An Introductory Lecture to Environmental Epidemiology

Part 5. Ecological Studies.

Mark S. Goldberg

INRS-Institut Armand-Frappier, University of Quebec, and

McGill University

July 2000

Ecological Studies

• Definition: An investigation of the distribution of health and its determinants between groups of individuals.

• The degree to which studies are purely ecological can vary considerably.

Reasons for Ecological Studies

• Data on the individual level not available

• Individual exposure measurements not available, but grouped level data are (e.g., mean radon gas levels from county-wide surveys)

• Comparison between large jurisdictional units (e.g., comparison of breast cancer rates with mean daily fat intake between countries)

• Easy, quick, and inexpensive

• Design limitations (e.g., Harvard Six-cities study; see Part 1)

• Interest in ecological effects (e.g., does increasing taxes on tobacco reduce consumption in different jurisdictions?)

Measurement variables

• Aggregated measures: summaries of attributes calculated from data on individuals for whole populations in well-defined geographic regions

• Examples: mean income; percentage of families below the poverty line; mean number of household members

• Group level measures: estimates of (environmental) attributes that have individual analogues. Usually obtained from surveys.

• Examples: maximum daily exposure to ozone; mean annual exposures to radon gas; daily mean levels of environmental tobacco smoke in public buildings

• Global measures (contextual): attributes that pertain to groups and do not have analogues at the individual level

• Examples: total area of green space; number of private medical clinics; population density

Types of studies

• Individual level: Well defined target and study populations and data available on individuals for all (or most) covariates.

• Example: Cross-sectional study of respiratory symptoms and exposure to environmental tobacco smoke among children living in Mexico City.

• Purely ecologic: No data on individuals

• Example: Average per capita consumption of snuff and age-sex-race standardized mortality rates of oral cancer. Comparisons at the county level.

• Partially ecologic: Some individual data available. • Example: A study of low birth weight and

environmental exposures to biogas from a landfill site (See Part 1).

• - Individual data: age of mother, sex, birth weight, gestational age of baby, and geographic area of residence

• - Ecological: geographic region of residence as a surrogate for exposure to biogas in the ambient air

Types of Ecologic Studies

• Case-control

• Cohort and longitudinal

• Cross-sectional

• Time trend studies

• Immigrant studies

Levels of Inference

• Biologic inferences on populations– Individual-level studies

– Ecologic-level studies

• In individual-level studies, inferences are made to the target populations using data collected from individuals

• In ecologic-level studies, inferences are made strictly to the groups that are under investigation

• Ecologic inferences usually refer to contextual effects

• Example: An ecological study investigating health care utilization for prenatal care between areas of Lima, Peru, as a function of number of clinics per region, etc...

• If a study is purely ecological, then biological inferences to target populations may be made as if the studies were conducted on individuals (referred to as “cross-level inference”)

• Only under strict conditions will these inferences be correct

Ecological Fallacy

• Assumptions: – 1) that the effects estimated at the

individual level are the relevant ones for making biological inferences

– 2) that the effects are a linear function of the predictors; i.e. E[yi] = + xi

• Assume the above relationship {E[yi] = + xi} to hold on an individual level and that the parameter of interest for the purposes of biological inference is .

• Assume now that the population is segregated into groups and that the analysis proceeds by comparing the grouped mean between the k groups (no individual data available).

• The slope including group effects is:

• = G + W

• where is the overall between-person slope (i.e., over all persons in all groups), G is the between-group slope (ecological effect), W is the within-group slope, and , are ratios of the between-group and within-group variances to the total variance of x ( + =1).

• When there are no group effects then = W, so W is the correct regression coefficient

• When there are group effects W , so that G W

• Ecological bias or “cross-level bias” occurs when G W

• See Piantadosi, AJE 1988;127:893-904

Conditions for No Ecological Bias

• Background rate of disease (in the unexposed) does not vary across groups– background rates may vary, apart from

statistical variation, due to unequal distributions of risk factors across groups

– AND

• These is no confounding within groups• AND

• There is no effect modification by group

• In general, the ecological linear regression model will estimate the difference in rates between groups.

• The ecological regression coefficient is equal to the sum of:– difference in rates at the individual level

– bias from the association between the confounding factor and group

– bias from the interaction between a factor and group (only if the difference in rates does not vary by group will there be no interaction)

Examples of Ecological Bias

• Group is an effect modifier– i.e., effect of exposure varies across

groups

– can arise from differential distribution of effect modifiers across groups

– can occur even if after control for ecological covariates

Ecological Bias: Effect Modification by Group, No Confounding Eoesophageal cancer and smoking

Individual Level AnalysisRegion 1 Region 2 Region 3 Total

Smoking Yes No Yes No Yes No Yes NoNo of cases 13 3 12 3.6 12 4.2 36 10.8Population 100000. 100000. 80000.120000. 60000. 140000. 240000.360000.Rate/ 100.000 12 3 15 3 20 3 15 3Rate ratio 4 5 6.7 5Rate difference 9 12 17 12Overall SMR 5 (Standardized to non-smokers; i.e., no confounding by group)no confounging by group

Ecological Level Analysis% smokers 0.5 0.4 0.3Cancer rate 7.5 7.8 8.1

Ecological regressionrate = 9 - 3 * %smokersIn the absence of individual data aboveEstimated ecological rate ratio = 0.67 (1-3/9)

From Greenland and Morgenstern, Int J Epidem 1989; 18:269-74

Confounding by Non-Confounders

• Variable is not a confounder on the individual level– may occur if background rates vary

by group

– if rate differences between groups not constant

Ecological Bias: Ecological Confounding of a non-Confounder on the Individual Level

