An illustration of the modelling of cost and efficacy data from a clinical trial

Health care providers, purchasers and policy makers need to make informed decisions regarding the provision of cost-effective care. When a new health care intervention is to be compared with the current standard, an economic evaluation alongside an evaluation of health benefits provides useful information for the decision making process. We consider the information on cost-effectiveness which arises from an individual clinical trial comparing the two interventions. Recent methods for conducting a cost-effectiveness analysis for a clinical trial have focused on the net benefit parameter. The net benefit parameter, a function of costs and health benefits, is positive if the new intervention is cost-effective compared with the standard. In this paper we describe frequentist and Bayesian approaches to cost-effectiveness analysis which have been suggested in the literature and apply them to data from a clinical trial comparing laparoscopic surgery with open mesh surgery for the repair of inguinal hernias. We extend the Bayesian model to allow the total cost to be divided into a number of different components. The advantages and disadvantages of the different approaches are discussed. In January 2001, NICE issued guidance on the type of surgery to be used for inguinal hernia repair. We discuss our example in the light of this information. Copyright © 2003 John Wiley & Sons, Ltd.

Epidemiological risk assessment using linked network and grid based modelling: Phytophthora ramorum and Phytophthora kernoviae in the UK

We developed a stochastic simulation model incorporating most processes likely to be important in the spread of Phytophthora ramorum and similar diseases across the British landscape (covering Rhododendron ponticum in woodland and nurseries, and Vaccinium myrtillus in heathland). The simulation allows for movements of diseased plants within a realistically modelled trade network and long-distance natural dispersal. A series of simulation experiments were run with the model, representing an experiment varying the epidemic pressure and linkage between natural vegetation and horticultural trade, with or without disease spread in commercial trade, and with or without inspections-with-eradication, to give a 2 x 2 x 2 x 2 factorial started at 10 arbitrary locations spread across England. Fifty replicate simulations were made at each set of parameter values. Individual epidemics varied dramatically in size due to stochastic effects throughout the model. Across a range of epidemic pressures, the size of the epidemic was 5-13 times larger when commercial movement of plants was included. A key unknown factor in the system is the area of susceptible habitat outside the nursery system. Inspections, with a probability of detection and efficiency of infected-plant removal of 80% and made at 90-day intervals, reduced the size of epidemics by about 60% across the three sectors with a density of 1% susceptible plants in broadleaf woodland and heathland. Reducing this density to 0.1% largely isolated the trade network, so that inspections reduced the final epidemic size by over 90%, and most epidemics ended without escape into nature. Even in this case, however, major wild epidemics developed in a few percent of cases. Provided the number of new introductions remains low, the current inspection policy will control most epidemics. However, as the rate of introduction increases, it can overwhelm any reasonable inspection regime, largely due to spread prior to detection. (C) 2009 Elsevier B.V. All rights reserved.

Spatiotemporal modelling of CheY complexes in Escherichia coli chemotaxis

The chemotaxis pathway of Escherichia coli is one of the best studied and modelled biological signalling pathways. Here we extend existing modelling approaches by explicitly including a description of the formation and subcellular localization of intermediary complexes in the phosphotransfer pathway. The inclusion of these complexes shows that only about 60% of the total output response regulator (CheY) is uncomplexed at any moment and hence free to interact with its target, the flagellar motor. A clear strength of this model is its ability to predict the experimentally observable subcellular localization of CheY throughout a chemotactic response. We have found good agreement between the model output and experimentally determined CheY localization patterns. (C) 2009 Elsevier Ltd. All rights reserved.

