S V SubramanianProfessor of Population Health and Geography

Harvard Universityhttp://www.hsph.harvard.edu/faculty/sv-subramanian/

What’s wrong with single-level epidemiology?

Public Lecture Series

Duke-National University of Singapore Medical SchoolDecember 13, 2013

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• The problem with single level models

• Revisiting a classic

• Importance of multilevel perspectives

• Concluding remarks

Outline

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Single level perspectives

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Ancel Keys

Seven Country Study

Thomas Dawber

Framingham Heart Study

• Framingham– 1948 and on-going– One town in Massachusetts,

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– Inferential Unit: Individuals– Population variability: a

nuisance– Unit of analysis: Individuals,

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– http://www.framinghamheartstudy.org/about/history.html

• Seven Country– 1958 – 1970– 7 countries: Yugoslavia, Italy,

Greece, Finland, Netherlands, USA, Japan

– Inferential Unit: Populations– Population variability: of

substantive interest– Unit of analysis:

Sites/Countries

– http://www.sph.umn.edu/epi/history/sevencountries.asp

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Risk factors for Cardiovascular Disease

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American Sociological Review, Vol. 15, No. 3 (Jun., 1950), pp. 351-357

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Individual Illiteracy BlackIlliteracy 1

Black 0.203 1

American Sociological Review, Vol. 15, No. 3 (Jun., 1950), pp. 351-357

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State %Illiteracy %Black%Illiteracy 1

%Black 0.773 1

Individual Illiteracy BlackIlliteracy 1

Black 0.203 1

American Sociological Review, Vol. 15, No. 3 (Jun., 1950), pp. 351-357

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American Sociological Review, Vol. 15, No. 3 (Jun., 1950), pp. 351-357

Individual Illiteracy Foreign-bornIlliteracy 1

Foreign-born 0.118 1

State %Illiteracy %Foreign-born%Illiteracy 1

%Foreign-born -0.526 1

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• On the ecological relationship

– The purpose of this paper will have been accomplished if it prevents the future computation of meaningless correlations.

American Sociological Review, Vol. 15, No. 3 (Jun., 1950), pp. 351-357

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• On the ecological relationship

– The purpose of this paper will have been accomplished if it prevents the future computation of meaningless correlations.

• On the individual relationship

– The purpose of this paper will have been accomplished if it stimulates the study of similar problems with use of meaningful correlation between the properties of individuals.

American Sociological Review, Vol. 15, No. 3 (Jun., 1950), pp. 351-357

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• Conclusion not supported by analysis

• Questionable Assumption– “In each study that uses ecological correlations, the obvious purpose is

to discover something about the behavior of individuals”.

• Methodological individualism– Technically accurate but substantively misleading in asserting the

primacy of “individual” relationships for understanding the association between race and illiteracy in the US

• Conflates ecology with aggregate– the whole need not simply be the sum of its parts

Critique

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• 3rd most cited paper in ASR (>1000 citations)

• Dire warnings of “ecological fallacy” - a cornerstone of ALL epidemiologic textbooks.

• Motivated collection of individual survey data

Robinson’s Reach

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Multilevel, or more precisely,Two-level perspectives

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• Data: 1930 US Census• Structure: 98 241 245 individuals in 49 States• Outcome: Illiterate or not• Predictors:

– Individual: Race/Nativity (White Native, Foreign-born Native, and Black)

– State: Percentage of Black Population; and Jim Crow or not

• Model: Two-level Binomial Logistic Model using Monte Carlo Markov Chain (MCMC) estimation with Metropolis-Hastings Algorithm

Revisiting Robinson’s Example

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Race-illiteracy association appears to be sensitive to States’ circumstances

Ignoring states

Accounting for

states

OR (95% CI) OR (95% CI)

Native White 1 1

Black 11.66 (11.63, 11.69) 5.86 (5.84, 5.88)

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Null After accounting for race

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State “effects” not sensitive to racial composition

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Washington

Oregon

California

District of Columbia

Nevada

New Mexico

Louisiana

Kentucky

North Carolina

Tennessee

Native Whites

Oregon

New York

South Dakota

Minnesota

Nevada

South Carolina

Alabama

Louisiana

Mississippi

North Carolina

Blacks

Illite

racy

Substantial heterogeneity in the illiteracy-race association

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“Everywhere is nowhere”

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Black

Foreign-born White

Native White

Race and Racial Context

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• Presence of Jim Crow Law– i.e., federal and state laws that permitted racial

discrimination under the concept of “separate but equal”

State not simply “aggregates” of individuals

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• Presence of Jim Crow Law– i.e., federal and state laws that permitted racial

discrimination under the concept of “separate but equal”

• Reality: “separate and unequal”– Per capita educational expenditure in public schools

• Georgia: White Child = $11.30; “Colored” Child = $0.00.• Alabama: White Child = $26.47; “Colored” Child = $3.81

State not simply “aggregates” of individuals

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States with and without Jim Crow Laws in Education

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Association between state Jim Crow laws, race, and illiteracy

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The problem with Robinson’s analysis was thinking at only ONE level, leading

to an impoverished interpretation of the data.

