This thesis develops novel statistical methodology for estimating the incidence and the prevalence of Human Immunodeficiency Virus (HIV) using routinely collected surveillance data. The robust estimation of HIV incidence and prevalence is crucial to correctly evaluate the effectiveness of targeted public health interventions and to accurately predict the HIV- related burden imposed on healthcare services. Bayesian CD4-based multi-state back-calculation methods are a key tool for monitoring the HIV epidemic, providing estimates of HIV incidence and diagnosis rates by disentangling their competing contribution to the observed surveillance data. Improving the effectiveness of public health interventions, requires targeting specific age-groups at high risk of infection; however, existing methods are limited in that they do not allow for such subgroups to be identified. Therefore the methodological focus of this thesis lies in developing a rigorous statistical framework for age-dependent back-calculation in order to achieve the joint estimation of age-and-time dependent HIV incidence and diagnosis rates. Key challenges we specifically addressed include ensuring the computational feasibility of proposed methods, an issue that has previously hindered extensions of back-calculation, and achieving the joint modelling of time-and-age specific incidence. The suitability of non-parametric bivariate smoothing methods for modelling the age-and-time specific incidence has been investigated in detail within comprehensive simulation studies. Furthermore, in order to enhance the generalisability of the proposed model, we developed back-calculation that can admit surveillance data less rich in detail; these handle surveillance data collected from an intermediate point of the epidemic, or only available on a coarse scale, and concern both age-dependent and age-independent back-calculation. The applicability of the proposed methods is illustrated using routinely collected surveillance data from England and Wales, for the HIV epidemic among men who have sex with men (MSM).

Many genes demonstrate highly dynamic pulsatile expression, with characteristic bursts of activity. Dynamic expression of the human prolactin (hPrl) gene in pituitary cells has previously been investigated identifying key temporal characteristics, influenced by the process of chromatin remodelling. Earlier work on the related pituitary human growth hormone (hGH) proximal promoter (-496/+1bp) indicated that it displayed similar dynamic behaviour. The human GH gene contains an extensive long-distance regulatory sequence, including a locus control region (-14/-32kbp) that has been shown to regulate chromatin remodelling and confer tissue-specificity of hGH expression. In this work I aimed to study dynamic regulation of the hGH gene promoter in detail. Initially I investigated the efficiency of several methods to express the luciferase gene in a 180kb hGH genomic fragment using bacterial artificial chromosome recombineering, to allow the investigation of single cell transcription dynamics. Although a functional recombinant BAC was not finalised during the course of the work, I carried out detailed time course studies using shorter hGH-reporter constructs. Using quantitative microscopy to study live single cells, I compared the dynamic characteristics of a 5kb hPrl promoter fragment with those of -840/+1bp and -3348/+1bp hGH-luciferase promoter-reporter constructs. Whilst previous hPrl analysis utilised a binary mathematical model assuming a simplified two-state (ON/OFF) process of gene transcription, I validated and applied a novel stochastic switch model (SSM), assuming instead that transcription rate can switch between any variable states at any time. Through doing so I observed an asymmetry in transcription rate switching, suggesting an all-or-nothing activation of a single UP-switch, with a greater number of rate decreasing DOWN-switches. The -3348/+1bp construct produced double the number of DOWN-switches, whilst the -840/+1bp construct produced 1.5 DOWN-switches in a 48h period. The cycling of transcriptional activity seen by the shorter construct was modified through the addition of forskolin, activating cAMP signalling. However, significant modification of the transcriptionally inactive refractory period seen with the -3348/+1bp construct (reduced from 3h to 1.9h) required histone modification through application of trichostatin A, a HDAC inhibitor. In conclusion, different promoter elements confer different transcriptional timing and dynamics. A subtler transcriptional modelling, such as used here in the SSM, reveals new insights into the phenomena of transcriptional switching, but the mechanisms involved remain to be determined.

