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.

Adaptive approximate Bayesian computation

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappe et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.

The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation

The theta-logistic is a widely used generalisation of the logistic model of regulated biological processes which is used in particular to model population regulation. Then the parameter theta gives the shape of the relationship between per-capita population growth rate and population size. Estimation of theta from population counts is however subject to bias, particularly when there are measurement errors. Here we identify factors disposing towards accurate estimation of theta by simulation of populations regulated according to the theta-logistic model. Factors investigated were measurement error, environmental perturbation and length of time series. Large measurement errors bias estimates of theta towards zero. Where estimated theta is close to zero, the estimated annual return rate may help resolve whether this is due to bias. Environmental perturbations help yield unbiased estimates of theta. Where environmental perturbations are large, estimates of theta are likely to be reliable even when measurement errors are also large. By contrast where the environment is relatively constant, unbiased estimates of theta can only be obtained if populations are counted precisely Our results have practical conclusions for the design of long-term population surveys. Estimation of the precision of population counts would be valuable, and could be achieved in practice by repeating counts in at least some years. Increasing the length of time series beyond ten or 20 years yields only small benefits. if populations are measured with appropriate accuracy, given the level of environmental perturbation, unbiased estimates can be obtained from relatively short censuses. These conclusions are optimistic for estimation of theta. (C) 2008 Elsevier B.V All rights reserved.

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.

Population-level assessment of risks of pesticides to birds and mammals in the UK

It is generally acknowledged that population-level assessments provide,I better measure of response to toxicants than assessments of individual-level effects. population-level assessments generally require the use of models to integrate potentially complex data about the effects of toxicants on life-history traits, and to provide a relevant measure of ecological impact. Building on excellent earlier reviews we here briefly outline the modelling options in population-level risk assessment. Modelling is used to calculate population endpoints from available data, which is often about Individual life histories, the ways that individuals interact with each other, the environment and other species, and the ways individuals are affected by pesticides. As population endpoints, we recommend the use of population abundance, population growth rate, and the chance of population persistence. We recommend two types of model: simple life-history models distinguishing two life-history stages, juveniles and adults; and spatially-explicit individual-based landscape models. Life-history models are very quick to set up and run, and they provide a great deal or insight. At the other extreme, individual-based landscape models provide the greatest verisimilitude, albeit at the cost of greatly increased complexity. We conclude with a discussion of the cations of the severe problems of parameterising models.

Habitat correlates of distribution and local population decline of the endemic Sardinian newt Euproctus platycephalus

Habitat-based statistical models relating patterns of presence and absence of species to habitat variables could be useful to resolve conservation-related problems and highlight the causes of population declines. In this paper, we apply such a modelling approach to an endemic amphibian, the Sardinian mountain newt Euproctus platycephalus, considered by IUCN a critically endangered species. Sardinian newts inhabit freshwater habitat in streams, small lakes and pools on the island of Sardinia (Italy). Reported declines of newt populations are not yet supported by quantitative data, however, they are perceived or suspected across the species' historical range. This study represents a first attempt trying to statistically relate habitat characteristics to Sardinian newt occurrence and persistence. Linear regression analysis revealed that newts are more likely to be found in sites with colder water temperature, less riparian vegetation and, marginally, absence of fish. The implications of the results for the conservation of the species are discussed, and suggestions for the short-term management of newt inhabited sites suggested. (C) 2003 Elsevier Ltd. All rights reserved.

Efficient and cost-effective experimental determination of kinetic constants and data: the success of a Bayesian systematic approach to drug transport, receptor binding, continuous culture and cell transport kinetics

Details about the parameters of kinetic systems are crucial for progress in both medical and industrial research, including drug development, clinical diagnosis and biotechnology applications. Such details must be collected by a series of kinetic experiments and investigations. The correct design of the experiment is essential to collecting data suitable for analysis, modelling and deriving the correct information. We have developed a systematic and iterative Bayesian method and sets of rules for the design of enzyme kinetic experiments. Our method selects the optimum design to collect data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. The rules select features of the design such as the substrate range and the number of measurements. We show here that this method can be directly applied to the study of other important kinetic systems, including drug transport, receptor binding, microbial culture and cell transport kinetics. It is possible to reduce the errors in the estimated parameters and, most importantly, increase the efficiency and cost-effectiveness by reducing the necessary amount of experiments and data points measured. (C) 2003 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Estimation of population growth or decline in genetically monitored populations