Monthly average temperature modelling

This research is associated with the goal of the horticultural sector of the Colombian southwest, which is to obtain climatic information, specifically, to predict the monthly average temperature in sites where it has not been measured. The data correspond to monthly average temperature, and were recorded in meteorological stations at Valle del Cauca, Colombia, South America. Two components are identified in the data of this research: (1) a component due to the temporal aspects, determined by characteristics of the time series, distribution of the monthly average temperature through the months and the temporal phenomena, which increased (El Nino) and decreased (La Nina) the temperature values, and (2) a component due to the sites, which is determined for the clear differentiation of two populations, the valley and the mountains, which are associated with the pattern of monthly average temperature and with the altitude. Finally, due to the closeness between meteorological stations it is possible to find spatial correlation between data from nearby sites. In the first instance a random coefficient model without spatial covariance structure in the errors is obtained by month and geographical location (mountains and valley, respectively). Models for wet periods in mountains show a normal distribution in the errors; models for the valley and dry periods in mountains do not exhibit a normal pattern in the errors. In models of mountains and wet periods, omni-directional weighted variograms for residuals show spatial continuity. The random coefficient model without spatial covariance structure in the errors and the random coefficient model with spatial covariance structure in the errors are capturing the influence of the El Nino and La Nina phenomena, which indicates that the inclusion of the random part in the model is appropriate. The altitude variable contributes significantly in the models for mountains. In general, the cross-validation process indicates that the random coefficient model with spatial spherical and the random coefficient model with spatial Gaussian are the best models for the wet periods in mountains, and the worst model is the model used by the Colombian Institute for Meteorology, Hydrology and Environmental Studies (IDEAM) to predict temperature.

Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon-known as heterotachy-can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our 'pattern-heterogeneity' mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of 'significance' such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.

Effect of sulphation on the oestrogen agonist activity of the phytoestrogens genistein and daidzein in MCF-7 human breast cancer cells

The phytoestrogens genistein, daidzein and the daidzein metabolite equol have been shown previously to possess oestrogen agonist activity. However, following consumption of soya diets, they are found in the body not only as aglycones but also as metabolites conjugated at their 4'- and 7-hydroxyl groups with sulphate. This paper describes the effects of monosulphation on the oestrogen agonist properties of these three phytoestrogens in MCF-7 human breast cancer cells in terms of their relative ability to compete with [H-3]oestradiol for binding to oestrogen receptor (ER), to induce a stably transfected oestrogen-responsive reporter gene (ERE-CAT) and to stimulate cell growth. In no case did sulphation abolish activity. The 4'-sulphadon of genistein reduced oestrogen agonist activity to a small extent in whole-cell assays but increased the relative binding affinity to ER. The 7-sulphation of genistein, and also of equol, reduced oestrogen agonist activity substantially in all assays. By contrast, the position of monosulphation of daidzein acted in an opposing manner on oestrogen agonist activity. Sulphation at the 4'-position of daidzein resulted in a modest reduction in oestrogen agonist activity but sulphation of daidzein at the 7-position resulted in an increase in oestrogen agonist activity. Molecular modelling and docking studies suggested that the inverse effects of sulphation could be explained by the binding of daidzein into the ligand-binding domain of the ER in the opposite orientation compared with genistein and equol. This is the first report of sulphation enhancing activity of an isoflavone and inverse effects of sulphation between individual phytoestrogens.

Modelling the formation of necrotic regions in avascular tumours

The mechanisms underlying the formation of necrotic regions within avascular tumours are not well understood. In this paper, we examine the relative roles of nutrient deprivation and of cell death, from both the proliferating phase of the cell cycle via apoptosis and from the quiescent phase via necrosis, in changing the structure within multicellular tumour spheroids and particularly the accumulation of dead cell material in the centre. A mathematical model is presented and studied that accounts for nutrient diffusion, changes in cell cycling rates, the two different routes to cell death as well as active motion of cells and passive motion of the dead cell material. In studying the accumulation of dead cell matter we do not distinguish between the route by which each was formed. The resulting mathematical model is examined for a number of scenarios. Results show that in many cases the size of the necrotic core is closely correlated with low levels in nutrient concentration. However, in certain cases, particularly where the rate of necrosis is large, the resulting necrotic core can lead to regions of non-negligible nutrient concentration-dependent upon the mode of cell death.

