An old problem revisited - and solved: Upton and Dalton's linear production response: A note

This note presents a robust method for estimating response surfaces that consist of linear response regimes and a linear plateau. The linear response-and-plateau model has fascinated production scientists since von Liebig (1855) and, as Upton and Dalton indicated, some years ago in this Journal, the response-and-plateau model seems to fit the data in many empirical studies. The estimation algorithm evolves from Bayesian implementation of a switching-regression (finite mixtures) model and demonstrates routine application of Gibbs sampling and data augmentation-techniques that are now in widespread application in other disciplines.

How big is your neighbourhood? Spatial implications of market participation among Filipino smallholders

We present a procedure for estimating two quantities defining the spatial externality in discrete-choice commonly referred to as 'the neighbourhood effect'. One quantity, the propensity for neighbours to make the same decision, reflects traditional preoccupations; the other quantity, the magnitude of the neighbourhood itself, is novel. Because both quantities have fundamental bearing on the magnitude of the spatial externality, it is desirable to have a robust algorithm for their estimation. Using recent advances in Bayesian estimation and model comparison, we devise such an algorithm and illustrate its application to a sample of northern-Filipino smallholders. We determine that a significant, positive, neighbourhood effect exists; that, among the 12 geographical units comprising the sample, the neighbourhood spans a three-unit radius; and that policy prescriptions are significantly altered when calculations account for the spatial externality.

Production efficiency in the von Liebig model

The objective of this paper is to revisit the von Liebig hypothesis by reexamining five samples of experimental data and by applying to it recent advances in Bayesian techniques. The samples were published by Hexem and Heady as described in a further section. Prior to outlining the estimation strategy, we discuss the intuition underlying our approach and, briefly, the literature on which it is based. We present an algorithm for the basic von Liebig formulation and demonstrate its application using simulated data (table 1). We then discuss the modifications needed to the basic model that facilitate estimation of a von Liebig frontier and we demonstrate the extended algorithm using simulated data (table 2). We then explore, empirically, the relationships between limiting water and nitrogen in the Hexem and Heady corn samples and compare the results between the two formulations (table 3). Finally, some conclusions and suggestions for further research are offered.

Time patterns in UK demand for alcohol and tobacco: an application of the EM algorithm

Capturing the pattern of structural change is a relevant task in applied demand analysis, as consumer preferences may vary significantly over time. Filtering and smoothing techniques have recently played an increasingly relevant role. A dynamic Almost Ideal Demand System with random walk parameters is estimated in order to detect modifications in consumer habits and preferences, as well as changes in the behavioural response to prices and income. Systemwise estimation, consistent with the underlying constraints from economic theory, is achieved through the EM algorithm. The proposed model is applied to UK aggregate consumption of alcohol and tobacco, using quarterly data from 1963 to 2003. Increased alcohol consumption is explained by a preference shift, addictive behaviour and a lower price elasticity. The dynamic and time-varying specification is consistent with the theoretical requirements imposed at each sample point. (c) 2005 Elsevier B.V. All rights reserved.

Bayesian clustering of farm types using the mixtures model

A Bayesian method of classifying observations that are assumed to come from a number of distinct subpopulations is outlined. The method is illustrated with simulated data and applied to the classification of farms according to their level and variability of income. The resultant classification shows a greater diversity of technical charactersitics within farm types than is conventionally the case. The range of mean farm income between groups in the new classification is wider than that of the conventional method and the variability of income within groups is narrower. Results show that the highest income group in 2000 included large specialist dairy farmers and pig and poultry producers, whilst in 2001 it included large and small specialist dairy farms and large mixed dairy and arable farms. In both years the lowest income group is dominated by non-milk producing livestock farms.

Gaining acceptability for the Bayesian decision-theoretic approach in dose-escalation studies

There has recently been increasing demand for better designs to conduct first-into-man dose-escalation studies more efficiently, more accurately and more quickly. The authors look into the Bayesian decision-theoretic approach and use simulation as a tool to investigate the impact of compromises with conventional practice that might make the procedures more acceptable for implementation. Copyright © 2005 John Wiley & Sons, Ltd.

Bayesian decision procedures for dose-escalation based on evidence of undesirable events and therapeutic benefit.