This article introduces a new general method for genealogical inference that samples independent genealogical histories using importance sampling (IS) and then samples other parameters with Markov chain Monte Carlo (MCMC). It is then possible to more easily utilize the advantages of importance sampling in a fully Bayesian framework. The method is applied to the problem of estimating recent changes in effective population size from temporally spaced gene frequency data. The method gives the posterior distribution of effective population size at the time of the oldest sample and at the time of the most recent sample, assuming a model of exponential growth or decline during the interval. The effect of changes in number of alleles, number of loci, and sample size on the accuracy of the method is described using test simulations, and it is concluded that these have an approximately equivalent effect. The method is used on three example data sets and problems in interpreting the posterior densities are highlighted and discussed.

A novel Bayesian approach to drug design with simple and complex enzymes: Use with lens aldehyde dehydrogenase and the glyoxalase pathway

Purpose: Acquiring details of kinetic parameters of enzymes is crucial to biochemical understanding, drug development, and clinical diagnosis in ocular diseases. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. Methods: We have developed Bayesian utility functions to minimise kinetic parameter variance involving differentiation of model expressions and matrix inversion. These have been applied to the simple kinetics of the enzymes in the glyoxalase pathway (of importance in posttranslational modification of proteins in cataract), and the complex kinetics of lens aldehyde dehydrogenase (also of relevance to cataract). Results: Our successful application of Bayesian statistics has allowed us to identify a set of rules for designing optimum kinetic experiments iteratively. Most importantly, the distribution of points in the range is critical; it is not simply a matter of even or multiple increases. At least 60 % must be below the KM (or plural if more than one dissociation constant) and 40% above. This choice halves the variance found using a simple even spread across the range.With both the glyoxalase system and lens aldehyde dehydrogenase we have significantly improved the variance of kinetic parameter estimation while reducing the number and costs of experiments. Conclusions: We have developed an optimal and iterative method for selecting features of design such as substrate range, number of measurements and choice of intermediate points. Our novel approach minimises parameter error and costs, and maximises experimental efficiency. It is applicable to many areas of ocular drug design, including receptor-ligand binding and immunoglobulin binding, and should be an important tool in ocular drug discovery.

Efficient and accurate experimental design for enzyme kinetics: Bayesian studies reveal a systematic approach

In areas such as drug development, clinical diagnosis and biotechnology research, acquiring details about the kinetic parameters of enzymes is crucial. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. We demonstrate that a Bayesian approach (the use of prior knowledge) can produce major gains quantifiable in terms of information, productivity and accuracy of each experiment. Developing the use of Bayesian Utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has enabled the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K-M and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. (C) 2003 Elsevier Science B.V. All rights reserved.

Qualitative modelling of sustainable energy scenarios: An application and extension of the Bon Qualitative Input-Output model

Climate change is one of the major challenges facing economic systems at the start of the 21st century. Reducing greenhouse gas emissions will require both restructuring the energy supply system (production) and addressing the efficiency and sufficiency of the social uses of energy (consumption). The energy production system is a complicated supply network of interlinked sectors with 'knock-on' effects throughout the economy. End use energy consumption is governed by complex sets of interdependent cultural, social, psychological and economic variables driven by shifts in consumer preference and technological development trajectories. To date, few models have been developed for exploring alternative joint energy production-consumption systems. The aim of this work is to propose one such model. This is achieved in a methodologically coherent manner through integration of qualitative input-output models of production, with Bayesian belief network models of consumption, at point of final demand. The resulting integrated framework can be applied either (relatively) quickly and qualitatively to explore alternative energy scenarios, or as a fully developed quantitative model to derive or assess specific energy policy options. The qualitative applications are explored here.

