Research Interests in Human Health and Ecological Risks
Synopsis
With support from various public and private institutions such as the National Institutes of Health and the Electric Power Research Institute, Applied Biomathematics has been conducting methodological research on various topics in human and ecological risk analysis. The topics of current focus include
- autocorrelation of environmental exposures
- general features of time-dependent risk analysis
- ecological risk analysis for food chain models
- multispecies approaches to habitat conservation
- methods for assuring quality of Monte Carlo simulations
- assessing the validity of risk assessments
- remediation planning in a probabilistic framework
- risk communication
Exposure
autocorrelation
Contrary to what one might conclude from review of the mathematical expressions currently used in risk analysis, total exposure does not equal average daily exposure times days exposed. Suppose we are interested in estimating the probability distribution among exposed individuals of their total exposures over some time period. Using simple convolution (i.e., what @Risk or Crystal Ball does) with the distribution of toxicant concentrations and the distribution of individuals’ bodyweights leads to an answer whose variance can be grossly overestimated if exposures are iterated over the time period. The reason is that this calculation assumes that the magnitude of every exposure event through time is the same for an individual. In other words, if a person is given a small exposure once, then he will always experience exposures of the same size over the entire time period. This approach fails to appreciate that the toxicant concentration encountered may be different for different exposure events. When time periods are long, as they are for lifetime exposures needed in cancer risk assessments, the resulting error can be substantial. Even if the temporal autocorrelation among sequential exposures for an individual is exceedingly high (e.g., 0.99), sufficiently many iterations will eventually overwhelm the autocorrelation. The simplistic calculation is appropriate only if exposure events are perfectly correlated (which seems unlikely in most practical cases). Nevertheless, this approach has been almost universally used since exposure assessments have been conducted within the probabilistic framework. Several recent high-profile assessments have made this mistake. In most cases, the effect of the error is to very strongly overestimate the chance of large lifetime exposures. We need techniques that can be used to improve the estimate for the distribution of total exposure that do not require a full description of the autocorrelation function or an elaborate simulation of event-to-event variation in exposures.
Time-dependent risk analysis
Throughout its development as a science, human health risk analysis has consistently avoided facing the temporal aspects of the processes it models. This has led to the use of asymptotic or integrating models in many situations where time-dependent models would clearly be better. As a result, the field has never really developed the techniques necessary to make time-dependent risk analyses. The calculations of lifetime body burdens for environmental contaminants are almost surely wrong, and probably wrong by many orders of magnitude. We argue that intelligent decision making about environmental protection and regulation requires much better estimates that explicitly address the temporal processes involved. About ten years ago, conservation biologists faced this same technical problem in trying to estimate the risk of extinction with deterministic, asymptotic and time-dependent models. The predictions from the models are very different and, further, only the time-dependent model is correct. We need techniques and software for use in human health risk assessments that can explicitly handle the temporal dimension of risk.
Ecological risk analysis for food chains
Most of ecotoxicological risk assessment is performed at the individual level, with endpoints such as LC-50 and LD-50. Recently, assessments at the population and species levels have gained momentum as a result of accumulated information on the dynamics of well-studied target (or indicator) species. Risk assessment at the ecosystem level has always been a major topic of discussion and a long-term goal of applied ecology in general, and ecotoxicology in particular. However, quantitative assessments at the ecosystem level are hampered by a lack of detailed data on the interactions among species, coupled with the complexity of these interactions. We aim to bridge the gap between individual and ecosystem level assessments by using the available data in models of trophic chains that are simple enough to be parameterized with our current knowledge.
Our approach is to expand to the ecosystem level of ecological risk analysis at a level of complexity that is compatible with the current knowledge about the dynamics of food webs and with the available data on interactions in marine and freshwater communities. While it is relatively simple to construct food web models with hundreds, even thousands of species, models with this level of detail are not reliable due to the compounded uncertainty of the large number of species interactions (competition, predation, mutualism) that are poorly understood, and are difficult, if not impossible, to quantify. This complexity has hampered the application of ecosystem-level models to practical problems of ecological risk assessment. We propose that the first step towards building an ecosystem-level risk assessment methodology for aquatic systems should involve models of trophic chains composed of variables such as nutrients, toxicants, phytoplankton, zooplankton and fish. Aggregating whole trophic levels into single variables is undoubtedly a vast simplification, but it allows the estimation of model parameters based on available data, because of the fewer number of parameters necessary to model an aquatic system in sufficient detail.
