Modelling covariance structure in ascending dose studies of isolated tissues and organs

This paper describes the analysis of two pharmacology assays: the guinea pig papillary muscle assay (an example of an isolated tissue assay) and an assay looking at pressure changes in isolated rat lungs. Both assays use an ascending dose design to minimize carryover effects. This is often necessary in these studies, due to the limited life span of the tissues. Various mixed models, with different covariance structures, are fitted to find the most appropriate model. These are then compared to two other possible methods of analysis: paired t‐tests and two‐way analysis of variance. For both assays, the mixed model was found to be the best approach. These examples illustrate the importance of modelling covariance structure correctly in any ascending dose study, whether in isolated organs/tissues, in animals or phase I volunteers. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling the persistence of conditional variances

This paper will discuss the current research in building models of conditional variances using the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) formulations. The discussion will be motivated by a simple asset pricing theory which is particularly appropriate for examining futures contracts with risk averse agents. A new class of models defined to be integrated in variance is then introduced. This new class of models includes the variance analogue of a unit root in the mean as a special case. The models are argued to be both theoretically important for the asset pricing models and empirically relevant. The conditional density is then generalized from a normal to a Student-t with unknown degrees of freedom. By estimating the degrees of freedom, implications about the conditional kurtosis of these models and time aggregated models can be drawn. A further generalization allows the conditional variance to be a non-linear function of the squared innovations. Throughout empirical e imates of the logarithm of the exchange rate between the U.S. dollar and the Swiss franc are presented to illustrate the models.     

Modelling micro-texture

There are many instances when texture contains valuable information in images, and various methods have been used for texture analysis. We distinguish between micro-textures and macro-textures. The paper models micro-texture using the general spin Ising model from statistical mechanics. This model allows for any number of grey levels and any set of pair interactions. For a given texture, we select an appropriate set of pair interactions and estimate the correspomding parameter values, using linked cluster expansions of the auto-covariances and the partition function. The series expansions are valid for parameters smaller than the critical parameters for which an infinite system would exhibit a phase transition. Hence, sufficiently small-grained micro-textures may be modelled. To ensure that the data meet this requirement, we simulate the model using the Markov chain Meet Carlo method and estimate its critical parameters using the series expansions. We demonstrate these methods on both real and simulated images.     

Modelling micro-texture

There are many instances when texture contains valuable information in images, and various methods have been used for texture analysis. We distinguish between micro-textures and macro-textures. The paper models micro-texture using the general spin Ising model from statistical mechanics. This model allows for any number of grey levels and any set of pair interactions. For a given texture, we select an appropriate set of pair interactions and estimate the correspomding parameter values, using linked cluster expansions of the auto-covariances and the partition function. The series expansions are valid for parameters smaller than the critical parameters for which an infinite system would exhibit a phase transition. Hence, sufficiently small-grained micro-textures may be modelled. To ensure that the data meet this requirement, we simulate the model using the Markov chain Meet Carlo method and estimate its critical parameters using the series expansions. We demonstrate these methods on both real and simulated images.     

Modelling the management of underground water assets

Central to the activities of any industry is the modernization of its assets. This paper describes the application of statistical methods to the asset management plan of a large water company. A model for the underground assets is given in detail, and the extensive computations required are illustrated. A Bayesian model shows the consequences of various policy options and provides realistic measures of the uncertainty connected with them.     

Modelling the management of underground water assets

Central to the activities of any industry is the modernization of its assets. This paper describes the application of statistical methods to the asset management plan of a large water company. A model for the underground assets is given in detail, and the extensive computations required are illustrated. A Bayesian model shows the consequences of various policy options and provides realistic measures of the uncertainty connected with them.     