Modelling 2,4-dichlorophenol bioavailability and bioaccumulation by the freshwater fingernail clam Sphaerium corneum using artificial particles and humic acids

The complex and variable composition of natural sediments makes it very difficult to predict the bioavailability and bioaccumulation of sediment-bound contaminants. Several approaches have been proposed to overcome this problem, including an experimental model using artificial particles with or without humic acids as a source of organic matter. For this work, we have applied this experimental model, and also a sample of a natural sediment, to investigate the uptake and bioaccumulation of 2,4-dichlorophenol (2,4-DCP) by Sphaerium corneum. Additionally, the particle-water partition coefficients (K-d) were calculated. The results showed that the bioaccumulation of 2,4-DCP by clams did not depend solely on the levels of chemical dissolved, but also on the amount sorbed onto the particles and the characteristics and the strength of that binding. This study confirms the value of using artificial particles as a suitable experimental model for assessing the fate of sediment-bound contaminants. (c) 2006 Elsevier Ltd. All rights reserved.

Did pterosaurs feed by skimming? Physical modelling and anatomical evaluation of an unusual feeding method

Similarities between the anatomies of living organisms are often used to draw conclusions regarding the ecology and behaviour of extinct animals. Several pterosaur taxa are postulated to have been skim-feeders based largely on supposed convergences of their jaw anatomy with that of the modern skimming bird, Rynchops spp. Using physical and mathematical models of Rynchops bills and pterosaur jaws, we show that skimming is considerably more energetically costly than previously thought for Rynchops and that pterosaurs weighing more than one kilogram would not have been able to skim at all. Furthermore, anatomical comparisons between the highly specialised skull of Rynchops and those of postulated skimming pterosaurs suggest that even smaller forms were poorly adapted for skim-feeding. Our results refute the hypothesis that some pterosaurs commonly used skimming as a foraging method and illustrate the pitfalls involved in extrapolating from limited morphological convergence.

Modelling disease spread and control in networks: implications for plant sciences

Networks are ubiquitous in natural, technological and social systems. They are of increasing relevance for improved understanding and control of infectious diseases of plants, animals and humans, given the interconnectedness of today's world. Recent modelling work on disease development in complex networks shows: the relative rapidity of pathogen spread in scale-free compared with random networks, unless there is high local clustering; the theoretical absence of an epidemic threshold in scale-free networks of infinite size, which implies that diseases with low infection rates can spread in them, but the emergence of a threshold when realistic features are added to networks (e.g. finite size, household structure or deactivation of links); and the influence on epidemic dynamics of asymmetrical interactions. Models suggest that control of pathogens spreading in scale-free networks should focus on highly connected individuals rather than on mass random immunization. A growing number of empirical applications of network theory in human medicine and animal disease ecology confirm the potential of the approach, and suggest that network thinking could also benefit plant epidemiology and forest pathology, particularly in human-modified pathosystems linked by commercial transport of plant and disease propagules. Potential consequences for the study and management of plant and tree diseases are discussed.

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

Numbers of antral follicles during follicular waves in cattle: Evidence for high variation among animals, very high repeatability in individuals, and an inverse association with serum follicle-stimulating hormone concentrations

The extent, causes, and physiological significance of the variation in number of follicles growing during ovarian follicular waves in human beings and cattle are unknown. Therefore, the present study examined the variability and repeatability in numbers of follicles 3 mm or greater in diameter during the follicular waves in bovine estrous cycles, and we determined if the variation in number of follicles during waves was associated with alterations in secretion of FSH, estradiol, inhibin, and insulin-like growth factor I (IGF-I). Dairy cattle were subjected to twice-daily ultrasound analysis to count total number of antral follicles 3 mm or greater in diameter throughout 138 different follicular waves. In another study, blood samples were taken at frequent intervals from cows that consistently had low or very high numbers of follicles during waves and were subjected to immunoassays. Results indicate the following: First, despite an approximately sevenfold variation in number of follicles during waves among animals and marked differences in age, stage of lactation, and season of the year, a very highly repeatable (0.95) number of follicles 3 mm or greater in diameter is maintained during the ovulatory and nonovulatory follicular waves of individuals. Second, variation in number of follicles 3 mm or greater in diameter during waves and the inverse association of number of follicles during waves with FSH are not directly explained by alterations in the patterns of secretion of estradiol, inhibin, or IGF-I. Third, ovarian ultrasound analysis can be used reliably by investigators to identify cattle that consistently have low or high numbers of follicles during waves, thus providing a novel experimental model to determine the causes and physiological significance of the high variation in antral follicle number during follicular waves among single-ovulating species, such as cattle or humans.