Causal versus spurious spatial exposure–response associations in health risk analysis

Figures & data

Table 1. Examples of spatial associations for various diseases.

Source	Effect	Attribution method and reference
Municipal solid waste incinerators in four French administrative departments	Cancer morbidity	GAM and Bayesian hierarchical models of association between cancer risk and an index of estimated exposure derived from dispersion modeling assumptions. “GAM models were fitted. For all the localizations of cancer studied with the exception of lung cancer in men, a nearly linear association between the risk of cancer and the index of exposure to incinerators was observed” (Goria et al., 2009).
Spanish paper and board industries which report their emissions to the European Pollutant Emission Register (EPER)	Lung cancer mortality	“This was an ecological study that modelled the Standardised Mortality Ratio (SMR) for lung cancer in 8073 Spanish towns over the period 1994–2003. Population exposure to industrial pollution was estimated on the basis of distance from town of residence to pollution source. An exploratory, near-versus-far analysis was conducted, using mixed Poisson regression models and an analysis of the effect of municipal proximity within a 50-kilometre radius of each of the 18 installations. Results varied for the different facilities. In two instances there was an increasing mortality gradient with proximity to the installation, though this was exclusively observed among men” (Monge-Corella et al., 2008).
Spanish industrial installations that are governed by the Integrated Pollution Prevention and Control (IPPC) Directive and the European Pollutant Release and Transfer Register Regulation	Pleural cancer mortality	“Analysis showed statistically significant RRs in both sexes in the vicinity [defined as <2 km] of 7 of the 24 industrial groups studied …These results support that residing in the vicinity of IPPC-registered industries that release pollutants to the air constitutes a risk factor for pleural cancer” (López-Abente et al., 2012).
Power plants in Spain	Lung, laryngeal and bladder cancer	“Ecological study designed to model sex-specific standardized mortality ratios … Population exposure to pollution was estimated on the basis of distance from town of residence to pollution source. Using mixed Poisson regression models … excess mortality … was detected in the vicinity [defined as within 5 km] of pre-1990 installations for lung cancer(1.066, 1.041–1.091 in the overall population; 1.084, 1.057–1.111 in men), and laryngeal cancer among men (1.067, 0.992–1.148)” (García-Pérez et al., 2009).
Spanish metal industries included in the EPER	Leukemia-related mortality	Similar in design to previous paper by the same authors (García-Pérez et al., 2010).
Ultramafic rock deposits	Mesothelioma	Pan et al. “Logistic regression analysis from a subset of 1133 mesothelioma cases and 890 control subjects with pancreatic cancer showed that the odds of mesothelioma decreased approximately 6.3% for every 10 km farther from the nearest ultramafic deposit (a putative source of asbestos), an odds ratio of 0.937 (95% confidence interval = 0.895–0.982), adjusted for age, sex, and occupational exposure to asbestos” (Pan et al., 2005).
Spanish metal industries	Prostate cancer mortality	Extended standard Poisson regression model with a multiplicative non-linear function to model effect of distance from an industrial facility, assuming an elevated risk close to the source and not at large distance. Concluded there was “evidence of association between the spatial distribution of prostate cancer mortality aggregated by census tracts and proximity to metal industrial facilities located within the area, after adjusting for socio-demographic characteristics at municipality level” (Ramis et al., 2011).
Air pollution	Children’s asthma	“The distance from a point source to the subject's residence area represented a surrogate exposure measurement. Odds ratios for a 1-km decrease in distance were obtained by conditional logistic regression. Risk of asthma attack was associated with residing near a grain mill (odds ratio (OR) = 1.35), petroleum refinery (OR = 1.44), asphalt plant (OR = 1.23), or power plant (OR = 1.28) (all p's < 0.05). Residence near major air emissions sources (>100 tons/year) increased asthma attack risk by 108% (p < 0.05). These results showed that proximity to some air pollution sources is associated with increased risks of asthma attacks” (Loyo-Berrios et al., 2007).

Table 2. Methods for testing causal hypotheses.