Concentrations of toxicants are often not uniform throughout an ecosystem. For example, the discharge of a toxicant into a lake from a single point creates a distribution (sometimes called a "plume") that depends on physical characteristics of the system, and the chemical characteristics of the toxicant and the aquatic medium. Such distributions are often predicted with physical models (e.g., of fluid dynamics) with great spatial resolution, and can be incorporated into geographic information systems ( GIS). We propose to integrate such spatial data on the distribution of a toxicant into the ecological models. Different trophic levels of the ecological model would require these data in different resolutions. Whereas the spatial data may be used at a high resolution or the phytoplankton level, they may need to be "averaged" for the whole lake and marine ecosystem for the fish level. Thus, this step of the research will require developing the ecological models at different spatial scales.
Multispecies approaches to habitat conservation
There are several situations in which the suitability or ecological value of sites, parcels or regions from a multispecies perspective might be used in decision making and natural resource management. These include assessment of human impact, mitigation for impact, and management for biodiversity. The Endangered Species Act (ESA) of 1973 prohibits actions which might jeopardize the continued existence of threatened or endangered species. Commonly in response to this legislation, individuals or private companies set aside some of the site in question as a protected reserve while impacting the remaining area. Alternatively, a separate parcel may be purchased for conservation ("mitigation banking"), so that the entire site may be impacted. Therefore, methods to evaluate and rank the "value" of a particular site in terms of its ecological components are needed by utility companies, government agencies, private citizens, real-estate developers, companies specializing in resource extraction and conservation organizations. Due to limited funds for purchasing land conservationists are forced to choose what to protect. Such decisions focus on a single threatened or endangered species and its habitat requirements. While this approach works well for single-species protection, it is driven by the specific requirements of the focus or keystone species while ignoring those of other components of these ecosystems.
The proposed approach is based on the suitability of habitat for a list of species. For each species, the habitat suitability will be expressed as a raster (grid) map with values ranging from 0 (unsuitable) to 1 (most suitable). Habitat suitabilities are calculated based on the species habitat requirements such as a preference for a type of vegetation, proximity to bodies of water, size of home range or territory, type of soil required for optimal growth, etc. Estimating the habitat suitability usually involves statistically procedures which relate the presence of the species to various biological and geographical features or entities. Each of these individual maps can then be combined into a single aggregate map that expresses the worth, in conservation terms, of the site(s). The habitat suitability maps would be combined mathematically by using a weighted average of all of the maps.
This approach can be used in management in two ways. One is the assessment of the "conservation value" of predefined parcels for purposes of conservation planning or mitigation. These might be based on ownership boundaries and may include lands that are considered for purchase for protection, or lands that are subject to regulation or mitigation. Such pre-determined parcels may be valued by the sum of the multispecies habitat suitability values for all cells (points/pixels) within that parcel. The sum of habitat values takes into account both the size of the parcel (a larger parcel will have a higher sum, all other things being equal), and the quality of the habitat (a parcel with higher average of multi-species habitat quality will have a higher sum, all other things being equal).
Another use is in identifying patches or locations with high "multispecies habitat suitability", for purposes of reserve design. The combined map can be used to identify areas that are suitable for the collection of the species included in the analysis, using an algorithm to identify contiguous patches of high habitat suitability. Such patch-recognition algorithms have been developed by Applied Biomathematics.
Quality assurance of Monte Carlo methods
The straightforward application of risk analysis via Monte Carlo methods to environmental problems often yields underestimates of the chances of severe environmental consequences. There are two reasons for this: Firstly, risk analysis using Monte Carlo methods requires that the statistical distributions for the input variables be precisely specified even when empirical evidence supporting the particular choices is sparse. Secondly, analysts almost always simply assume variables are in dependent of one another even when they are obviously not (e.g., body mass and skin surface area in dermal exposure studies). Although methods to simulate correlations among variables exist, they are not sufficient for use in risk analysis and, in any case, are useless when the dependencies are not empirically well known.
