Louis Anthony Tony Cox

University of Colorado | UCD · Department of Biostatistics and Informatics

Many government agencies and expert groups have estimated a dose-rate of perfluorooctanoate (PFOA) that would protect human health. Most of these evaluations are based on the same studies (whether of humans, laboratory animals, or both), and all note various uncertainties in our existing knowledge. Nonetheless, the values of these various, estimate...

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-o...

In 2022, the US EPA published an important risk assessment concluding that "Compared to the current annual standard, meeting a revised annual standard with a lower level is estimated to reduce PM2.5-associated health risks in the 30 annually-controlled study areas by about 7-9% for a level of 11.0 µg/m3… and 30-37% for a level of 8.0 µg/m3." These...

The decision biases discussed in previous chapters can distort cost-benefit evaluations of uncertain risks, leading to risk management policy decisions with predictably high retrospective regret. This chapter argues that well-documented decision biases encourage learning-aversion, or predictably sub-optimal learning and premature decision-making in...

Large-scale, geographically distributed, and long-term risks arise from diverse underlying causes ranging from pandemics to poverty to underinvestment in protecting against natural hazards or failures of sociotechnical, economic, and financial systems. Protecting against such large-scale risks poses formidable challenges for any theory of effective...

Decision analysis and risk analysis have grown up around a set of organizing questions: what might go wrong, how likely is it to do so, how bad might the consequences be, what should be done to maximize expected utility and minimize expected loss or regret, and how large are the remaining risks? In probabilistic causal models capable of representin...

How can and should epidemiologists and risk assessors assemble and present evidence for causation of mortality or morbidities by identified agents such as fine particulate matter or other air pollutants? As a motivating example, some scientists have warned recently that ammonia from the production of meat significantly increases human mortality rat...

Extreme and catastrophic events pose challenges for normative models of risk management decision making. They invite development of new methods and principles to complement existing normative decision and risk analysis. Because such events are rare, it is difficult to learn about them from experience. They can prompt both too little concern before...

Population attributable fraction (PAF), probability of causation, burden of disease, and related quantities derived from relative risk ratios are widely used in applied epidemiology and health risk analysis to quantify the extent to which reducing or eliminating exposures would reduce disease risks. This causal interpretation conflates association...

To close this book with a view toward the future, this chapter present a Socratic dialogue with ChatGPT, a large language model (LLM), about the causal interpretation of epidemiological associations between fine particulate matter (PM2.5) and human mortality risks. ChatGPT and similar AI conversational systems reflect common patterns of human reaso...

Exposure-response curves are among the most widely used tools of quantitative health risk assessment. This chapter argues that what they mean is importantly ambiguous at a fundamental conceptual and definitional level. They leave unanswered such fundamental questions as whether and by how much reducing exposure would change average population risks...

Findings from behavioral economics experiments and brain imaging studies in people and other primates and investigations of the interplay between emotions, attention, learning, and cognitive decision-making, are entering the main stream of popular science expositions and shedding new light on what it means to be human. How and why humans exhibit un...

How can decision analysts and risk analysts help to improve policy and decision-making when the correct probabilistic relation between alternative acts and their probable consequences is unknown? This practical challenge of risk management with model uncertainty arises in problems from preparing for climate change to managing emerging diseases to o...

This chapter turns to data science and analytics methods for improving decision-making and for using data and modeling to help overcome the psychological obstacles to accurate risk perception and belief formation discussed in Chap. 1. It continues Chap. 1’s survey of recent literature, summarizing key ideas from the following five books: Superforec...

For an AI agent to make trustworthy decision recommendations under uncertainty on behalf of human principals, it should be able to explain why its recommended decisions make preferred outcomes more likely and what risks they entail. Such rationales use causal models to link potential courses of action to resulting outcome probabilities. They reflec...

Risk analysis is largely about how to think more clearly and usefully about what actions to take when perceptions and understanding of the current situation are incomplete and consequences of different choices are uncertain. Suggestions for improving decision-making under uncertainty come from many sources, including the mathematical prescriptions...

Exposure-response curves are among the most widely used tools of quantitative health risk assessment. However, we propose that exactly what they mean is usually left ambiguous, making it impossible to answer such fundamental questions as whether and by how much reducing exposure by a stated amount would change average population risks and distribut...

Several recent news stories have alarmed many politicians and members of the public by reporting that indoor air pollution from gas stoves causes about 13% of childhood asthma in the United States. Research on the reproducibility and trustworthiness of epidemiological risk assessments has identified a number of common questionable research practice...

