Causal Analytics for Applied Risk Analysis Louis Anthony Cox, Jr

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Part 2

Descriptive Analytics in Public and Occupational Health

Chapter 3

Descriptive Analytics for Public Health: Socioeconomic and Air Pollution Correlates of Adult Asthma, Heart Attack, and Stroke Risks
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 what factors does it depend, with what other risks or characteristics does it cluster? Such questions arise not only for public and occupational health and safety risks, but also for risks of failures or degraded performance in engineering infrastructure or technological systems, financial systems, political systems, or other “systems of systems” (Guo and Haimes, 2016). Simply knowing how large a risk is now and whether it is increasing, staying steady, or decreasing may be enough to decide whether a proposed costly intervention to reduce it is worth considering further. This chapter shows how to use basic tools of descriptive analytics, especially interaction plots (showing the conditional expected value of one variable at different levels of one or more other variables), together with more advanced methods from Chapter 2, such as regression trees, partial dependence plots, Bayesian networks (BNs), to describe risks and how they vary with other factors. A brief discussion and motivation of these methods is given for readers who have skipped Chapter 2. Chapter 4 introduces additional descriptive techniques, including plots that use non-parametric regression to pass smooth curves or surfaces through data clouds. It shows how they can be used, together with simple mathematical analysis, to resolve a puzzle that has occasioned some debate among toxicologists: that some studies have concluded that workers form disproportionately high levels of benzene metabolites at very low occupational exposure concentrations compared to higher concentrations, while other studies conclude that metabolism of benzene at low concentrations is approximately linear, and proportional to concentrations in inhaled air. Chapter 5 emphasizes the value of descriptive plots, upper-bounding analyses, and qualitative assumptions, as well as more quantitative risk assessment modeling, in bounding the size of human health risks from use of antibiotics in food animals. Chapter 6 calculates plausible bounds on the sizes of the quantitative risks to human health of infection with a drug-resistant “super-bug” from swine farming operations. Together, these chapters illustrate how descriptive analytics can be used to obtain and present useful quantitative characterizations of human health risks despite realistic scientific uncertainties about the details of relevant causal processes.

Asthma in the United States is an important public health issue. Many physicians, regulators, and scientists have expressed concern that exposures to criterion air pollutants have contributed to a rising tide of asthma cases and symptoms. The following sections describe associations between self-reported asthma experiences and various socioeconomic factors in survey data, as well as pollution data from other sources. Interaction plots are used to investigate and visualize statistical associations among variables. We then apply Bayesian network learning algorithms and other non-parametric machine-learning algorithms to further describe these statistical dependencies and to clarify possible causal interpretations. Associations with self-reported heart attack and stroke experience confirm that well-established relations between smoking and heart attack or stroke risks are seen in this data set (Shah and Cole, 2010; Oliveira et al., 2007).

Readers with limited interest in asthma, stroke, and heart attack risks may skim the rest of this chapter without impairing understanding of subsequent chapters. However, we recommend looking at the figures, as they illustrate the use of interaction plots and other diagrams to show how risks cluster and how they vary with other factors. A brief summary of the empirical findings is that self-reported heart attack and stroke experience are positively associated with each other and with self-reported asthma risks. Intriguingly, young divorced women with low incomes are at greatest risk of asthma, especially if they are ever-smokers. Income is an important confounder of other relations. (For example, in logistic regression modeling, PM2.5 is positively associated (p < 0.06) with both stroke risk and heart attack risk when these are regressed only against PM2.5, sex, age, and ever-smoking status, but not when they are regressed against these variables and income.) In this data set, PM2.5 is significantly negatively associated with asthma risk in regression models, with a10 g/m3 decrease in PM2.5 corresponding to about a 6% increase in the probability of asthma, possibly because of confounding by smoking, which is negatively associated with PM2.5 and positively associated with asthma risk. A variety of non-parametric methods are used to quantify these associations and to explore potential causal interpretations.
Data Sources

To investigate the association between air pollutants (O3 and PM2.5) and self-reported adult asthma, stroke, and heart attack risks, we merged the following data sources: (a) The most recent 5 years of available survey response data from a survey of over 228,000 individuals from 15 states, retrieved from the Center for Disease Control and Prevention (CDC) Behavioral Risk Factor Surveillance (BRFSS) System (; and (b) Environmental Protection Agency (EPA) data on O3 and PM2.5 concentrations for the counties in which these individuals lived at the time of the survey, retrieved from the US EPA web site ( Counties were used as the common key for merging annual average air pollution levels with individual response data. Table 3.1 summarizes the number of individual responses from each state for each of several questions. These responses are coded so that a response of “Yes” has a value of 1 and a value of “No” has a value of zero. Other responses, or non-responses, are coded as missing data. Thus, for example, 38% of the 8618 respondents from Arizona were male (giving a mean value of 0.38 to the variable “Sex = Male” (henceforth abbreviated as “Sex”) with values of 1 for men and 0 for women). As suggested by this example, the respondents in the BRFSS do not constitute a simple random sample of the population. The BRFSS survey supplies county weights for reweighting responses to better reflect the entire population. However, this chapter does not seek to extrapolate relations outside the surveyed population, but focuses on quantifying conditional relations within this sample, e.g., studying how probability of asthma varies by age and sex and other variables, without considering how to adjust for differences between the joint frequency distribution of these variables in the survey population and in the more general population.

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