Comparing model averaging with other model selection strategies for benchmark dose estimation

Model averaging (MA) has been proposed as a method of accommodating model uncertainty when estimating risk. Although the use of MA is inherently appealing, little is known about its performance using general modeling conditions. We investigate the use of MA for estimating excess risk using a Monte Carlo simulation. Dichotomous response data are simulated under various assumed underlying dose–response curves, and nine dose–response models (from the USEPA Benchmark dose model suite) are fit to obtain both model specific and MA risk estimates. The benchmark dose estimates (BMDs) from the MA method, as well as estimates from other commonly selected models, e.g., best fitting model or the model resulting in the smallest BMD, are compared to the true benchmark dose value to better understand both bias and coverage behavior in the estimation procedure. The MA method has a small bias when estimating the BMD that is similar to the bias of BMD estimates derived from the assumed model. Further, when a broader range of models are included in the family of models considered in the MA process, the lower bound estimate provided coverage close to the nominal level, which is superior to the other strategies considered. This approach provides an alternative method for risk managers to estimate risk while incorporating model uncertainty.

Confidence limits on one-stage model parameters in benchmark risk assessment

In modern environmental risk analysis, inferences are often desired on those low dose levels at which a fixed benchmark risk is achieved. In this paper, we study the use of confidence limits on parameters from a simple one-stage model of risk historically popular in benchmark analysis with quantal data. Based on these confidence bounds, we present methods for deriving upper confidence limits on extra risk and lower bounds on the benchmark dose. The methods are seen to extend automatically to the case where simultaneous inferences are desired at multiple doses. Monte Carlo evaluations explore characteristics of the parameter estimates and the confidence limits under this setting.

Improved strategies for coverage estimation by using replicated line-intercept sampling

Coverage, i.e., the area covered by the target attribute in the study region, is a key parameter in many surveys. Coverage estimation is usually performed by adopting a replicated protocol based on line-intercept sampling coupled with a suitable linear homogeneous estimator. Since coverage is a parameter which may be interestingly represented as the integral of a suitable function, improved Monte Carlo strategies for implementing the replicated protocol are introduced in order to achieve estimators with small variance rates. In addition, new specific theoretical results on Monte Carlo integration methods are given to deal with the integrand functions arising in the special coverage estimation setting.

Hierarchical modeling for extreme values observed over space and time

We propose a hierarchical modeling approach for explaining a collection of spatially referenced time series of extreme values. We assume that the observations follow generalized extreme value (GEV) distributions whose locations and scales are jointly spatially dependent where the dependence is captured using multivariate Markov random field models specified through coregionalization. In addition, there is temporal dependence in the locations. There are various ways to provide appropriate specifications; we consider four choices. The models can be fitted using a Markov Chain Monte Carlo (MCMC) algorithm to enable inference for parameters and to provide spatio–temporal predictions. We fit the models to a set of gridded interpolated precipitation data collected over a 50-year period for the Cape Floristic Region in South Africa, summarizing results for what appears to be the best choice of model.

Bootstrap methods for simultaneous benchmark analysis with quantal response data

A primary objective in quantitative risk assessment is the characterization of risk which is defined to be the likelihood of an adverse effect caused by an environmental toxin or chemcial agent. In modern risk-benchmark analysis, attention centers on the “benchmark dose” at which a fixed benchmark level of risk is achieved, with a lower confidence limits on this dose being of primary interest. In practice, a range of benchmark risks may be under study, so that the individual lower confidence limits on benchmark dose must be corrected for simultaneity in order to maintain a specified overall level of confidence. For the case of quantal data, simultaneous methods have been constructed that appeal to the large sample normality of parameter estimates. The suitability of these methods for use with small sample sizes will be considered. A new bootstrap technique is proposed as an alternative to the large sample methodology. This technique is evaluated via a simulation study and examples from environmental toxicology.

Replace the NOAEL and LOAEL with the BMDL01 and BMDL10

Although benchmark-dose methodology has existed for more than 20 years, benchmark doses (BMDs) still have not fully supplanted the no-observed-adverse-effect level (NOAEL) and lowest-observed-adverse-effect level (LOAEL) as points of departure from the experimental dose–response range for setting acceptable exposure levels of toxic substances. Among the issues involved in replacing the NOAEL (LOAEL) with a BMD are (1) which added risk level(s) above background risk should be targeted as benchmark responses (BMRs), (2) whether to apply the BMD methodology to both carcinogenic and noncarcinogenic toxic effects, and (3) how to model continuous health effects that aren’t observed in a natural risk-based context like dichotomous health effects. This paper addresses these issues and recommends specific BMDs to replace the NOAEL and LOAEL.

