Tom Britton

Stochastic epidemic models and their statistical analysis

I: Stochastic Modelling.- 1. Introduction.- 1.1. Stochastic versus deterministic models.- 1.2. A simple epidemic model: The Reed-Frost model.- 1.3. Stochastic epidemics in large communities.- 1.4. History of epidemic modelling.- Exercises.- 2. The standard SIR epidemic model.- 2.1. Definition of the model.- 2.2. The Sellke construction.- 2.3. The Markovian case.- 2.4. Exact results.- Exercises.- 3. Coupling methods.- 3.1. First examples.- 3.2. Definition of coupling.- 3.3. Applications to epidemics.- Exercises.- 4. The threshold limit theorem.- 4.1. The imbedded process.- 4.2. Preliminary convergence results.- 4.3. The casemn/n??> 0 asn? ?.- 4.4. The casemn=mfor alln.- 4.5. Duration of the Markovian SIR epidemic.- Exercises.- 5. Density dependent jump Markov processes.- 5.1. An example: A simple birth and death process.- 5.2. The general model.- 5.3. The Law of Large Numbers.- 5.4. The Central Limit Theorem.- 5.5. Applications to epidemic models.- Exercises.- 6. Multitype epidemics.- 6.1. The standard SIR multitype epidemic model.- 6.2. Large population limits.- 6.3. Household model.- 6.4. Comparing equal and varying susceptibility.- Exercises.- 7. Epidemics and graphs.- 7.1. Random graph interpretation.- 7.2. Constant infectious period.- 7.3. Epidemics and social networks.- 7.4. The two-dimensional lattice.- Exercises.- 8. Models for endemic diseases.- 8.1. The SIR model with demography.- 8.2. The SIS model.- Exercises.- II: Estimation.- 9. Complete observation of the epidemic process.- 9.1. Martingales and log-likelihoods of counting processes.- 9.2. ML-estimation for the standard SIR epidemic.- Exercises.- 10. Estimation in partially observed epidemics.- 10.1. Estimation based on martingale methods.- 10.2. Estimation based on the EM-algorithm.- Exercises.- 11. Markov Chain Monte Carlo methods.- 11.1. Description of the techniques.- 11.2. Important examples.- 11.3. Practical implementation issues.- 11.4. Bayesian inference for epidemics.- Exercises.- 12. Vaccination.- 12.1. Estimating vaccination policies based on one epidemic.- 12.2. Estimating vaccination policies for endemic diseases.- 12.3. Estimation of vaccine efficacy.- Exercises.- References.

Diversification of Neoaves: integration of molecular sequence data and fossils

Patterns of diversification and timing of evolution within Neoaves, which includes almost 95% of all bird species, are virtually unknown. On the other hand, molecular data consistently indicate a Cretaceous origin of many neoavian lineages and the fossil record seems to support an Early Tertiary diversification. Here, we present the first well-resolved molecular phylogeny for Neoaves, together with divergence time estimates calibrated with a large number of stratigraphically and phylogenetically well-documented fossils. Our study defines several well-supported clades within Neoaves. The calibration results suggest that Neoaves, after an initial split from Galloanseres in Mid-Cretaceous, diversified around or soon after the K/T boundary. Our results thus do not contradict palaeontological data and show that there is no solid molecular evidence for an extensive pre-Tertiary radiation of Neoaves.

Reliability of Bayesian Posterior Probabilities and Bootstrap Frequencies in Phylogenetics

Many empirical studies have revealed considerable differences between nonparametric bootstrapping and Bayesian posterior probabilities in terms of the support values for branches, despite claimed predictions about their approximate equivalence. We investigated this problem by simulating data, which were then analyzed by maximum likelihood bootstrapping and Bayesian phylogenetic analysis using identical models and reoptimization of parameter values. We show that Bayesian posterior probabilities are significantly higher than corresponding nonparametric bootstrap frequencies for true clades, but also that erroneous conclusions will be made more often. These errors are strongly accentuated when the models used for analyses are underparameterized. When data are analyzed under the correct model, nonparametric bootstrapping is conservative. Bayesian posterior probabilities are also conservative in this respect, but less so.

Adipocyte Turnover: Relevance to Human Adipose Tissue Morphology

OBJECTIVE Adipose tissue may contain few large adipocytes (hypertrophy) or many small adipocytes (hyperplasia). We investigated factors of putative importance for adipose tissue morphology. RESEARCH DESIGN AND METHODS Subcutaneous adipocyte size and total fat mass were compared in 764 subjects with BMI 18–60 kg/m2. A morphology value was defined as the difference between the measured adipocyte volume and the expected volume given by a curved-line fit for a given body fat mass and was related to insulin values. In 35 subjects, in vivo adipocyte turnover was measured by exploiting incorporation of atmospheric 14C into DNA. RESULTS Occurrence of hyperplasia (negative morphology value) or hypertrophy (positive morphology value) was independent of sex and body weight but correlated with fasting plasma insulin levels and insulin sensitivity, independent of adipocyte volume (β-coefficient = 0.3, P < 0.0001). Total adipocyte number and morphology were negatively related (r = −0.66); i.e., the total adipocyte number was greatest in pronounced hyperplasia and smallest in pronounced hypertrophy. The absolute number of new adipocytes generated each year was 70% lower (P < 0.001) in hypertrophy than in hyperplasia, and individual values for adipocyte generation and morphology were strongly related (r = 0.7, P < 0.001). The relative death rate (∼10% per year) or mean age of adipocytes (∼10 years) was not correlated with morphology. CONCLUSIONS Adipose tissue morphology correlates with insulin measures and is linked to the total adipocyte number independently of sex and body fat level. Low generation rates of adipocytes associate with adipose tissue hypertrophy, whereas high generation rates associate with adipose hyperplasia.