We present a Socratic dialogue with ChatGPT, a large language model (LLM), on the causal interpretation of epidemiological associations between fine particulate matter (PM2.5) and human mortality risks. ChatGPT, reflecting probable patterns of human reasoning and argumentation in the sources on which it has been trained, initially holds that "It is...

This paper summarizes recent insights into causal biological mechanisms underlying the carcinogenicity of asbestos. It addresses their implications for the shapes of exposure-response curves and considers recent epidemiologic trends in malignant mesotheliomas (MMs) and lung fiber burden studies. Since the commercial amphiboles crocidolite and amosi...

How can and should epidemiologists and risk assessors assemble and present evidence for causation of mortality or morbidities by identified agents such as fine particulate matter or other air pollutants? As a motivating example, some scientists have warned recently that ammonia from the production of meat significantly increases human mortality rat...

The Predictive Analytics Toolkit (PAT) was developed to facilitate use of new approach methodologies (NAMs) to predict health hazards and risks from chemicals. PAT is a user-friendly web application that integrates many R packages to enable development and testing of prediction models without any programming. We drew from the work of Ring et al. 20...

The Steering Committee of the Alliance for Risk Assessment (ARA) opened a call for scientists interested in resolving what appeared to be a conundrum in estimating of the half-life of perfluorooctanoate (PFOA) in humans. An Advisory Committee was formed from nominations received and a subsequent invitation led to the development of three small inde...

We argue that population attributable fractions, probabilities of causation, burdens of disease, and similar association-based measures often do not provide valid estimates or surrogates for the fraction or number of disease cases that would be prevented by eliminating or reducing an exposure because their calculations do not include crucial mechan...

Population attributable fraction (PAF), probability of causation, burden of disease, and related quantities derived from relative risk ratios are widely used in applied epidemiology and health risk analysis to quantify the extent to which reducing or eliminating exposures would reduce disease risks. This causal interpretation conflates association...

For an AI agent to make trustworthy decision recommendations under uncertainty on behalf of human principals, it should be able to explain why its recommended decisions make preferred outcomes more likely and what risks they entail. Such rationales use causal models to link potential courses of action to resulting outcome probabilities. They reflec...

Applying risk assessment and management tools to plutonium disposition is a long‐standing challenge for the U.S. government. The science is complicated, which has helped push risk assessment and management tools in new creative directions. Yet, communicating effectively about increasingly complicated risk‐science issues like plutonium disposition r...

Are dose–response relationships for benzene and health effects such as myelodysplastic syndrome (MDS) and acute myeloid leukemia (AML) supra-linear, with disproportionately high risks at low concentrations, e.g. below 1 ppm? To investigate this hypothesis, we apply recent mode of action (MoA) and mechanistic information and modern data science tech...

Causal inference regarding exposures to ambient fine particulate matter (PM2.5) and mortality estimated from observational studies is limited by confounding, among other factors. In light of a variety of causal inference frameworks and methods that have been developed over the past century to specifically quantify causal effects, three research tea...

This chapter applies Bayesian network (BN) learning methods and other techniques from Chap. 9 to the following health risk question: Does exposure to the metal molybdenum (Mo), as indicated by Mo concentrations in urine, reduce total testosterone (T) concentrations in blood serum of men, posing a potential risk to male fertility? Some recent papers...

Why have occupational safety regulations in the United States not been more successful in protecting worker health from mesothelioma risks, while apparently succeeding relatively well in reducing silicosis risks? This chapter seeks to apply insights from the simulation models developed in Chaps. 4 and 5 to address this important practical question...

Perhaps no other topic in risk analysis is more difficult, more controversial, or more important to risk management policy analysts and decision-makers than how to draw valid, correctly qualified conclusions from observational data. Chapters 1, 2, 7, and 8 have warned against the common practice of using statistical regression models in place of ca...

It has sometimes been proposed that supralinear dose-response functions—that is, dose-response functions in which low doses are disproportionately potent in causing harm—describe the risks from many well-studied public and occupational hazards including asbestos, benzene, lead, particulate air pollution, and ionizing radiation; and that this implie...

Concentration-response (C-R) functions relating concentrations of pollutants in ambient air to mortality risks or other adverse health effects provide the basis for many public health risk assessments, benefits estimates for clean air regulations, and recommendations for revisions to existing air quality standards (Schwartz et al. 2002). The assump...

Chapter 1 noted that expert judgments about causality are widely used in current regulatory risk assessment and policy making. They are often expressed within a weight-of-evidence (WoE) framework, with causal determination categories being used to summarize huge amounts of complex evidence and to help inform and drive major regulatory decisions. Th...