Beta-normal distribution in dose–response modeling and risk assessment for quantitative responses

To establish allowable daily intakes for humans from animal bioassay experiments, benchmark doses corresponding to low levels of risk have been proposed to replace the no-observed-adverse-effect level for non-cancer endpoints. When the experimental outcomes are quantal, each animal can be classified with or without the disease. The proportion of affected animals is observed as a function of dose and calculation of the benchmark dose is relatively simple. For quantitative responses, on the other hand, one method is to convert the continuous data to quantal data and proceed with benchmark dose estimation. Another method which has found more popularity (Crump, Risk Anal 15:79–89; 1995) is to fit an appropriate dose–response model to the continuous data, and directly estimate the risk and benchmark doses. The normal distribution has often been used in the past as a dose–response model. However, for non-symmetric data, the normal distribution can lead to erroneous results. Here, we propose the use of the class of beta-normal distribution and demonstrate its application in risk assessment for quantitative responses. The most important feature of this class of distributions is its generality, encompassing a wide range of distributional shapes including the normal distribution as a special case. The properties of the model are briefly discussed and risk estimates are derived based on the asymptotic properties of the maximum likelihood estimates. An example is used for illustration.

Maximum likelihood fitting of the Poisson lognormal distribution

In this paper some properties and analytic expressions regarding the Poisson lognormal distribution such as moments, maximum likelihood function and related derivatives are discussed. The author provides a sharp approximation of the integrals related to the Poisson lognormal probabilities and analyzes the choice of the initial values in the fitting procedure. Based on these he describes a new procedure for carrying out the maximum likelihood fitting of the truncated Poisson lognormal distribution. The method and results are illustrated on real data. The computer program for calculations is freely available.

Flexible hierarchical mark-recapture modeling for open populations using WinBUGS

Hierarchical mark-recapture models offer three advantages over classical mark-recapture models: (i) they allow expression of complicated models in terms of simple components; (ii) they provide a convenient way of modeling missing data and latent variables in a way that allows expression of relationships involving latent variables in the model; (iii) they provide a convenient way of introducing parsimony into models involving many nuisance parameters. Expressing models using the complete data likelihood we show how many of the standard mark-recapture models for open populations can be readily fitted using the software WinBUGS. We include examples that illustrate fitting the Cormack–Jolly–Seber model, multi-state and multi-event models, models including auxiliary data, and models including density dependence.

A stochastic forest fire growth model

We consider a stochastic fire growth model, with the aim of predicting the behaviour of large forest fires. Such a model can describe not only average growth, but also the variability of the growth. Implementing such a model in a computing environment allows one to obtain probability contour plots, burn size distributions, and distributions of time to specified events. Such a model also allows the incorporation of a stochastic spotting mechanism.

A note on non-parametric and semi-parametric modeling of wildfire hazard in Los Angeles County, California

This paper explores the use of, and problems that arise in, kernel smoothing and parametric estimation of the relationships between wildfire incidence and various meteorological variables. Such relationships may be treated as components in separable point process models for wildfire activity. The resulting models can be used for comparative purposes in order to assess the predictive performance of the Burning Index.

Hierarchical spatial point process analysis for a plant community with high biodiversity

A complex multivariate spatial point pattern of a plant community with high biodiversity is modelled using a hierarchical multivariate point process model. In the model, interactions between plants with different post-fire regeneration strategies are of key interest. We consider initially a maximum likelihood approach to inference where problems arise due to unknown interaction radii for the plants. We next demonstrate that a Bayesian approach provides a flexible framework for incorporating prior information concerning the interaction radii. From an ecological perspective, we are able both to confirm existing knowledge on species’ interactions and to generate new biological questions and hypotheses on species’ interactions.

A note on data augmentation and iterative simulation for survival rate estimation

In this paper we examine the use of data augmentation techniques for simplifying iterative simulation in the context of both Bayesian and classical statistical inference for survival rate estimation. We examine two distinct model families common in population ecology to illustrate our ideas, ring-recovery models and capture–recapture models, and we present the computational advantage of this approach. We discuss also the fact that problems associated with identifiability in the classical framework can be overcome using data augmentation, but highlight the dangers in doing so under both inferential paradigms.