The thesis focuses on consideration of possible ways how to realize multi-state modulators for a laboratory instrument. This instrument will illustrate signals, which partake on generation QAM modulation. The design of the laboratory instrument includes theoretic schemata and the execution of a prototype. There are theoretical facts of multi-state signals and multi-state modulations in this thesis. A simple block diagram of the laboratory instrument is made by the theory of creating quadrature amplitude modulation. For each block there are made several schemata, which are compiled to the global scheme. A printed circuit board and the structure items are made by the aid of the global scheme. The next part is devoted to a software facility for a used microprocessor, which ensures the whole function of the laboratory instrument. The final section deals with measuring, which checks the function of the modulator and the right setting coder’s constellation diagrams.

No / This paper studies the selective maintenance problem for multi-state series systems working in variable loading conditions in the next mission. In the mission, a component's degradation depends on its current state and the load applied on it. A load-dependent degradation model is proposed for multi-state components operating in variable loading conditions. This model is inspired by the load-sharing model where many components share a common workload and the failure rate of a component depends on the state of other components. A Monte-Carlo simulation method is presented to simulate the multi-state component's degradation and to evaluate the system reliability. The final objective is to determine the best selective maintenance strategy to maximize the expected system reliability in the next mission within available resources. An illustrative example, reliability estimation results, and analysis of optimal selective maintenance scenarios for different levels of budget limitation are provided.

No / This paper studies the selective maintenance problem for multi-state systems with structural dependence. Each component can be in one of multiple working levels and several maintenance actions are possible to a component in a maintenance break. The components structurally form multiple hierarchical levels and dependence groups. A directed graph is used to represent the precedence relations of components in the system. A selective maintenance optimization model is developed to maximize the system reliability in the next mission under time and cost constraints. A backward search algorithm is used to determine the assembly sequence for a selective maintenance scenario. The maintenance model helps maintenance managers in determining the best combination of maintenance activities to maximize the probability of successfully completing the next mission. Examples showing the use of the proposed method are presented.

Yes / This paper presents a study on selective maintenance for multi-state series-parallel systems with economically dependent components. In the selective maintenance problem, the maintenance manager has to decide which components should receive maintenance activities within a finite break between missions. All the system reliabilities in the next operating mission, the available budget and the maintenance time for each component from its current state to a higher state are taken into account in the optimization models. In addition, the components in series-parallel systems are considered to be economically dependent. Time and cost savings will be achieved when several components are simultaneously repaired in a selective maintenance strategy. As the number of repaired components increases, the saved time and cost will also increase due to the share of setting up between components and another additional reduction amount resulting from the repair of multiple identical components. Different optimization models are derived to find the best maintenance strategy for multi-state series-parallel systems. A genetic algorithm is used to solve the optimization models. The decision makers may select different components to be repaired to different working states based on the maintenance objective, resource availabilities and how dependent the repair time and cost of each component are. © 2013 Elsevier Ltd. All rights reserved. / Natural Sciences and Engineering Research Council of Canada (NSERC) and Vietnam International Education Development (VIED)

The diploma project is focused on investigating the reliability of multi-state technical systems. A summary of the basic conception of renewal theory and stochastic processes is given in this paper. The possibility of solving multi-state systems reliability by using Markov models or simulation is shown. The software Reliab. S. M. S. O. 1.0 was created for solving non-homogeneous series, parallel, series-parallel and parallel-series systems. Outputs of this software are described in chapter 10. This work also contains $\beta$-factor method and theory of common-cause failures. The diploma project was supported by project from MSMT of the Czech Republic no. 1M06047 "Centre for Quality and Reliability of Production" and by grant from Grant Agency of the Czech Republic (Czech Science Foundation) reg. no. 103/08/1658 "Advanced optimum design of composed concrete structures".