Method and references	Basic idea	Appropriate study design
Conditional independence tests (Freedman, 2004; Friedman & Goldszmidt, 1998)	Is hypothesized effect statistically independent of other (“ancestor”) variables, given values of hypothesized direct causes (“parents”) in causal graph model? If so, this strengthens causal interpretation. Example: Is dependence of disease risk on location explained by variations in measured exposures at different locations? Is hypothesized effect statistically independent of hypothesized cause, given values of other variables? If so, this undermines causal interpretation. Example: Does effect of exposure on disease risk disappear after accounting for education and income?	Cross-sectional data Can also be applied to multi-period data (e.g. in dynamic Bayesian networks)
Panel data analysis (Angrist & Pischke, 2009; Stebbings, 1978)	Are changes in exposures followed by changes in the effects that they are hypothesized to help cause? If not, this undermines causal interpretation; if so, this strengthens causal interpretation. Example: Are changes in air pollutant levels in different cities followed (but not preceded) by corresponding changes in respiratory mortality rates?	Panel data study: Collect a sequence of observations on same subjects or units over time
Granger causality test (Eichler & Didelez, 2010)	Does the history of the hypothesized cause improve ability to predict the future of the hypothesized effect? If so, this strengthens causal interpretation; otherwise, it undermines causal interpretation. Example: Can daily mortality rates in different cities be predicted better from time series histories of daily pollutant levels and mortality rates than from the time series history of daily mortality rates alone?	Time series data on hypothesized causes and effects
Quasi-experimental design and analysis (Campbell & Stanley, 1966)	Can control groups and other comparisons refute alternative (non-causal) explanations for observed associations between hypothesized causes and effects? For example, can coincident trends and regression to the mean be refuted as possible explanations? If so, this strengthens causal interpretation.	Longitudinal observational data on subjects exposed and not exposed to interventions that change the hypothesized cause(s) of effects.
Intervention analysis, change point analysis (Gilmour et al., 2006; Helfenstein, 1991)	Does the best-fitting model of the observed data change significantly at or following the time of an intervention? If so, this strengthens causal interpretation. Do the quantitative changes in hypothesized causes predict and explain the subsequently observed quantitative changes in hypothesized effects? If so, this strengthens causal interpretation. Example: Do cardiovascular disease mortality rates fall significantly faster in cities that banned smoking in public areas than in cities that did not, with the rate of decrease jumping after the ban in each case?	Time series observations on hypothesized effects, and knowledge of timing of intervention(s) Quantitative time series data for hypothesized causes and effects
Counterfactual and potential outcome models (Moore et al., 2012; Robins et al., 2000;)	Do exposed individuals have significantly different response probabilities than they would have had if they had not been exposed? Example: Do inhabitants of a city which bans coal-burning have lower mortality risk after the ban than they would have had without it?	Cross-sectional and/or longitudinal data, with selection biases and feedback among variables allowed
Causal network models of change propagation (Dash & Druzdzel, 2008; Hack et al., 2010)	Do changes in exposures (or other causes) create a cascade of changes through a network of causal mechanisms (represented by equations), resulting in changes in the effect variables? Example: Do relatively large variations in daily levels of fine particulate matter (PM2.5) air pollution create corresponding variations in markers of oxidative stress in the lungs?	Observations of variables in a dynamic system out of equilibrium
Negative controls (for exposures or for effects) (Lipsitch et al., 2010)	Do exposures predict health effects better than they predict effects that cannot be caused by exposures? Example: Does being vaccinated against influenza have a stronger association with reduction in influenza hospitalizations than with reduction in trauma hospitalizations? Are hospitalizations reduced more during flu season than before or after flu season? If not, then the association may reflect biases or confounding (e.g. perhaps relatively low-risk patients are more likely to be vaccinated).	Observational studies

Figure 1. Ultramafic rock deposits in California (southern part, truncated in this figure, has no deposits).

Table 3. Traffic fatality rates depend on distance from ultramafic rock.

	Regression summary for dependent variable: TRAFFICALL RATE (2000 Data By Extended Tract. R = 0.42525247; R^2= 0.18083966; Adjusted R^2= 0.18025812; F(5,7043) = 310.97; p < 0.0000; Std.Err. of estimate: 59.452)
N = 7049	b*	Std.Err. of b*	b	Std.Err. of b	t(7043)	p Value
Intercept			92.01	1.54	59.6	0.000000
UM1	−0.04	0.07	−0.09	0.15	−0.6	0.562355
UM2	−1.71	0.21	−3.75	0.45	−8.4	0.000000
UM3	2.19	0.24	4.84	0.52	9.3	0.000000
UM4	0.34	0.13	0.76	0.29	2.7	0.008008
UM5	−0.69	0.02	−0.81	0.03	−29.6	0.000000

Table 4. Multivariate regression model for traffic fatalities within 50 km of ultramafic rock.

	Regression summary for dependent variable: TRAFFICALL RATE, UM1 <50 km; R = 0.51 R2 = 0.26 Adjusted R^2= 0.26
N = 4942	b*	Std.Err. of b*	b	Std.Err. of b	t(4937)	p Value	Valid N
PopDensity	−0.43	0.01	−0.00	0.00	−33.1	0.000000	4948
UM1	−0.09	0.01	−0.37	0.05	−7.0	0.000000	4948
Pop65 + Pov	0.08	0.01	0.14	0.02	6.4	0.000000	4948
pBlueCollar	0.37	0.01	135.94	4.75	28.6	0.000000	4948
Intercept			83.10	2.18	38.1	0.000000

Table 5. Multivariate regression model traffic fatalities within 10 km of ultramafic rock.