Modelling of connected processes

The problem of comparing, contrasting and combining information from different sets of data is an enduring one in many practical applications of statistics. A specific problem of combining information from different sources arose in integrating information from three different sets of data generated by three different sampling campaigns at the input stage as well as at the output stage of a grey-water treatment process. For each stage, a common process trend function needs to be estimated to describe the input and output material process behaviours. Once the common input and output process models are established, it is required to estimate the efficiency of the grey-water treatment method. A synthesized tool for modelling different sets of process data is created by assembling and organizing a number of existing techniques: (i) a mixed model of fixed and random effects, extended to allow for a nonlinear fixed effect, (ii) variogram modelling, a geostatistical technique, (iii) a weighted least squares regression embedded in an iterative maximum-likelihood technique to handle linear/nonlinear fixed and random effects and (iv) a formulation of a transfer-function model for the input and output processes together with a corresponding nonlinear maximum-likelihood method for estimation of a transfer function. The synthesized tool is demonstrated, in a new case study, to contrast and combine information from connected process models and to determine the change in one quality characteristic, namely pH, of the input and output materials of a grey-water filtering process.     

Modelling impact heterogeneity

Summary.  The treatments embodied in social interventions are characterized by their heterogeneity, delivered as they often are by different individuals operating in different social and geographical contexts. One implication of this heterogeneity is that average treatment effects will often be less useful than estimates of differential impacts across contexts. The paper shows how multilevel models can be used to estimate variability of impact and to account for systematic effects. These models are specified for multisite interventions, for studies using cluster allocation and for designs that incorporate matching. The paper indicates how qualitative and quantitative approaches to evaluation could be linked.     

Modelling the data measurement process for the index of production

Many statistical series that are available from official agencies, such as the Office for National Statistics in the UK and the Bureau of Economic Analysis in the USA, are subject to an extensive process of revision and refinement. This feature of the data is often not explicitly recognized by users even though it may be important to their use of the data. The starting-point of this study is to conceptualize and model the data measurement process as it is relevant to the index of production (IOP). The IOP attracts considerable attention because of its timely publication and importance as an indicator of the UK's industrial base. This study shows that there is one common stochastic trend (and one common factor in terms of observable variables) `driving' 13 vintages of data on the IOP. Necessary and sufficient conditions are derived for the `final' vintage of data on the IOP to be the permanent component of the series in the Gonzalo–Granger sense, and the revisions to be the transitory components. These conditions are not satisfied for the IOP; hence, the per-manent component is a function of all the published vintages.     

Stereological Modelling of Random Particles

Stochastic models for three-dimensional particles have many applications in applied sciences. Lévy–based particle models are a flexible approach to particle modelling. The structure of the random particles is given by a kernel smoothing of a Lévy basis. The models are easy to simulate but statistical inference procedures have not yet received much attention in the literature. The kernel is not always identifiable and we suggest one approach to remedy this problem. We propose a method to draw inference about the kernel from data often used in local stereology and study the performance of our approach in a simulation study.     

Modelling consumers' use of products

Patterns of consumers' use of products are of interest to manufacturers. This paper is concerned with modelling diary data on the use of one product, shampoo, recorded to the nearest hour by over 500 men during 1 week. A binary response multilevel model is developed, building on similar models for consumer purchase data. The model allows for a dependence on the number of days since last use. The results of fitting various versions of this model are discussed. A problem is that the number of days since last use is missing for all times up to the first use. An approximate EM approach is considered to deal with this problem.     

Modelling Variability in the Branching Structure of Strawberry Inflorescences

The branching structure of inflorescences of the cultivated strawberry ( Fragaria × ananassa Duch.) is very variable. This paper demonstrates that some aspects of this variability are well described by a simple stochastic model of branching that has two adjustable parameters. The model is shown to provide a good fit to data from a set of almost 700 inflorescences of the cultivar Elsanta, collected over two successive years. For one parameter the maximum likelihood estimator is a moment estimator which is fully efficient even if the detailed branching structure of the inflorescences is not recorded. This parameter provides a convenient summary of branching vigour. The maximum likelihood estimator of the second parameter must be determined iteratively and can be quite inefficient unless the full branching structure is recorded. The model demonstrates that branching structure is affected by the order in which inflorescences emerge on the plant.     

