guidelines for best analysis practice that are endorsed by key stakeholders would also enable a more coherent and consistent path for change.Open Acces

Proceedings of the 36th International Workshop Statistical Modelling July 18-22, 2022 - Trieste, Italy

The 36th International Workshop on Statistical Modelling (IWSM) is the first one held in presence after a two year hiatus due to the COVID-19 pandemic. This edition was quite lively, with 60 oral presentations and 53 posters, covering a vast variety of topics. As usual, the extended abstracts of the papers are collected in the IWSM proceedings, but unlike the previous workshops, this year the proceedings will be not printed on paper, but it is only online. The workshop proudly maintains its almost unique feature of scheduling one plenary session for the whole week. This choice has always contributed to the stimulating atmosphere of the conference, combined with its informal character, encouraging the exchange of ideas and cross-fertilization among different areas as a distinguished tradition of the workshop, student participation has been strongly encouraged. This IWSM edition is particularly successful in this respect, as testified by the large number of students included in the program