	Regression summary for dependent variable: TRAFFICALL RATE R = 0.48; R^2= 0.23; Adjusted R^2= 0.23 Include condition: UM1 < 10 km
N = 1616	b*	Std.Err. of b*	b	Std.Err. of b	t(1611)	p Value
Intercept			52.23	4.31	12.1	0.000000
UM1	0.05	0.02	1.26	0.54	2.3	0.019075
pBlueCollar	0.33	0.02	129.60	8.86	14.6	0.000000
Pop65 + Pov	0.11	0.02	0.19	0.04	4.7	0.000002
PopDensity	−0.33	0.02	−0.00	0.00	−14.1	0.000000

Table 6. Relative risk of Kaposi’s sarcoma (relative to pancreatic cancer) decreases with distance from nearest ultramafic rock deposit (UM1), for UM1 <10 km.

	Regression summary for dependent variable: KS: PANC ratio R = 0.69; R^2= 0.47; Adjusted R^2= 0.475 Include condition: UM1 < 10 km
N = 1616	b*	Std.Err. of b*	b	Std.Err. of b	t(1611)	p Value
Intercept			0.14	0.01	23.1	0.000000
UM1	−0.27	0.02	−0.01	0.00	−14.4	0.000000
pBlueCollar	−0.20	0.02	−0.13	0.01	−10.5	0.000000
Pop65 + Pov	0.10	0.02	0.00	0.00	5.2	0.000000
PopDensity	0.49	0.02	0.00	0.00	25.0	0.000000

Table 7. Relative risk of Kaposi’s sarcoma (relative to pancreatic cancer) increases with distance from nearest ultramafic rock deposit (UM1).

	Regression summary for dependent variable: KS: PANC ratio R = 0.51; R^2= 0.26; Adjusted R^2= 0.26
N = 7049	b*	Std.Err. of b*	b	Std.Err. of b	t(7044)	p Value
Intercept			0.08	0.00	43.1	0.000000
UM1	0.11	0.01	0.00	0.00	10.3	0.000000
pBlueCollar	−0.23	0.01	−0.08	0.00	−21.0	0.000000
Pop65 + Pov	0.06	0.01	0.00	0.00	5.5	0.000000
PopDensity	0.51	0.01	0.00	0.00	47.3	0.000000

Figure 2. Non-parametric regression of traffic fatality rates versus UM1.

Figure 3. Non-parametric regression of Kaposi’s sarcoma-to-pancreatic cancer incidence counts ratio (KS:PANC) versus UM1 shows different associations at different distances.

Figure 4. Non-parametric regression of mesothelioma rate versus UM1 shows different associations at different distances.

Figure 5. Non-parametric regression of mesothelioma-to-pancreatic cancer incidence count ratio (MESO:PANC) versus UM1 shows different associations at different distances.

Table 8. Multivariate model for traffic fatalities versus distance from the centroid of data.

	Regression summary for dependent variable: TRAFFICALL RATE R = 0.51; R^2= 0.26; Adjusted R^2= 0.26
N = 7049	b*	Std.Err. of b*	b	Std.Err. of b	t(7043)	p Value
Intercept			59.04	2.67	22.1	0.000000
UM1	0.08	0.01	0.18	0.02	8.1	0.000000
pBlueCollar	0.35	0.01	129.39	4.03	32.1	0.000000
Pop65 + Pov	0.08	0.01	0.15	0.02	7.9	0.000000
PopDensity	−0.42	0.01	−0.00	0.00	−38.8	0.000000
Distance from centroid	0.09	0.01	5.40	0.64	8.5	0.000000

Table 9. Multivariate model for Kaposi’s sarcoma versus distance from the centroid of data.

	Regression summary for dependent variable: KSALL RATE R = 0.51; R^2= 0.26; Adjusted R^2= 0.26
N = 7049	b*	Std.Err. of b*	b	Std.Err. of b	t(7043)	p Value
Intercept			7.10	0.29	24.5	0.000000
UM1	0.10	0.01	0.02	0.00	10.0	0.000000
pBlueCollar	−0.22	0.01	−8.91	0.44	−20.4	0.000000
Pop65 + Pov	0.06	0.01	0.01	0.00	5.5	0.000000
PopDensity	0.51	0.01	0.00	0.00	47.2	0.000000
Distance from centroid	0.06	0.01	0.39	0.07	5.6	0.000000

Table 10. Multivariate model for mesothelioma versus distance from the centroid of data.

	Regression summary for dependent variable: MESOALL RATE R = 0.37; R^2= 0.14; Adjusted R^2= 0.14
N = 7038	b*	Std.Err. of b*	b	Std.Err. of b	t(7032)	p Value
Intercept			8.85	0.09	103.2	0.000000
UM1	0.15	0.01	0.01	0.00	13.2	0.000000
pBlueCollar	0.04	0.01	0.46	0.13	3.5	0.000423
Pop65 + Pov	−0.03	0.01	−0.00	0.00	−2.6	0.008805
PopDensity	−0.16	0.01	−0.00	0.00	−14.0	0.000000
Distance from centroid	0.29	0.01	0.53	0.02	25.7	0.000000

Figure 6. Traffic fatality rates versus latitude and longitude for 7049 California Census tracts (contour view).

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