Lung cancer and radonIndividual Level Analysis

Region 1 Region 2 Region 3Smokers NonsmokersSmokers NonsmokersSmokers Nonsmokers

Radon level Yes No Yes No Yes No Yes No Yes No Yes NoNo of cases 52 74 5.2 7.4 56 52 8.4 7.8 60 30 14 7Population(in thousands) 26 74 26 74 28 52 42 78 30 30 70 70Rate per 100,000 200 100 20 10 200 100 20 10 200 100 20 10Rate by smoking level126 12.6 135 13.5 15 1.5Rate ratio for smoking 10 10 10Radon-smoking assocn. 1 1 1Rate difference for radon100 10 100 10 100 10Rate ratio for radon 2 2 2 2 2 2

Ecological Level Analysis% smokers 0.5 0.4 0.3% high radon 0.26 0.35 0.5Cancer rate 69.3 62.1 55.5

Ecological regression rate = 84 - 59 * %high radonEstimated ecological rate ratio = 1+ (-59/84)=.30rate = 29 + 7 * %high radon + 76 * %smokingEstimated ecological rate ratio = 1.1 (mean smoking for prevalence=0.4)

Adjustment for Ecological Confounder Increases Bias

• Variable is not a confounder on the individual level (factors not associated)– background rates differ by group

– rate differences vary by group

Ecological Bias: Ecological Confounder Increases BiasEoesophageal cancer and alcohol

Individual Level AnalysisRegion 1 Region 2 Region 3Smokers NonsmokersSmokers NonsmokersSmokers Nonsmokers

Alcohol Yes No Yes No Yes No Yes No Yes No Yes NoNo of cases 13 2.5 1.5 0.7 14.7 1.1 1.1 1 15 0.6 1.9 0.9Population(in thousand50 50 30 70 58.8 21 21 98.8 60 12 38 90Rate per 100,000 25 5 5 1 25 5 5 1 25 5 5 1Rate by smoking level15 2.2 19.7 1.8 21.7 2.2RR: smoking 6.6 11 9.9Alc-smk assocn. 2.3 12.1 11.8Rate diff.: alcohol 20 4 20 4 20 4RR: alcohol 5 5 5 5 5 5

Ecological Level Analysis% smokers 0,5 0,4 0,36% alcohol 0,4 0,4 0,49Cancer rate 8,6 8,9 9,2

Ecological regression rate = 6.8 + 5 * %alcoholEstimated ecological rate ratio = 1+ (5/6.8)=1.73rate = 29 + 7 * %alcohol + 76 * %smoking

Estimated ecological rate ratio = 1.2 (evaluated at mean smoking prevalence of 0.42)

From Greenland and Morgenstern, Int J Epidem 1989; 18:269-74

Nondifferential Misclassification of Exposure

• For both linear and log-linear models nondifferential misclassification of exposure (binary variable) leads to an overestimation of effect in ecological studies, even if there are no other sources of ecological bias

• See Brenner AJE 1992;135:85-95

Non-Linear Effects of Covariates

• If there is a nonlinear association between the outcome, the exposure and the covariate, ecological bias may occur– due to the linear ecological model not

holding in the underlying population (e.g., Risk(x,c) = (1 + ßx) exp(c))

– not correctly summarizing the ecological covariates across groups (using just means instead of other more complex summaries)

Possible Solutions

• Obtain detailed information on covariates so that not just mean levels are used in the analysis

• Obtain joint distributions of covariates and exposures

• Use another analytic approach (individual-level or semi-individual-level studies)

Example: Association between Radon in Homes and Lung Cancer

• Studies of uranium miners and smelters have shown strong positive exposure-response relationships between level of radon gas and lung cancer

• Ecological studies of lung cancer rates and mean level of radon by county in the US and elsewhere have shown strong negative correlations

Case-control Study in Sweden

• 1360 cases and 2847 controls

• Age 35-74 years, 1980-84, living in 109 municipalities

• Radon monitored in 9000 homes occupied by subjects since 1947 for > 2 years

• Time-weighted concentrations estimated per subject

• Carried out an analysis of individual data and ecological data

• Ecological radon levels: Average radon exposure aggregated in each municipality from controls living there

• Ecological analysis: Odds ratios per county calculated (only males with >10 cases per county)

Ecological Association of Lung Cancer and Radon by County,

Sweden

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

0 50 100 150 200

Estimated radon levels in controls

Od

ds r

ati

os

ti

os

.1.81.61.41.2

0.80.60.40.2

Association of Radon and Lung Cancer Risk: Comparison of Individual and Ecological Estimates

Regression Individual level EcologicalModel RR 95%CI RR 95%CIAge, sex, urbanization, occupation 1.1 0.99-1.15 1 0.79-1.17Plus: Individual smoking 1.1 0.98-1.13Plus: Aggregated smoking 1 0.79-1.17Plus: Individual smoking and latitude 1.1 1.02-1.24Plus: Aggregated smoking and latitude 1.1 0.80-1.29

RR calculated per 100 Bq-cubic metre

Source: Lagarde and Pershagen AJE 1999;149:268-74.

References• ECOLOGICAL STUDIES

• Chapter 23, “Ecological Studies”, Hal Morgenstern, in Rothman and Greenland

• Richardson et al., Int J Epidem 1987;16:111-120.

• Piantadosi et al., Am J Epidem 1988;127:893-904.

• Greenland and Morgenstern, Int J Epidem 1989;18:269-274.

• Brenner et al., Am J Epidem 1992;135:85-95.

• Brenner et al., Epidemiology 1992;3:456-9.

• Greenland and Robbins, Am J Epidem 1994;139:747-760.