Modelling the effects of repellent chemicals on foraging bees

Summary.  Many pesticide sprays that are used for crop protection are harmful to honey-bees. It can therefore be beneficial to add to the spray chemical compounds that are repellent to bees, to discourage them from feeding on recently sprayed crops. Experiments were conducted using an artificial feeding station to assess the repellent effects of various compounds. In this system, bees arrive at the feeding station, choose between feeding dishes to which different chemicals have been added, feed for a variable period and then depart. The number of bees at each feeding dish is recorded at intervals of 1 min. We discuss the analysis of data from this type of experiment, based on a queuing theory model.     

On Local Polynomial Modelling of the Additive Risk Model

The additive risk model provides an alternative modelling technique for failure time data to the proportional hazards model. In this article, we consider the additive risk model with a nonparametric risk effect. We study estimation of the risk function and its derivatives with a parametric and an unspecified baseline hazard function respectively. The resulting estimators are the local likelihood and the local score estimators. We establish the asymptotic normality of the estimators and show that both methods have the same formula for asymptotic bias but different formula for variance. It is found that, in some special cases, the local score estimator is of the same efficiency as the local likelihood estimator though it does not use the information about the baseline hazard function. Another advantage of the local score estimator is that it has a closed form and is easy to implement. Some simulation studies are conducted to evaluate and compare the performance of the two estimators. A numerical example is used for illustration.     

Modelling the role of variables in model-based cluster analysis

In the framework of cluster analysis based on Gaussian mixture models, it is usually assumed that all the variables provide information about the clustering of the sample units. Several variable selection procedures are available in order to detect the structure of interest for the clustering when this structure is contained in a variable sub-vector. Currently, in these procedures a variable is assumed to play one of (up to) three roles: (1) informative, (2) uninformative and correlated with some informative variables, (3) uninformative and uncorrelated with any informative variable. A more general approach for modelling the role of a variable is proposed by taking into account the possibility that the variable vector provides information about more than one structure of interest for the clustering. This approach is developed by assuming that such information is given by non-overlapped and possibly correlated sub-vectors of variables; it is also assumed that the model for the variable vector is equal to a product of conditionally independent Gaussian mixture models (one for each variable sub-vector). Details about model identifiability, parameter estimation and model selection are provided. The usefulness and effectiveness of the described methodology are illustrated using simulated and real datasets.     

Modelling and simulation in the pharmaceutical industry--some reflections

Modelling and simulation (M&S) is increasingly being applied in (clinical) drug development. It provides an opportune area for the community of pharmaceutical statisticians to pursue. In this article, we highlight useful principles behind the application of M&S. We claim that M&S should be focussed on decisions, tailored to its purpose and based in applied sciences, not relying entirely on data-driven statistical analysis. Further, M&S should be a continuous process making use of diverse information sources and applying Bayesian and frequentist methodology, as appropriate. In addition to forming a basis for analysing decision options, M&S provides a framework that can facilitate communication between stakeholders. Besides the discussion on modelling philosophy, we also describe how standard simulation practice can be ineffective and how simulation efficiency can often be greatly improved.     

Modelling non-response in the National Child Development Study

Summary.  There is widespread concern that the cumulative effects of the non-response that is bound to affect any long-running longitudinal study will lead to mistaken inferences about change. We focus on the National Child Development Study and show how non-response has accumulated over time. We distinguish between attrition and wave non-response and show how these two kinds of non-response can be related to a set of explanatory variables. We model the discrete time hazard of non-response and also fit a set of multinomial logistic regressions to the probabilities of different kinds of non-response at a particular sweep. We find that the best predictors of non-response at any sweep are generally variables that are measured at the previous sweep but, although non-response is systematic, much of the variation in it remains unexplained by our models. We consider the implications of our results for both design and analysis.