Applied science is largely about how to use observations to learn, express, and verify predictive generalizations—causal laws stating that if certain antecedent conditions hold, then certain consequences will follow. Non-deterministic or incompletely known causal laws may only determine conditional probabilities or occurrence rates for consequences...

How can scientists and risk assessors best communicate with each other, the media, the public, and policy makers what is known, what is guessed, and what is still unknown or uncertain about how changes in air pollution affect human mortality? Current practice includes emphatic pronouncements, striking headlines, and colorful infographics about deat...

This chapter begins an investigation that occupies the rest of the book: examining how the causal analysis methods discussed in Part 2, along with the methodological points about interpretation of regression coefficients raised in earlier chapters, especially Chaps. 1, 2, 7, and 8, can be applied to the important public health topic of health risks...

This chapter examines how the Bayesian network (BN) learning and analysis methods discussed I Chap. 9 can help to meet several methodological challenges that arise in interpreting significant regression coefficients in exposure-response regression modeling. As a motivating example, consider the challenge of interpreting positive regression coeffici...

Associations between fine particulate matter (PM2.5) exposure concentrations and a wide variety of undesirable outcomes are routinely reported. Adverse outcomes associated with PM2.5 range from autism, auto theft, and COVID-19 mortality to elderly mortality, suicide, and violent crime. Many influential articles argue that reducing National Ambient...

Chapter 3 pointed out that chronic inflammation mediates an extraordinarily wide range of diseases. Recent progress in understanding intracellular inflammasome assembly, priming, activation, cytokine signaling, and interactions with mitochondrial reactive oxygen species (ROS), lysosome disruption, cell death, and prion-like polymerization and sprea...

This is the first of four chapters that explain and apply the dynamic simulation approach to health risk assessment modeling introduced in Chap. 2. The exposition in this chapter is motivated by an observation made by toxicologist Julie Goodman of Gradient, who coauthored the article on which this chapter is based (Cox Jr et al. 2020): most of the...

Chapter 2 suggested that dynamic simulation models, Bayesian networks, and causal analysis can add value to statistical regression modeling for understanding causal exposure concentration-response (C-R) relationships well enough to predict how changes in exposure would affect health risks—a task that typically requires causal insights that regressi...

This chapter extends to spatial statistics the main theme from Chap. 7: that positive exposure-response coefficients in regression models are not valid substitutes for quantitative risk assessment, because statistical coefficients do not usually reveal causal relationships. Many recent health risk assessments have noted that adverse health outcomes...

An aim of applied science in general and of epidemiology in particular is to draw sound causal inferences from observations. For public health policy analysts and epidemiologists, this includes drawing inferences about whether historical changes in exposures have actually caused the consequences predicted for, or attributed to, them. The example of...

Chapter 13 established that income is an important confounder of some air pollution-associated health effects: low income increases health risks and is also associated with living in areas having higher air pollution levels. This raises the public health question: would reducing air pollution levels without addressing the other correlates of low in...

Can a single fiber of amphibole asbestos increase the risk of lung cancer or malignant mesothelioma (MM)? Traditional linear no-threshold (LNT) risk assessment assumptions imply that the answer is yes: there is no safe exposure level. This chapter draws on recent scientific progress in inflammation biology, especially elucidation of the activation...

Recent advances in understanding of biological mechanisms and adverse outcome pathways for many exposure-related diseases show that certain common mechanisms involve thresholds and nonlinearities in biological exposure concentration-response (C-R) functions. These range from ultrasensitive molecular switches in signaling pathways, to assembly and a...

This book highlights quantitative risk assessment and modeling methods for assessing health risks caused by air pollution, as well as characterizing and communicating remaining uncertainties. It shows how to apply modern data science, artificial intelligence and machine learning, causal analytics, mathematical modeling, and risk analysis to better...

Do faster slaughter line speeds for young chickens increase risk of Salmonella contamination? We analyze data collected in 2018–2019 from 97 slaughter establishments processing young chickens to examine the extent to which differences in slaughter line speeds across establishments operating under the same inspection system explain observed differen...

Decision analysis and risk analysis have grown up around a set of organizing questions: what might go wrong, how likely is it to do so, how bad might the consequences be, what should be done to maximize expected utility and minimize expected loss or regret, and how large are the remaining risks? In probabilistic causal models capable of representin...