The critical issue is not so much how wide the range of possible impacts might be, but rather whether the estimates of the risks are conservative or optimistic. A simple-minded application of Monte Carlo methods with default assumptions about input distributions and their correlations can yield results that are overly optimistic. They can underestimate the chances that a person will receive a large dose of some environmental toxicant, or the chances that an endangered species will go extinct.
Simple methods based on the notion of interval probabilities have recently been developed that can effect the calculations in a risk assessment without requiring the analyst to specify precise distributions or assume anything about the dependence among variables. This approach, called probability bounds analysis, can be used to conduct what are, in essence, quality assurance reviews of probabilistic risk assessments. Research is needed to demonstrate the workability of these methods on the kinds of analytical problems encountered by environmental risk assessors in both human health and (non-human) ecological risk analyses.
Assessing the validity of risk assessments
Increasingly, risk assessments are being made as an integral part of the justification for public policy decisions. These risk assessments are classic "gray literature" reports which rarely receive the public attention they might deserve. They probably do not get the professional scrutiny they deserve either. Part of the problem is that the assessments are usually complex documents, often multidisciplinary in scope. It is not unusual, for instance, for a single assessment to use methods and arguments from chemistry, geology, hydrology, physiology, toxicology, pharmacology, demography, ecology, statistics, and risk analysis. As a result, such assessments are beyond the training of any single reader.
There is a strong need for software tools that can be used to automatically review the calculations used in risk assessments. The idea is to extend the notion of a spell checker which uses a computer to make a preliminary review of a document and assess whether its contents pass certain rudimentary checks for consistency and syntax.
We’ve developed methods that will automatically check that the units and equations used in a calculation run stream balance dimensionally (the sine qua non of a valid assessment). In applications of this software, a shocking number of serious (indeed, fundamental) errors have been found in published and unpublished risk assessments. We’ve also described a battery of additional checks, many of which can be deployed in software to automatically review the assumptions made in ecological risk assessments. Given the growing complexity of risk assessments, it is likely that such software tools will become ever more indispensible.
Remediation planning in a probabilistic framework
Estimating a remediation target under a deterministic risk assessment is straightforward. For instance, if exposure is computed as environmental concentration times intake, then a permitted concentration can be computed as the permitted exposure divided by the intake. When the assessment is probabilistic, however, the estimation of cleanup targets that ensure subsequent risks will not exceed certain levels is much more difficult. Ordinary division under a Monte Carlo or Latin hypercube strategy yields a distribution that results in exposures being much larger than permitted. Solving the remediation planning problem in a probabilistic framework requires a special operation known as deconvolution. Unfortunately, the available algorithms for deconvolution are notoriously unstable numerically.
A new, potentially useful method based on probability bounds allows the calculation of extreme distributions for environmental concentration that are guaranteed to result in exposures no more extreme than permitted. Using such a method, the bounds on the permitted exposure need not be specified completely. Specifications may be simple constraints on the distribution, e.g., 95% of realized exposures should be no larger than X and the average realized exposure should be no larger than Y.
Risk
communication
Risk analysts have been notoriously poor at risk communication (explaining and justifying their analyses and conclusions to stakeholders and the public). Their seeming insensitivity to the interests, values and intuitions of nonprofessionals has led to several public relations disasters, including very well publicized controversies at superfund sites. While controversy can often be healthy in public policy debates, there can be no question that misunderstanding, mistrust and miscommunication are to be avoided.
Many policy analysts have suggested that humans are irrational when it comes to risks and consequently make self-defeating decisions both personally and in the public sphere. Psychometricians have long documented the "faults" of human perception with respect to probability, the most important of which are insensitivity to prior probabilities, insensitivity to sample size, overestimation (overestimation) of risks for conjunctive (disjunctive) events, and the fault of ‘availability’ by which recent news of an incidence can radically alter the perceived risk for an event.
Part of the problem certainly lies with the failure of risk analysts to understand how humans perceive and weigh risks and benefits. It is clear, for instance, that human evolution did not favor the development of an internal calculus suitable for evaluating joint probabilities of independent events. Humans seem to employ a ‘possibilistic’ rather than strictly probabilistic calculus for making decisions. Research is needed to delineate the features of the calculus which humans comprehend and use in their perceptions of risk.
