Forecasting obesity trends in England

Summary.  Forecasts of trends in obesity in England for 2010 are produced by treating the available data, which contain the proportions of the population, categorized by age and sex, falling into different body mass index ranges, as compositional data sets, so that the implicit simplex restrictions are automatically satisfied. Forecasts are calculated by using linear trend models for the log-ratio transformations and are accompanied by prediction regions. The advantages of treating data on proportions compositionally are emphasized and compared with forecasts that have been obtained by ignoring this restriction.     

Using Bayesian graphical models to model biases in observational studies and to combine multiple sources of data: application to low birth weight and water disinfection by-products

Summary.  Data in the social, behavioural and health sciences frequently come from observational studies instead of controlled experiments. In addition to random errors, observational data typically contain additional sources of uncertainty such as missing values, unmeasured confounders and selection biases. Also, the research question is often different from that which a particular source of data was designed to answer, and so not all relevant variables are measured. As a result, multiple sources of data are often necessary to identify the biases and to inform about different aspects of the research question. Bayesian graphical models provide a coherent way to connect a series of local submodels, based on different data sets, into a global unified analysis. We present a unified modelling framework that will account for multiple biases simultaneously and give more accurate parameter estimates than standard approaches. We illustrate our approach by analysing data from a study of water disinfection by-products and adverse birth outcomes in the UK.     

Using relative utility curves to evaluate risk prediction

Summary.  Because many medical decisions are based on risk prediction models that are constructed from medical history and results of tests, the evaluation of these prediction models is important. This paper makes five contributions to this evaluation: the relative utility curve which gauges the potential for better prediction in terms of utilities, without the need for a reference level for one utility, while providing a sensitivity analysis for misspecification of utilities, the relevant region, which is the set of values of prediction performance that are consistent with the recommended treatment status in the absence of prediction, the test threshold, which is the minimum number of tests that would be traded for a true positive prediction in order for the expected utility to be non-negative, the evaluation of two-stage predictions that reduce test costs and connections between various measures of performance of prediction. An application involving the risk of cardiovascular disease is discussed.     

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach.     

Copula structure analysis

Summary.  We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulas a correlation-like structure remains, but different margins and non-existence of moments are possible. After introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behaviour of the statistics can be observed even for small sample sizes. Finally, we show our method at work for a financial data set and explain differences between our copula-based approach and the classical approach. Our new method yielear models also.     

Invariant co-ordinate selection

Summary.  A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue–eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection . By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant co- ordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given.     

Analysis of quality-of-life adjusted failure time data in the presence of competing, possibly informative, censoring mechanisms

We derive estimators of the mean of a function of a quality-of-life adjusted failure time, in the presence of competing right censoring mechanisms. Our approach allows for the possibility that some or all of the competing censoring mechanisms are associated with the endpoint, even after adjustment for recorded prognostic factors, with the degree of residual association possibly different for distinct censoring processes. Our methods generalize from a single to many censoring processes and from ignorable to non-ignorable censoring processes.     

Copula-based regression models: A survey

In this review paper we collect several results about copula-based models, especially concerning regression models, by focusing on some insurance applications.     

Non-asymptotic sequential confidence regions with fixed sizes for the multivariate nonlinear parameters of regression

In this paper we consider a sequential design for the estimation of nonlinear parameters of regression with guaranteed accuracy. Non-asymptotic confidence regions with fixed sizes for the least squares estimates are used. The obtained confidence region is valid for finite numbers of data points when the distributions of the observations are unknown.     

A simple two-stage design for quantitative responses with application to a study in diabetic neuropathic pain

Two-stage designs offer substantial advantages for early phase II studies. The interim analysis following the first stage allows the study to be stopped for futility, or more positively, it might lead to early progression to the trials needed for late phase II and phase III. If the study is to continue to its second stage, then there is an opportunity for a revision of the total sample size. Two-stage designs have been implemented widely in oncology studies in which there is a single treatment arm and patient responses are binary. In this paper the case of two-arm comparative studies in which responses are quantitative is considered. This setting is common in therapeutic areas other than oncology. It will be assumed that observations are normally distributed, but that there is some doubt concerning their standard deviation, motivating the need for sample size review. The work reported has been motivated by a study in diabetic neuropathic pain, and the development of the design for that trial is described in detail.