We examine how Bayesian network (BN) learning and analysis methods can help to meet several methodological challenges that arise in interpreting significant regression coefficients in exposure-response regression modeling. As a motivating example, we consider the challenge of interpreting positive regression coefficients for blood lead level (BLL)...

In the first half of 2020, much excitement in news media and some peer reviewed scientific articles was generated by the discovery that fine particulate matter (PM2.5) concentrations and COVID-19 mortality rates are statistically significantly positively associated in some regression models. This article points out that they are non-significantly n...

As part of the celebration of the 40th anniversary of the Society for Risk Analysis and Risk Analysis: An International Journal , this essay reviews the 10 most important accomplishments of risk analysis from 1980 to 2010, outlines major accomplishments in three major categories from 2011 to 2019, discusses how editors circulate authors’ accomplish...

Recent advances in understanding of biological mechanisms and adverse outcome pathways for many exposure-related diseases show that certain common mechanisms, from ultrasensitive molecular switches in signaling pathways to assembly and activation of inflammasomes to rupture of lysosomes and pyroptosis of cells, involve thresholds and nonlinearities...

Virginiamycin (VM), a streptogramin antibiotic, has been used to promote healthy growth and treat illnesses in farm animals in the United States and other countries. The combination streptogramin Quinupristin‐Dalfopristin (QD) was approved in the United States in 1999 for treating patients with vancomycin‐resistant Enterococcus faecium (VREF) infec...

Inflammasomes are a family of pro-inflammatory signaling complexes that orchestrate inflammatory responses in many tissues. The NLRP3 inflammasome has been implicated in several diseases associated with chronic inflammation. In this paper, we present an Adverse Outcome Pathway (AOP) for NLRP3-induced chronic inflammatory diseases that demonstrates...

This commentary adds to a lively discussion of causal modeling, reasoning and inference in the recent epidemiologic literature. We focus on fundamental philosophical and logical principles of causal reasoning in epidemiology, raising important points not emphasized in the recent discussion. To inform public health decisions that require answers to...

Can a single fiber of amphibole asbestos increase the risk of lung cancer or malignant mesothelioma (MM)? Traditional linear no-threshold (LNT) risk assessment assumptions imply that the answer is yes: there is no safe exposure level. This paper draws on recent scientific progress in inflammation biology, especially elucidation of the activation th...

Recent progress in uderstanding of hematopoiesis includes new insights into the kinetics, properties, regulation, and heterogeneity of hematopoietic stem cells (HSCs); better understanding of the molecular biology of immune and cytokine networks and of the complex roles of the stem cell niche in regulating hematopoiesis; interactions of cytokines a...

Why have occupational safety regulations in the United States not been more successful in protecting worker health from mesothelioma risks, while apparently succeeding relatively well in reducing silicosis risks? This paper briefly discusses biological bases for thresholds and nonlinearities in exposure-response functions for respirable crystalline...

In most areas of applied research, sound science entails use of clear definitions, explicit derivations of conclusions, reproducible tests of predictions against observations, and careful qualification of causal interpretations and conclusions to acknowledge remaining ambiguities or conflicts in evidence. I propose that these same principles should...

A proposed matrix bridging between the results supplied by epidemiologists and those demanded by risk assessors proposes that a key piece of information sought by risk assessors is the shape of the exposure-response curve (e.g., linear vs. nonlinear, threshold vs. no threshold, etc.). This comment emphasizes that there are several different exposur...

Rational decisions seek to cause preferred outcomes by selecting actions or policies that make them more likely. Decision optimization models therefore typically include causal models of how outcome probabilities depend on the decision maker's choices, as well as on other direct causes such as the uncontrollable state of nature – a catchall term fo...

Advanced test systems and knowledge of biology, how chemical exposures occur, and the mechanisms, pathways and dose-dependent changes that can lead to toxicity are rapidly catalyzing the transformation away from traditional approaches to new approach methodologies for predicting potential hazards and risks. The explicit incorporation of inference m...

Holistic expert judgments about causality are widely used in regulatory risk assessments, with causal determination categories being used to summarize huge amounts of complex evidence and to help inform and drive major regulatory decisions. The causal determination categories used typically cover a relatively narrow range (e.g., from “causal relati...

Causal graph models such as causal Bayesian networks and influence diagrams are highly useful for describing how the probability distributions of some variables depend on the values of others; predicting the values of as‐yet unobserved variables from the values of observed ones; forecasting how changes in current controllable actions, decisions, or...

Time‐series forecasting models that extrapolate future values of variables from past ones are often limited by their inability to anticipate how the relation between past and future values will change if new interventions or policy changes are undertaken. Since one of the chief purposes of prediction and forecasting is to guide present choices amon...