Estimating divergence times in large phylogenetic trees

A new method, PATHd8, for estimating ultrametric trees from trees with edge (branch) lengths proportional to the number of substitutions is proposed. The method allows for an arbitrary number of reference nodes for time calibration, each defined either as absolute age, minimum age, or maximum age, and the tree need not be fully resolved. The method is based on estimating node ages by mean path lengths from the node to the leaves but correcting for deviations from a molecular clock suggested by reference nodes. As opposed to most existing methods allowing substitution rate variation, the new method smoothes substitution rates locally, rather than simultaneously over the whole tree, thus allowing for analysis of very large trees. The performance of PATHd8 is compared with other frequently used methods for estimating divergence times. In analyses of three separate data sets, PATHd8 gives similar divergence times to other methods, the largest difference being between crown group ages, where unconstrained nodes get younger ages when analyzed with PATHd8. Overall, chronograms obtained from other methods appear smoother, whereas PATHd8 preserves more of the heterogeneity seen in the original edge lengths. Divergence times are most evenly spread over the chronograms obtained from the Bayesian implementation and the clock-based Langley-Fitch method, and these two methods produce very similar ages for most nodes. Evaluations of PATHd8 using simulated data suggest that PATHd8 is slightly less precise compared with penalized likelihood, but it gives more sensible answers for extreme data sets. A clear advantage with PATHd8 is that it is more or less instantaneous even with trees having several thousand leaves, whereas other programs often run into problems when analyzing trees with hundreds of leaves. PATHd8 is implemented in freely available software.

Generating Simple Random Graphs with Prescribed Degree Distribution

Let F be a probability distribution with support on the non-negative integers. Four methods for generating a simple undirected graph with (approximate) degree distribution F are described and compared. Two methods are based on the so called configuration model with modifications ensuring a simple graph, one method is an extension of the classical Erdös-Rényi graph where the edge probabilities are random variables, and the last method starts with a directed random graph which is then modified to a simple undirected graph. All methods are shown to give the correct distribution in the limit of large graph size, but under different assumptions on the degree distribution F and also using different order of operations.

Stochastic epidemic models: a survey.

This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.

Lipolysis—Not inflammation, cell death, or lipogenesis—Is involved in adipose tissue loss in cancer cachexia†

Cancer cachexia is an important, negative prognostic marker that has been linked to systemic inflammation and cell death through unclear mechanisms. A key feature of cancer cachexia is loss of white adipose tissue (WAT) because of increased adipocyte lipolysis and possibly reduced lipid synthesis (lipogenesis). In this study, the authors investigated whether alterations in fat cell numbers, lipogenesis, or cytokine and/or leukocyte infiltration could account for some of the functional changes observed in WAT in cancer cachexia.

Statistical studies of infectious disease incidence

Methods for the analysis of data on the incidence of an infectious disease are reviewed, with an emphasis on important objectives that such analyses should address and identifying areas where further work is required. Recent statistical work has adapted methods for constructing estimating functions from martingale theory, methods of data augmentation and methods developed for studying the human immunodeficiency virus–acquired immune deficiency syndrome epidemic. Infectious disease data seem particularly suited to analysis by Markov chain Monte Carlo methods. Epidemic modellers have recently made substantial progress in allowing for community structure and heterogeneity among individuals when studying the requirements for preventing major epidemics. This has stimulated interest in making statistical inferences about crucial parameters from infectious disease data for such community settings.

Phylogenetic dating with confidence intervals using mean path lengths.

The mean path length (MPL) method, a simple method for dating nodes in a phylogenetic tree, is presented. For small trees the age estimates and corresponding confidence intervals, calibrated with fossil data, can be calculated by hand, and for larger trees a computer program gives the results instantaneously (a Pascal program is available upon request). Necessary input data are a rooted phylogenetic tree with edge lengths (internode lengths) approximately corresponding to the number of substitutions between the nodes. Given this, the MPL method produces relative age estimates with confidence intervals for all nodes of the tree. With the age of one or several nodes of the tree being known from reference fossils, the relative age estimates induce absolute age estimates and confidence intervals of the nodes of the tree. The MPL method relies on the assumptions that substitutions occur randomly and independently in different sites in the DNA sequence and that the substitution rates are approximately constant in time, i.e., assuming a molecular clock. A method is presented for identification of the nodes in the tree at which significant deviations from the clock assumption occur, such that dating may be done using different rates in different parts of the tree. The MPL method is illustrated with the Liliales, a group of monocot flowering plants.