Predictive Bayesian Microbial Dose-Response Assessment Based on Suggested Self-Organization in Primary Illness Response: Cryptosporidium parvum

The probability of illness caused by very low doses of pathogens cannot generally be tested due to the numbers of subjects that would be needed, though such assessments of illness dose response are needed to evaluate drinking water standards. A predictive Bayesian dose-response assessment method was proposed previously to assess the unconditional probability of illness from available information and avoid the inconsistencies of confidence-based approaches. However, the method uses knowledge of the conditional dose-response form, and this form is not well established for the illness endpoint. A conditional parametric dose-response function for gastroenteric illness is proposed here based on simple numerical models of self-organized host-pathogen systems and probabilistic arguments. In the models, illnesses terminate when the host evolves by processes of natural selection to a self-organized critical value of wellness. A generalized beta-Poisson illness dose-response form emerges for the population as a whole. Use of this form is demonstrated in a predictive Bayesian dose-response assessment for cryptosporidiosis. Results suggest that a maximum allowable dose of 5.0 x 10(-7) oocysts/exposure (e.g., 2.5 x 10(-7) oocysts/L water) would correspond with the original goals of the U.S. Environmental Protection Agency Surface Water Treatment Rule, considering only primary illnesses resulting from Poisson-distributed pathogen counts. This estimate should be revised to account for non-Poisson distributions of Cryptosporidium parvum in drinking water and total response, considering secondary illness propagation in the population.     

A Bayesian Benefit-Risk Model Applied to the South Florida Building Code

A Bayesian compound Poisson benefit-risk model is described in this paper, and used to evaluate recent revisions to the South Florida Building Code (SFBC). The model accounts for natural variability in hurricane frequency and severity, and uncertainty in the effectiveness of the revised code. Ranges of residential growth rate, code effectiveness, construction cost increase, and planning period length are assumed, to show the ranges of cost-to-performance ratio within which the code will make sense economically. The expected cost of residential hurricane damage over 50 years for ten South Florida counties assuming continuation of previous building practices was $93 billion, equivalent to the residential damage of 5.2 Andrews. Assuming a reduction in the growth of damageable housing in South Florida from 5.5% to 2% as a result of code revision, estimated damages under the new code were $45 billion. At a per-house construction cost increase of 5%, the probability of at least recovering the estimated $40 billion cost of the specified wind-resistant construction was estimated to be 47%. Expected return on investment was estimated at $7 billion over 50 years. The expected return lies between a $44 billion loss and a $47 billion gain, when growth in damageable housing is allowed to range from 1% to 4% and construction cost increases are assumed to lie between 3% and 8%. Actual monetary return for a 5% cost increase and 2% growth in damageable housing ranges from a $20 billion loss to a $100 billion gain with 95% probability, as a result of weather variability alone. Results support SFBC revisions on solely economic grounds, a conclusion strengthened considerably in light of potentially avoided deaths and hurricane traumas. The model represents one approach to evaluating economic aspects of the sustainability of new technological measures on the basis of available information.     

The Evolution of Skill-Biased Effects on American Wages in the 1980s and 1990s

This study estimates the contributions of skill-biased technological change and international trade to the rise in the skill premium during the 1980s and 90s using the Feenstra and Hanson (Q J Econ 114(3):907–940, 1999) two-stage methodology. Newly available data on high-technology capital provide separate measures of computer and software investment. New estimates suggest that investment in software contributed to a substantial portion of the observed increase in the skill premium while investment in computers lead to a reduction in the rate of skill premium growth. Contrary to the findings of Feenstra and Hanson for the 1980s, neither software nor computers had a significant effect on wages during the 1980s. Foreign outsourcing does not appear to have significantly affected wages during the 1990s. The contribution to theory is that software is more complementary to increases in worker productivity due to human skills. Computers, on the other hand, reduced the growth of wage inequality by giving unskilled labor a more efficient set of tools with which to work.