In this paper, Bayesian decision procedures are developed for dose-escalation studies based on bivariate observations of undesirable events and signs of therapeutic benefit. The methods generalize earlier approaches taking into account only the undesirable outcomes. Logistic regression models are used to model the two responses, which are both assumed to take a binary form. A prior distribution for the unknown model parameters is suggested and an optional safety constraint can be included. Gain functions to be maximized are formulated in terms of accurate estimation of the limits of a therapeutic window or optimal treatment of the next cohort of subjects, although the approach could be applied to achieve any of a wide variety of objectives. The designs introduced are illustrated through simulation and retrospective implementation to a completed dose-escalation study. Copyright © 2006 John Wiley & Sons, Ltd.

An evaluation of a Bayesian method of dose escalation based on bivariate binary responses

Recently, various approaches have been suggested for dose escalation studies based on observations of both undesirable events and evidence of therapeutic benefit. This article concerns a Bayesian approach to dose escalation that requires the user to make numerous design decisions relating to the number of doses to make available, the choice of the prior distribution, the imposition of safety constraints and stopping rules, and the criteria by which the design is to be optimized. Results are presented of a substantial simulation study conducted to investigate the influence of some of these factors on the safety and the accuracy of the procedure with a view toward providing general guidance for investigators conducting such studies. The Bayesian procedures evaluated use logistic regression to model the two responses, which are both assumed to be binary. The simulation study is based on features of a recently completed study of a compound with potential benefit to patients suffering from inflammatory diseases of the lung.

An evaluation of Bayesian designs for dose-escalation studies in healthy volunteers

In this paper, Bayesian decision procedures previously proposed for dose-escalation studies in healthy volunteers are reviewed and evaluated. Modifications are made to the expression of the prior distribution in order to make the procedure simpler to implement and a more relevant criterion for optimality is introduced. The results of an extensive simulation exercise to establish the proper-ties of the procedure and to aid choice between designs are summarized, and the way in which readers can use simulation to choose a design for their own trials is described. The influence of the value of the within-subject correlation on the procedure is investigated and the use of a simple prior to reflect uncertainty about the correlation is explored. Copyright (c) 2005 John Wiley & Sons, Ltd.

A hierarchical Bayesian model for predicting the functional consequences of amino-acid polymorphisms

Genetic polymorphisms in deoxyribonucleic acid coding regions may have a phenotypic effect on the carrier, e.g. by influencing susceptibility to disease. Detection of deleterious mutations via association studies is hampered by the large number of candidate sites; therefore methods are needed to narrow down the search to the most promising sites. For this, a possible approach is to use structural and sequence-based information of the encoded protein to predict whether a mutation at a particular site is likely to disrupt the functionality of the protein itself. We propose a hierarchical Bayesian multivariate adaptive regression spline (BMARS) model for supervised learning in this context and assess its predictive performance by using data from mutagenesis experiments on lac repressor and lysozyme proteins. In these experiments, about 12 amino-acid substitutions were performed at each native amino-acid position and the effect on protein functionality was assessed. The training data thus consist of repeated observations at each position, which the hierarchical framework is needed to account for. The model is trained on the lac repressor data and tested on the lysozyme mutations and vice versa. In particular, we show that the hierarchical BMARS model, by allowing for the clustered nature of the data, yields lower out-of-sample misclassification rates compared with both a BMARS and a frequen-tist MARS model, a support vector machine classifier and an optimally pruned classification tree.

Decision-making in a phase II clinical trial: a new approach combining Bayesian and frequentist concepts

The aim of a phase H clinical trial is to decide whether or not to develop an experimental therapy further through phase III clinical evaluation. In this paper, we present a Bayesian approach to the phase H trial, although we assume that subsequent phase III clinical trials will hat,e standard frequentist analyses. The decision whether to conduct the phase III trial is based on the posterior predictive probability of a significant result being obtained. This fusion of Bayesian and frequentist techniques accepts the current paradigm for expressing objective evidence of therapeutic value, while optimizing the form of the phase II investigation that leads to it. By using prior information, we can assess whether a phase II study is needed at all, and how much or what sort of evidence is required. The proposed approach is illustrated by the design of a phase II clinical trial of a multi-drug resistance modulator used in combination with standard chemotherapy in the treatment of metastatic breast cancer. Copyright (c) 2005 John Wiley & Sons, Ltd.