The typical research of Alzheimer's disease includes a series of cognitive states. Multi-state models are often used to describe the history of disease evolvement. Competing risks models are a sub-category of multi-state models with one starting state and several absorbing states. Analyses for competing risks data in medical papers frequently assume independent risks and evaluate covariate effects on these events by modeling distinct proportional hazards regression models for each event. Jeong and Fine (2007) proposed a parametric proportional sub-distribution hazard (SH) model for cumulative incidence functions (CIF) without assumptions about the dependence among the risks. We modified their model to assure that the sum of the underlying CIFs never exceeds one, by assuming a proportional SH model for dementia only in the Nun study. To accommodate left censored data, we computed non-parametric MLE of CIF based on Expectation-Maximization algorithm. Our proposed parametric model was applied to the Nun Study to investigate the effect of genetics and education on the occurrence of dementia. After including left censored dementia subjects, the incidence rate of dementia becomes larger than that of death for age < 90, education becomes significant factor for incidence of dementia and standard errors for estimates are smaller. Multi-state Markov model is often used to analyze the evolution of cognitive states by assuming time independent transition intensities. We consider both constant and duration time dependent transition intensities in BRAiNS data, leading to a mixture of Markov and semi-Markov processes. The joint probability of observing a sequence of same state until transition in a semi-Markov process was expressed as a product of the overall transition probability and survival probability, which were simultaneously modeled. Such modeling leads to different interpretations in BRAiNS study, i.e., family history, APOE4, and sex by head injury interaction are significant factors for transition intensities in traditional Markov model. While in our semi-Markov model, these factors are significant in predicting the overall transition probabilities, but none of these factors are significant for duration time distribution.

Multi-state models are often used to evaluate the effect of death as a competing event to the development of dementia in a longitudinal study of the cognitive status of elderly subjects. In this dissertation, both multi-state Markov model and semi-Markov model are used to characterize the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient, cognitive states and death as a competing risk. Firstly, a multi-state Markov model with three transient states: intact cognition, mild cognitive impairment (M.C.I.) and global impairment (G.I.) and one absorbing state: dementia is used to model the cognitive panel data. A Weibull model and a Cox proportional hazards (Cox PH) model are used to fit the time to death based on age at entry and the APOE4 status. A shared random effect correlates this survival time with the transition model. Secondly, we further apply a Semi-Markov process in which we assume that the wait- ing times are Weibull distributed except for transitions from the baseline state, which are exponentially distributed and we assume no additional changes in cognition occur between two assessments. We implement a quasi-Monte Carlo (QMC) method to calculate the higher order integration needed for the likelihood based estimation. At the end of this dissertation we extend a non-parametric “local EM algorithm” to obtain a smooth estimator of the cause-specific hazard function (CSH) in the presence of competing risk. All the proposed methods are justified by simulation studies and applications to the Nun Study data, a longitudinal study of late life cognition in a cohort of 461 subjects.

The research on multi-state Markov transition model is motivated by the nature of the longitudinal data from the Nun Study (Snowdon, 1997), and similar information on the BRAiNS cohort (Salazar, 2004). Our goal is to develop a flexible methodology for handling the categorical longitudinal responses and competing risks time-to-event that characterizes the features of the data for research on dementia. To do so, we treat the survival from death as a continuous variable rather than defining death as a competing absorbing state to dementia. We assume that within each subject the survival component and the Markov process are linked by a shared latent random effect, and moreover, these two pieces are conditionally independent given the random effect and their corresponding predictor variables. The problem of the dependence among observations made on the same subject (repeated measurements) is addressed by assuming a first order Markovian dependence structure. A closed-form expression for the individual and thus overall conditional marginal likelihood function is derived, which we can evaluate numerically to produce the maximum likelihood estimates for the unknown parameters. This method can be implemented using standard statistical software such as SAS Proc Nlmixed©. We present the results of simulation studies designed to show how the model’s ability to accurately estimate the parameters can be affected by the distributional form of the survival term. Then we focus on addressing the problem by accommodating the residual life time of the subject’s confounding in the nonhomogeneous chain. The convergence status of the chain is examined and the formulation of the absorption statistics is derived. We propose using the Delta method to estimate the variance terms for construction of confidence intervals. The results are illustrated with applications to the Nun Study data in details.