A gradient Markov chain Monte Carlo algorithm for computing multivariate maximum likelihood estimates and posterior distributions: mixture dose-response assessment

Multivariate probability distributions, such as may be used for mixture dose‐response assessment, are typically highly parameterized and difficult to fit to available data. However, such distributions may be useful in analyzing the large electronic data sets becoming available, such as dose‐response biomarker and genetic information. In this article, a new two‐stage computational approach is introduced for estimating multivariate distributions and addressing parameter uncertainty. The proposed first stage comprises a gradient Markov chain Monte Carlo (GMCMC) technique to find Bayesian posterior mode estimates (PMEs) of parameters, equivalent to maximum likelihood estimates (MLEs) in the absence of subjective information. In the second stage, these estimates are used to initialize a Markov chain Monte Carlo (MCMC) simulation, replacing the conventional burn‐in period to allow convergent simulation of the full joint Bayesian posterior distribution and the corresponding unconditional multivariate distribution (not conditional on uncertain parameter values). When the distribution of parameter uncertainty is such a Bayesian posterior, the unconditional distribution is termed predictive. The method is demonstrated by finding conditional and unconditional versions of the recently proposed emergent dose‐response function (DRF). Results are shown for the five‐parameter common‐mode and seven‐parameter dissimilar‐mode models, based on published data for eight benzene–toluene dose pairs. The common mode conditional DRF is obtained with a 21‐fold reduction in data requirement versus MCMC. Example common‐mode unconditional DRFs are then found using synthetic data, showing a 71% reduction in required data. The approach is further demonstrated for a PCB 126‐PCB 153 mixture. Applicability is analyzed and discussed. Matlab^® computer programs are provided.     

Ecological and Economic Risk Analysis of Everglades: Phase I Restoration Alternatives

Evaluating alternatives for restoring the Everglades involves analysis of a complex ecological and economic system for which current knowledge is limited. Uncertain benefits and impacts are analyzed probabilistically in this paper, following otherwise accepted principles of net present value (NPV) analysis. Ecological benefits and impacts were considered in monetary terms. Probabilities for selected uncertain parameters were found by maximizing entropy. The first ecological risk conceptual model for the Everglades ecosystem was developed to show ecological interactions. "Current Plans" for restoration involve discharge of phosphorus-enriched water from artificial wetlands to relatively pristine Everglades marshes for 3–10 years, risking conversion of the ecosystem to a eutrophic cattail marsh. For two of the three areas studied, alternative "Bypass Plans" were shown to avoid the loss of up to 3000 acres of sawgrass marsh at a cost that is probabilistically justified by the value of the ecosystem preserved. Sensitivity of the results to projected ecological changes, eutrophic marsh valuation, natural marsh valuation, and future values as represented in the discount rate, was examined.     

A New Theoretical Discrete Growth Distribution with Verification for Microbial Counts in Water

Living microbes are discrete, not homogeneously distributed in environmental media, and the form of the distribution of their counts in drinking water has not been well established. However, this count may "scale" or range over orders of magnitude over time, in which case data representing the tail of the distribution, and governing the mean, would be represented only in impractically long data records. In the absence of such data, knowledge of the general form of the full distribution could be used to estimate the true mean accounting for low-probability, high-consequence count events and provide a basis for a general environmental dose-response function. In this article, a new theoretical discrete growth distribution (DGD) is proposed for discrete counts in environmental media and other discrete growth systems. The term growth refers not to microbial growth but to a general abiotic first-order growth/decay of outcome sizes in many complex systems. The emergence and stability of the DGD in such systems, defined in simultaneous work, are also described. The DGD is then initially verified versus 12 of 12 simulated long-term drinking water and short-term treated and untreated water microbial count data sets. The alternative Poisson lognormal (PLN) distribution was rejected for 2 (17%) of the 12 data sets with 95% confidence and, like other competitive distributions, was not found stable (in simultaneous work). Sample averages are compared with means assessed from the fitted DGD, with varying results. Broader validation of the DGD for discrete counts arising as outcomes of mathematical growth systems is suggested.     

