Parametric estimation of complex mixed models based on meta-model approach

Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The standard statistical approach is mixed-effects model, with regression functions that are now highly-developed to describe precisely the biological processes (solutions of multi-dimensional ordinary differential equations or of partial differential equation). When there is no analytical solution, a classical estimation approach relies on the coupling of a stochastic version of the EM algorithm (SAEM) with a MCMC algorithm. This procedure needs many evaluations of the regression function which is clearly prohibitive when a time-consuming solver is used for computing it. In this work a meta-model relying on a Gaussian process emulator is proposed to replace this regression function. The new source of uncertainty due to this approximation can be incorporated in the model which leads to what is called a mixed meta-model. A control on the distance between the maximum likelihood estimates in this mixed meta-model and the maximum likelihood estimates obtained with the exact mixed model is guaranteed. Eventually, numerical simulations are performed to illustrate the efficiency of this approach

Modeling of the HIV infection epidemic in the Netherlands: A multi-parameter evidence synthesis approach

Multi-parameter evidence synthesis (MPES) is receiving growing attention from the epidemiological community as a coherent and flexible analytical framework to accommodate a disparate body of evidence available to inform disease incidence and prevalence estimation. MPES is the statistical methodology adopted by the Health Protection Agency in the UK for its annual national assessment of the HIV epidemic, and is acknowledged by the World Health Organization and UNAIDS as a valuable technique for the estimation of adult HIV prevalence from surveillance data. This paper describes the results of utilizing a Bayesian MPES approach to model HIV prevalence in the Netherlands at the end of 2007, using an array of field data from different study designs on various population risk subgroups and with a varying degree of regional coverage. Auxiliary data and expert opinion were additionally incorporated to resolve issues arising from biased, insufficient or inconsistent evidence. This case study offers a demonstration of the ability of MPES to naturally integrate and critically reconcile disparate and heterogeneous sources of evidence, while producing reliable estimates of HIV prevalence used to support public health decision-making.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS488 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

CopulaDTA: An R Package for Copula Based Bivariate Beta-Binomial Models for Diagnostic Test Accuracy Studies in a Bayesian Framework

The current statistical procedures implemented in statistical software packages for pooling of diagnostic test accuracy data include hSROC regression and the bivariate random-effects meta-analysis model (BRMA). However, these models do not report the overall mean but rather the mean for a central study with random-effect equal to zero and have difficulties estimating the correlation between sensitivity and specificity when the number of studies in the meta-analysis is small and/or when the between-study variance is relatively large. This tutorial on advanced statistical methods for meta-analysis of diagnostic accuracy studies discusses and demonstrates Bayesian modeling using CopulaDTA package in R to fit different models to obtain the meta-analytic parameter estimates. The focus is on the joint modelling of sensitivity and specificity using copula based bivariate beta distribution. Essentially, we extend the work of Nikoloulopoulos by: i) presenting the Bayesian approach which offers flexibility and ability to perform complex statistical modelling even with small data sets and ii) including covariate information, and iii) providing an easy to use code. The statistical methods are illustrated by re-analysing data of two published meta-analyses. Modelling sensitivity and specificity using the bivariate beta distribution provides marginal as well as study-specific parameter estimates as opposed to using bivariate normal distribution (e.g., in BRMA) which only yields study-specific parameter estimates. Moreover, copula based models offer greater flexibility in modelling different correlation structures in contrast to the normal distribution which allows for only one correlation structure.Comment: 26 pages, 5 figure

Bayesian Learning and Predictability in a Stochastic Nonlinear Dynamical Model

Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple nonlinear marine biogeochemical model. A novel approach is proposed to the formulation of the stochastic process model, in which ecophysiological properties of plankton communities are represented by autoregressive stochastic processes. This approach captures the effects of changes in plankton communities over time, and it allows the incorporation of literature metadata on individual species into prior distributions for process model parameters. The approach is applied to a case study at Ocean Station Papa, using Particle Markov chain Monte Carlo computational techniques. The results suggest that, by drawing on objective prior information, it is possible to extract useful information about model state and a subset of parameters, and even to make useful long-term forecasts, based on sparse and noisy observations

Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version

A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence

A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that it is superior to the standard generalized linear mixed model in this context. Here, we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate generalized linear mixed model as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analyzing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality

Combining Revealed and Stated Preference Data to Estimate the Nonmarket Value of Ecological Services: An Assessment of the State of the Science

This paper reviews the marketing, transportation, and environmental economics literature on the joint estimation of revealed and stated preference data. The revealed preference and stated preference approaches are first described with a focus on the strengths and weaknesses of each. Recognizing these strengths and weaknesses, the potential gains from combining data are described. A classification system for combined data that emphasizes the type of data combination and the econometric models used is proposed. A methodological review of the literature is pursued based on this classification system. Examples from the environmental economics literature are highlighted. A discussion of the advantages and disadvantages of each type of jointly estimated model is then presented. Suggestions for future research, in particular opportunities for application of these models to environmental quality valuation, are presented.Nonmarket Valuation, Revealed Preference, Stated Preference