A bagging-based correction for the mixture model estimator of population size

Estimation of a population size by means of capture-recapture techniques is an important problem occurring in many areas of life and social sciences. We consider the frequencies of frequencies situation, where a count variable is used to summarize how often a unit has been identified in the target population of interest. The distribution of this count variable is zero-truncated since zero identifications do not occur in the sample. As an application we consider the surveillance of scrapie in Great Britain. In this case study holdings with scrapie that are not identified (zero counts) do not enter the surveillance database. The count variable of interest is the number of scrapie cases per holding. For count distributions a common model is the Poisson distribution and, to adjust for potential heterogeneity, a discrete mixture of Poisson distributions is used. Mixtures of Poissons usually provide an excellent fit as will be demonstrated in the application of interest. However, as it has been recently demonstrated, mixtures also suffer under the so-called boundary problem, resulting in overestimation of population size. It is suggested here to select the mixture model on the basis of the Bayesian Information Criterion. This strategy is further refined by employing a bagging procedure leading to a series of estimates of population size. Using the median of this series, highly influential size estimates are avoided. In limited simulation studies it is shown that the procedure leads to estimates with remarkable small bias.

Resource availability and the persistence of seed-eating bird populations in agricultural landscapes – a mechanistic modelling approach

1. Reductions in resource availability, associated with land-use change and agricultural intensification in the UK and Europe, have been linked with the widespread decline of many farmland bird species over recent decades. However, the underlying ecological processes which link resource availability and population trends are poorly understood. 2. We construct a spatial depletion model to investigate the relationship between the population persistence of granivorous birds within the agricultural landscape and the temporal dynamics of stubble field availability, an important source of winter food for many of those species. 3. The model is capable of accurately predicting the distribution of a given number of finches and buntings amongst patches of different stubble types in an agricultural landscape over the course of a winter and assessing the relative value of different landscapes in terms of resource availability. 4. Sensitivity analyses showed that the model is relatively robust to estimates of energetic requirements, search efficiency and handling time but that daily seed survival estimates have a strong influence on model fit. Understanding resource dynamics in agricultural landscapes is highlighted as a key area for further research. 5. There was a positive relationship between the predicted number of bird days supported by a landscape over-winter and the breeding population trend for yellowhammer Emberiza citrinella, a species for which survival has been identified as the primary driver of population dynamics, but not for linnet Carduelis cannabina, a species for which productivity has been identified as the primary driver of population dynamics. 6. Synthesis and applications. We believe this model can be used to guide the effective delivery of over-winter food resources under agri-environment schemes and to assess the impacts on granivorous birds of changing resource availability associated with novel changes in land use. This could be very important in the future as farming adapts to an increasingly dynamic trading environment, in which demands for increased agricultural production must be reconciled with objectives for environmental protection, including biodiversity conservation.

Modelling niches of arbitrary shape in genetic algorithms using Niche Linkage in the Dynamic Niche Clustering framework

We present some additions to a fuzzy variable radius niche technique called Dynamic Niche Clustering (DNC) (Gan and Warwick, 1999; 2000; 2001) that enable the identification and creation of niches of arbitrary shape through a mechanism called Niche Linkage. We show that by using this mechanism it is possible to attain better feature extraction from the underlying population.

How predation and landscape fragmentation affect vole population dynamics

Background: Microtine species in Fennoscandia display a distinct north-south gradient from regular cycles to stable populations. The gradient has often been attributed to changes in the interactions between microtines and their predators. Although the spatial structure of the environment is known to influence predator-prey dynamics of a wide range of species, it has scarcely been considered in relation to the Fennoscandian gradient. Furthermore, the length of microtine breeding season also displays a north-south gradient. However, little consideration has been given to its role in shaping or generating population cycles. Because these factors covary along the gradient it is difficult to distinguish their effects experimentally in the field. The distinction is here attempted using realistic agent-based modelling. Methodology/Principal Findings: By using a spatially explicit computer simulation model based on behavioural and ecological data from the field vole (Microtus agrestis), we generated a number of repeated time series of vole densities whose mean population size and amplitude were measured. Subsequently, these time series were subjected to statistical autoregressive modelling, to investigate the effects on vole population dynamics of making predators more specialised, of altering the breeding season, and increasing the level of habitat fragmentation. We found that fragmentation as well as the presence of specialist predators are necessary for the occurrence of population cycles. Habitat fragmentation and predator assembly jointly determined cycle length and amplitude. Length of vole breeding season had little impact on the oscillations. Significance: There is good agreement between our results and the experimental work from Fennoscandia, but our results allow distinction of causation that is hard to unravel in field experiments. We hope our results will help understand the reasons for cycle gradients observed in other areas. Our results clearly demonstrate the importance of landscape fragmentation for population cycling and we recommend that the degree of fragmentation be more fully considered in future analyses of vole dynamics.