Analytical Predictive Bayesian Assessment of Occupational Injury Risk: Municipal Solid Waste Collectors

Unlike other waste streams, municipal solid waste (MSW) is collected manually, and MSW collection has recently been found to be among the highest-risk occupations in the United States. However, as for other occupational groups, actual total injury rates, including the great majority of injuries not compensated and those compensated by other insurance, are not known. In this article a predictive Bayesian method of assessing total injury rates from available information without computation is presented, and used to assess the actual numbers of musculoskeletal and dermal injuries requiring clinical care of MSW workers in Florida. Closed-form predictive Bayesian distributions that narrow progressively in response to information, representing both uncertainty and variability, are presented. Available information included workers' compensation (WC) data, worker population data, and safety records for one private and one public collection agency. Subjective input comprised epidemiological and medical judgment based on a review of 165 articles. The number of injuries was assessed at 3,146 annually in Florida, or 54 +/- 18 injuries per 100 workers per year with 95% confidence. Further, WC data indicate that the injury rate is 50% higher for garbage collectors specifically, indicating a rate of approximately 80 per 100 workers. Results, though subject to uncertainty in worker numbers and classification and reporting bias, agreed closely with a survey of 251 MSW collectors, of whom 75% reported being injured (and 70% reported illness) within the past 12 months. The approach is recommended for assessment of total injury rates and, where sufficient information exists, for the more difficult assessment of occupational disease rates.     

Scale invariance of incident size distributions in response to sizes of their causes.

Incidents can be defined as low-probability, high-consequence events and lesser events of the same type. Lack of data on extremely large incidents makes it difficult to determine distributions of incident size that reflect such disasters, even though they represent the great majority of total losses. If the form of the incident size distribution can be determined, then predictive Bayesian methods can be used to assess incident risks from limited available information. Moreover, incident size distributions have generally been observed to have scale invariant, or power law, distributions over broad ranges. Scale invariance in the distributions of sizes of outcomes of complex dynamical systems has been explained based on mechanistic models of natural and built systems, such as models of self-organized criticality. In this article, scale invariance is shown to result also as the maximum Shannon entropy distribution of incident sizes arising as the product of arbitrary functions of cause sizes. Entropy is shown by simulation and derivation to be maximized as a result of dependence, diversity, abundance, and entropy of multiplicative cause sizes. The result represents an information-theoretic explanation of invariance, parallel to those of mechanistic models. For example, distributions of incident size resulting from 30 partially dependent causes are shown to be scale invariant over several orders of magnitude. Empirical validation of power law distributions of incident size is reviewed, and the Pareto (power law) distribution is validated against oil spill, hurricane, and insurance data. The applicability of the Pareto distribution, in particular, for assessment of total losses over a planning period is discussed. Results justify the use of an analytical, predictive Bayesian version of the Pareto distribution, derived previously, to assess incident risk from available data.     

The Discrete Weibull Distribution: An Alternative for Correlated Counts with Confirmation for Microbial Counts in Water

Distributions of pathogen counts in treated water over time are highly skewed, power‐law‐like, and discrete. Over long periods of record, a long tail is observed, which can strongly determine the long‐term mean pathogen count and associated health effects. Such distributions have been modeled with the Poisson lognormal (PLN) computed (not closed‐form) distribution, and a new discrete growth distribution (DGD), also computed, recently proposed and demonstrated for microbial counts in water (Risk Analysis 29, 841–856). In this article, an error in the original theoretical development of the DGD is pointed out, and the approach is shown to support the closed‐form discrete Weibull (DW). Furthermore, an information‐theoretic derivation of the DGD is presented, explaining the fit shown for it to the original nine empirical and three simulated (n = 1,000) long‐term waterborne microbial count data sets. Both developments result from a theory of multiplicative growth of outcome size from correlated, entropy‐forced cause magnitudes. The predicted DW and DGD are first borne out in simulations of continuous and discrete correlated growth processes, respectively. Then the DW and DGD are each demonstrated to fit 10 of the original 12 data sets, passing the chi‐square goodness‐of‐fit test (α= 0.05, overall p = 0.1184). The PLN was not demonstrated, fitting only 4 of 12 data sets (p = 1.6 × 10^?8), explained by cause magnitude correlation. Results bear out predictions of monotonically decreasing distributions, and suggest use of the DW for inhomogeneous counts correlated in time or space. A formula for computing the DW mean is presented.