Spatial smoothing techniques for the assessment of habitat suitability

Precise knowledge about factors influencing the habitat suitability of a certain species forms the basis for the implementation of effective programs to conserve biological diversity. Such knowledge is frequently gathered from studies relating abundance data to a set of influential variables in a regression setup. In particular, generalised linear models are used to analyse binary presence/absence data or counts of a certain species at locations within an observation area. However, one of the key assumptions of generalised linear models, the independence of observations is often violated in practice since the points at which the observations are collected are spatially aligned. In this paper, we describe a general framework for semiparametric spatial generalised linear models that allows for the routine analysis of non-normal spatially aligned regression data. The approach is utilised for the analysis of a data set of synthetic bird species in beech forests, revealing that ignorance of spatial dependence actually may lead to false conclusions in a number of situations.

Trap mortality in mark-recapture studies

When animals die in traps in a mark-recapture study, straightforward likelihood inferences are possible in a class of models. The class includes M₀, M_t, and M_b as reported by White et al. (Los Alamos National Laboratory, LA-8787-NERP, pp 235, 1982), those that do not involve heterogeneity. We include three Markov chain “persistence” models and show that they provide good fits in a trapping study of deer mice in the Cascade-Siskiyou National Monument of Southern Oregon where trapping mortality was high.

Testing homogeneity of capture probabilities of animals in a removal experiment

Consider the removal experiment used to estimate population sizes. Statistical methods towards testing the homogeneity of capture probabilities of animals, including a graphical diagnostic and a formal test, are presented and illustrated by real biological examples. Simulation is used to assess the test and compare it with the χ² test.

Urban geochemical mapping studies: how and why we do them

Geochemical mapping is a technique rooted in mineral exploration but has now found worldwide application in studies of the urban environment. Such studies, involving multidisciplinary teams including geochemists, have to present their results in a way that nongeochemists can comprehend. A legislatively driven demand for urban geochemical data in connection with the need to identify contaminated land and subsequent health risk assessments has given rise to a greater worldwide interest in the urban geochemical environment. Herein, the aims and objectives of some urban studies are reviewed and commonly used terms such as baseline and background are defined. Geochemists need to better consider what is meant by the term urban. Whilst the unique make up of every city precludes a single recommended approach to a geochemical mapping strategy, more should be done to standardise the sampling and analytical methods. How (from a strategic and presentational point of view) and why we do geochemical mapping studies is discussed.

Point patterns of forest fire locations

In this paper I demonstrate some of the techniques for the analysis of spatial point patterns that have become available due to recent developments in point process modelling software. These developments permit convenient exploratory data analysis, model fitting, and model assessment. Efficient model fitting, in particular, makes possible the testing of statistical hypotheses of genuine interest, even when interaction between points is present, via Monte Carlo methods. The discussion of these techniques is conducted jointly with and in the context of some preliminary analyses of a collection of data sets which are of considerable interest in their own right. These data sets (which were kindly provided to me by the New Brunswick Department of Natural Resources) consist of the complete records of wildfires which occurred in New Brunswick during the years 1987 through 2003. In treating these data sets I deal with data-cleaning problems, methods of exploratory data analysis, means of detecting interaction, fitting of statistical models, and residual analysis and diagnostics. In addition to demonstrating modelling techniques, I include a discussion on the nature of statistical models for point patterns. This is given with a view to providing an understanding of why, in particular, the Strauss model fails as a model for interpoint attraction and how it has been modified to overcome this difficulty. All actual modelling of the New Brunswick fire data is done only with the intent of illustrating techniques. No substantive conclusions are or can be drawn at this stage. Realistic modelling of these data sets would require incorporation of covariate information which I do not so far have available.

Multi-parameter renewal processes and simulation of forest fires

The concept of the renewal property is extended to processes indexed by a multidimensional time parameter. The definition given includes not only partial sum processes, but also Poisson processes and many other point processes whose jump points are not totally ordered. Various properties of renewal processes are discussed. Renewal processes are proposed as a basis for modelling the spread of a forest fire under a prevailing wind.

Evaluating the sampling pattern when detecting Zones of Abrupt Change

We present a method for detecting the zones where an irregularly sampled variable changes abruptly in the plane. Such zones are called Zones of Abrupt Change (ZACs). This method not only allows estimation of ZACs, but also testing of their statistical significance against the null hypothesis of a stationary correlated random field. The sampling pattern, in particular its local density, is crucial in the detection of potential ZACs. In this paper, we address the problem of evaluating the sampling pattern by assessing the power of the local test used for detecting ZACs. It is shown that mapping the power allows us to identify zones where ZACs may or may not be detected. The methodology is applied to a soil data set sampled at eight different dates in an agricultural field. Detecting ZACs for the soil water content allowed us to identify permanent structures in the agricultural field related to the boundaries between different soil types. Mapping the power for various sampling densities proved to be useful to determine the minimal sampling density necessary for detecting ZACs.