Ecologic studies

JF BoivinVersion 8 October 2010

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Outline

1. Examples

2. Definition

3. Ecologic fallacy

• Definition

• Valid ecologic study

• Rate difference varies

• Reference rate varies

4. Contextual effects

5. Rationale for ecologic studies

6. Ecologic confounders

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4

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Figure 1. Statistical (empirical Bayes) estimates of county-specific adjusted annual suicide rates in the United States. A Bayes estimate of 1.0 indicates that the rate for the county was equal to the national rate of 12 per 100 000 population, a Bayes estimate of 2.0 represents a doubling of the national rate, and a Bayes estimate of 0.5 represents half the national rate. The estimates are based on all data from 1996 to 1998, adjusted for age, sex, and race.

Example: Time-trend studies

Time Trends in Autism and in MMR Immunization Coverage in California

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Percentage of Children Receiving Measles-Mumps-Rubella (MMR) Immunization in Second Year of Life and Caseload of Children With Autism, by Year of Birth, California, 1980-1994

JAMA. 2001;285:1183-1185

Émile Durkheim• Émile Durkheim (1858 –1917) was a famous French

sociologist and pioneer in the development of modern sociology and anthropology.

• In a groundbreaking book published in 1897, entitled Le Suicide, Durkheim explored the differing suicide rates among Protestants and Catholics.

• In 19th century Europe, suicide rates were higher in countries that were more heavily Protestant. Durkheim found that suicide rates were highest in provinces that were heavily Protestant.

• He concluded that stronger social control among Catholics resulted in lower suicide rates.

• However, Durkheim's study of suicide was criticized as an example of the logical error termed the "ecological fallacy."

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Using ordinary least-squares linear regression on Durkheim's data, Morgenstern (1995) found a strong positive correlation (Figure below) between proportion protestant and suicide rates. The estimated rate ratio, comparing Protestants with other religions, was 7.6 (i.e. suicide rates among protestants was about 8 fold higher than other religions).

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Outline

1. Examples

2. Definition

3. Ecologic fallacy

• Definition

• Valid ecologic study

• Rate difference varies

• Reference rate varies

4. Contextual effects

5. Rationale for ecologic studies

6. Ecologic confounders

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Ecologic study

A study in which the units of analysis are populations or groups of people, rather than individuals.

(Last. 2001)

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Structure of an ecologic study: Counts

E+ E-

M1+

M1-

N1-N1+

D+

D-

?

?

?

?

Group 1

E+ E-

M2+

M2-

N2-N2+

D+

D-

?

?

?

?

Group 2

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Person-years

E+ E-

M1+

PY1T

D+

PY

?

PY1+

?

PY1-

Group 1

E+ E-

M2+

PY2T

D+

PY

?

PY2+

?

PY2-

Group 2

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Gibbons’ study

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1,000,000

Suicide

PY

?

200,000

?

800,000

County i

Yes No

10

1,000,000

Suicide

PY

?

100,000

?

900,000

County 1 Antidepressant

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Outline

1. Examples

2. Definition

3. Ecologic fallacy

• Definition

• Valid ecologic study

• Rate difference varies

• Reference rate varies

4. Contextual effects

5. Rationale for ecologic studies

6. Ecologic confounders

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Ecologic fallacy

“…the mistaken assumption that a statistical association observed between two ecologic (group-level) variables… is equal to the association between the corresponding variables at the individual level…”

(Encyclopedia of epidemiologic methods. 2000)

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Ecologic fallacy

“…arises when the disease rate in the unexposed (reference) population is correlated with exposure prevalence across groups or when the difference in rates between exposed and unexposed populations (biologic effect) varies across groups.”

(Encyclopedia of epidemiologic methods. 2000)

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No ecologic bias

E+ E-

32

20,000

D+

PY

24

12,000

8

8,000

Group 2 (Ontario)

IE = 200/100,000

Io = 100/100,000RD = 100/100,000RR = 2

Group rate = 32/20,000 = 160/100,000% exposure = 12,000/20,000 = 60%

Adapted from Rothman-Greenland Table 23-2

E+ E-

28

20,000

D+

PY

16

8,000

12

12,000

Group 1 (Québec)

IE = 200/100,000

Io = 100/100,000

RD = 100/100,000RR = 2

Group rate = 28/20,000 = 140/100,000% exposure = 8,000/20,000 = 40%

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No ecologic bias

110

120

140

130

150

160

170

180

190

200

100908070605040302010

RATE

(per

100

,000

)

% EXPOSURE

IRR = = 2=IE

Io 100/100,000

200/100,000

Québec

Ontario

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Ecologic bias(rate difference varies across groups)

E+ E-

27

20,000

D+

PY

20

13,000

7

7,000

Group 2 (Ontario)

IE = 154/100,000

Io = 100/100,000

RD = 54/100,000RR = 1.54

Group rate = 27/20,000 = 135/100,000% exposure = 13,000/20,000 = 65%

E+ E-

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20,000

D+

PY

20

7,000

13

13,000

Group 1 (Québec)