Chronic inflammation mediates an extraordinarily wide range of diseases. Recent progress in understanding intracellular inflammasome assembly, priming, activation, cytokine signaling, and interactions with mitochondrial reactive oxygen species, lysosome disruption, cell death, and prion-like polymerization and spread of inflammasomes among cells, h...

How can scientists and risk assessors best communicate with each other, the media, the public, and policy makers what is known, what is guessed, and what is still unknown or uncertain about how changes in air pollution affect human mortality? Current practice includes emphatic pronouncements, striking headlines, and colorful infographics about deat...

Perhaps no other topic in risk analysis is more difficult, more controversial, or more important to risk management policy analysts and decision-makers than how to draw valid, correctly qualified causal conclusions from observational data. Statistical methods can readily quantify associations between observed variables using measures such as relati...

How does risk of heart disease depend on age, sex, smoking, income, education, marital status, and outdoor concentrations of fine particulate matter (PM2.5)? We join data available from the Centers for Disease Control and Prevention (CDC) Behavioral Risk Factor Surveillance (BRFSS) System for years 2008-2012 to US Environmental Protection Agency (E...

Chapters 8 and 10 have introduced important themes of evaluation analytics: discovering through independent replication of previous work (Chap. 8) and by applying new methods such as modern predictive and causal analytics algorithms to previously collected observational data (Chap. 10) whether published claims are reproducible and whether predicted...

The descriptive, causal, predictive, and evaluation analytics illustrated in Chaps. 3– 11 are largely about risk assessment. That is, they are about quantifying how large risks are now; predicting how much smaller they would become if costly interventions were undertaken (e.g., shifting pigs from closed to open production or further reducing air po...

This is the first of four chapters emphasizing the application of descriptive analytics to characterize public and occupational health risks. Much of risk analysis addresses basic descriptive information: how big is a risk now, how is it changing over time or with age, how does it differ for people or situations with different characteristics, on w...

An aim of applied science in general, and of epidemiology in particular, is to draw sound causal inferences from observations. For public health policy analysts and epidemiologists, this includes drawing inferences about whether historical changes in exposures have actually caused the consequences predicted for, or attributed to, them. The example...

Over the past half century, an enduring intellectual and technical challenge for risk analysts, statisticians, toxicologists, and experts in artificial intelligence, machine-learning and bioinformatics has been to predict in vivo biological responses to realistic exposures, with demonstrably useful accuracy and confidence, from in vitro and chemica...

As explained in Chap. 2, mechanistic causal models of how effects propagate through a system typically require more detailed information to build and validate than other forms of causal analysis, including predictive and attributive causal modeling. Substantial applied and computational mathematical research, modeling, and algorithm development is...

It is an important truism that association is not causation. For example, people living in low-income areas may have higher levels of exposure to an environmental hazard and also higher levels of some adverse health effect than people living in wealthier areas. Yet this observed association, no matter how strong, consistent, statistically significa...

Describing quantitatively how large a risk is provides crucial information for helping to set risk management priorities. This chapter applies descriptive analytics to assess the size of the human health risks from a particular source. It continues the theme begun in Chap. 5 of examining human health risks from antibiotic-resistant infectious bacte...

Three classic pillars of risk analysis are risk assessment (how big is the risk and how sure can we be?), risk management (what shall we do about it?), and risk communication (what shall we say about it, to whom, when and how?). Chapter 1 proposed two complements to these: risk attribution (who or what addressable conditions actually caused an acci...

Countless books and articles on data science and analytics discuss descriptive analytics, predictive analytics, and prescriptive analytics. An additional analytics area that is much less discussed links this world of analytics, with its statistical model-based descriptions and predictions, to the world of practical decisions in which actions have c...

This chapter continues to consider questions of applied benefit-cost analysis and effective risk management, building on themes introduced in the previous two chapters. It expands the scope of the discussion to include a law-and-economics perspective on how different institutions—regulatory and judicial—involved in societal risk management can best...

This is the first of two chapters that apply predictive analytics to two very different risk prediction problems. As in the previous two chapters, the challenge in this one is to estimate human health risks from a pathogen in swine using a combination of plausible conservative estimates of relevant risk factors and probabilistic simulation. However...

This final chapter considers the challenging question of how much each generation should invest in building resilient infrastructure to protect against possible future natural disasters. If such disasters are infrequent, members of each generation may be tempted to defer investments in resilience and protective infrastructure (e.g., in building or...