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• Critical re-thinking of any single-level analyses: ecological or individual

• No longer need to chose A level of analysis: an inductive approach to ascertaining at what level does action lie

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Where do we go from here?

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1. Conceptualizing Micro and Macro Contexts– e.g., neighborhoods (micro contexts) often are

embedded in larger settings such as counties or states or regions (macro contexts)

2. Considering geographical and non-geographical contexts simultaneously (e.g., neighborhoods and schools)

Current multilevel applications suffer from the

problem of missing or omitted level.

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1. Importance of considering multiple (nested) geographies

Life expectancy patterns in the US

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• Response: Life expectancy• Predictor: Time (i.e., “technological progress”) • Structure

– Repeated cross-section– Three-level: years (1961-2000) at level-1

(n=122850) nested within 3150 counties at level-2 nested within 51 states at level-3.

• Model: Three-level random coefficient model

Data

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Variance Estimate SE Estimate SE

Between state 1.705 0.350Between county 2.984 0.076 1.422 0.036Between time 0.512 0.002 0.512 0.002

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Level at which action lies: Two Level

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Variance Estimate SE Estimate SE

Between state 1.705 0.350Between county 2.984 0.076 1.422 0.036Between time 0.512 0.002 0.512 0.002

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Level at which action lies: Three Level

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State Variation trumps County Variation

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Macro contexts as important, if not more, for life expectancy variations in

the US.

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2. Importance of non-geographical/spatial contexts (e.g., schools, workplaces,

hospitals, social networks)

• In prior multilevel research, we have not given sufficient attention to all potentially relevant contexts on health

– Most multilevel research to date has focused on one setting: neighborhoods

– However, other settings may be relevant for health

– Biased inferences

One context at a time

• 180 days/year• 6 or more hours/day• 12-13 years

Empirical illustration: schools versus neighborhoods

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Level-2 School 1 School 2 School 3 School 4

Neighborhood 1

☺☺☺☺

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Neighborhood 2

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Neighborhood 3

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Neighborhood 4

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The idea of cross classified

• In-home Survey: 20,745 students nested in 132 schools

• Mean 125.4 students/school• 2142 neighborhoods (census tracts)

– Mean 7.3 students/tract

Study population

3 outcomes:

Tobacco use

Depression

Weight status

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood -

School 5.6 (0.6) -

Number of days cigarettes smoked (last 30 days)

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood - 4.7 (0.5)

School -

Number of days cigarettes smoked (last 30 days)

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood - 4.7 (0.5) 0.35 (0.3)

School 5.6 (0.6) - 5.54 (0.8)

Number of days cigarettes smoked (last 30 days)

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood -

School 0.35 (0.04) -

Log odds of smoking

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood - 0.25 (0.03)

School -

Log odds of smoking

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood - 0.25 (0.03) 0.06 (0.02)

School 0.35 (0.04) - 0.36 (0.06)

Log odds of smoking

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood -

School 0.98 (0.11) -

Self reported Body Mass Index

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood - 0.73 (0.10)

School -

Self reported Body Mass Index

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood - 0.73 (0.10) 0.22 (0.08)

School 0.98 (0.11) - 0.87 (0.14)

Self reported Body Mass Index

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood -

School 2.05 (0.56) -

CES-D Scale (Depression)

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood - 1.84 (0.52)

School -

CES-D Scale (Depression)

Variance Estimate (Standard Error)

Hierarchical School

Hierarchical Neighborhood

Cross-Classified

Neighborhood - 1.84 (0.52) 0.45 (0.34)

School 2.05 (0.56) - 1.69 (0.59)

CES-D Scale (Depression)

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• Need critical re-thinking of ALL single-level epidemiological analyses– Dire warnings of “ecological fallacy”, but the science is full

of studies that risk “individualistic or atomistic fallacy”

• Need to carefully consider the units of analysis in epidemiological investigations and the problem of “omitted” levels

• Need to consider multiple contexts simultaneously (places/schools/worksites)

Concluding remarks