IE = 286/100,000

Io = 100/100,000

RD = 186/100,000RR = 2.86

Group rate = 33/20,000 = 165/100,000% exposure = 7,000/20,000 = 35%

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Ecologic bias

110

120

140

130

150

160

170

180

190

200

100908070605040302010

RATE

(per

100

,000

)

% EXPOSURE

IRR = = 0.5=IE

Io 200/100,000

100/100,000

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Ecologic bias(reference rate varies across groups)

E+ E-

46

20,000

D+

PY

40

16,000

6

4,000

Group 2 (Ontario)

IE = 250/100,000Io = 150/100,000

RD = 100/100,000RR = 1.67

Group rate = 46/20,000 = 230/100,000% exposure = 16,000/20,000 = 80%

E+ E-

28

20,000

D+

PY

16

8,000

12

12,000

Group 1 (Québec)

IE = 200/100,000

Io = 100/100,000

RD = 100/100,000RR = 2

Group rate = 28/20,000 = 140/100,000% exposure = 8,000/20,000 = 40%

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Ecologic bias

0

100

150

200

250

100908070605040302010

RATE

(per

100

,000

)

% EXPOSURE

IRR = = 5.5=IE

Io

275/100,000

50/100,000

26(Koepsell & Weiss)

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Outline

1. Examples

2. Definition

3. Ecologic fallacy

• Definition

• Valid ecologic study

• Rate difference varies

• Reference rate varies

4. Contextual effects

5. Rationale for ecologic studies

6. Ecologic confounders

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• Neighborhood social class as aggregate of individual social classes

Can differ from study subjects’ social class

• Neighborhood social class as contextual variable

Same contextual variable for all subjects

Example: ecologic effect

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Outline

1. Examples

2. Definition

3. Ecologic fallacy

• Definition

• Valid ecologic study

• Rate difference varies

• Reference rate varies

4. Contextual effects

5. Rationale for ecologic studies

6. Ecologic confounders

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1. Low cost and convenience

2. Measurement limitation of individual-level studies

3. Design limitations of individual-level studies• Koepsell and Weiss, Figure 12.1

4. Simplicity of analysis and presentation

5. Instrumental variables

Rationale for ecologic studies

33(Koepsell & Weiss)

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Outline

1. Examples

2. Definition

3. Ecologic fallacy

• Definition

• Valid ecologic study

• Rate difference varies

• Reference rate varies

4. Contextual effects

5. Rationale for ecologic studies

6. Ecologic confounders

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No ecologic bias

Country 1 Country 2 Country 3

Covariate Exposure PY Rate PY Rate PY Rate

Yes Yes 3000 600 4000 600 4000 600

  No 12000 500 8000 500 6000 500

  RR   1.2    1.2   1.2 

No Yes 2000 600 4000 600 6000 600

  No 8000 500 8000 500 9000 500

  RR   1.2   1.2    1.2 

Sum Yes 5000 600 8000 600 10000 600

  No 20000 500 16000 500 15000 500

  RR   1.2   1.2   1.2

(rates per 100,000 person-year)(Note: no individual-level confounding)

Ecologic analysis

% exposed 20% 33% 40%

% covariate 60% 50% 40%

Overall disease rate 520 533 540

Crude RR = 1.2

Adjusted RR = 1.2

Crude is valid!

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Country 1 Country 2 Country 3

Covariate Exposure PY Rate PY Rate PY Rate

Yes Yes 3000 600 4000 600 4000 600

  No 12000 500 8000 500 6000 500

  RR   1.2    1.2   1.2 

No Yes 2000 200 4000 200 6000 200

  No 8000 100 8000 100 9000 100

  RR   2   2    2 

Sum Yes 5000 440 8000 400 10000 360

  No 20000 340 16000 300 15000 260

  RR   1.3   1.3   1.4

(rates per 100,000 person-year)(Note: no individual-level confounding)

Ecologic analysis

% exposed 20% 33% 40%

% covariate 60% 50% 40%

Overall disease rate 360 333 300

Crude RR = 0.3

Adjusted RR = 1.3

Adjusted is valid!

Crude ecologic biasNo stratum-specific ecologic bias

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Country 1 Country 2 Country 3

Covariate Exposure PY Rate PY Rate PY Rate

Yes Yes 8000 500 13000 1500 14000 1000

  No 12000 500 12000 1500 6000 1000

  RR   1    1   1 

No Yes 2000 100 2000 300 6000 200

  No 28000 100 23000 300 24000 200

  RR   1   1    1 

Sum Yes 10000 420 15000 1340 20000 760

  No 40000 220 35000 711 30000 360

  RR   1.9   1.9   2.1

(rates per 100,000 person-year)

Ecologic analysis

% exposed 20% 30% 40%

% covariate 40% 50% 40%

Overall disease rate 260 900 520

Crude RR = 8.6

Adjusted RR = 8.6

No valid estimate available!

Ecologic bias (crude and stratum-specific)

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Another example

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