# 7.2.1 - Sample Ecological Data and Analysis

The following data illustrate a problem with the interpretation of ecological studies. The data include the numbers in an exposed and non-exposed group and the disease rate per 100,000 person-years within each of the three different groups.
With the data given, we can calculate the exposure rates per group as:

$$\text { Exposure rate }=\dfrac{P Y_{\text {of exposed }}}{\text { total } P Y}$$

Exposure Group 1 Group 2 Group 3
Cases PY

Rate/
100,000
PY

Cases PY Rate/
100,000
PY
Cases PY Rate/
100,000
PY
Exposed (x=1) 20 7000   20 10000   20 13000
Unexposed (x=0) 13 13000   10 10000   7 7000
Total 33 20000 165 30 20000 150 27 20000 135
Exposure Rate   35%     50%     65%

What is the relationship between exposure level and disease rate per 100,000 person-years?
Once we can calculate the exposure rate in each group, we see that as exposure rates increase, disease rates decrease.
The natural conclusion would seem to be that exposure protects individuals from the disease by decreasing the rate of disease.

So...would you want to be exposed to this factor in order to cut your disease risk? Or would you like to ask further questions?

What about the fact that we have no data measured at the individual level? For example, do we know the exposure level and the disease outcome for each person in the study? NO! In fact, all the cases could have actually occurred among the exposed individuals. This would be a problem if our hypothesis was that a biological process was responsible for the increased risk.
Consider these tables:

Stratum 1 and Stratum 2 are similar to the groups, of which there were 3, in the previous example. We don't know the numbers for each cell within any stratum, nor do we know A, B, C, or D for the combined data. Only the marginal counts are known - the number exposed and unexposed, and the numbers of cases and non-cases within each stratum. So, if our hypothesis for the risk pathway is biological, then we run the risk of an ecological fallacy. An ecological fallacy is possible when we use group-level data as evidence for risk pathways that operate at the individual level because we are ascribing group observations to the individual! (Note: Group-level data are appropriate if our hypothesis is that the disease pathway is from a group-level exposure. Group-level exposures are recognized as important in disease causation models with both individual and group processes).

## Individual-level Data and Analysis

To demonstrate the ecological fallacy, let's look at the individual-level data from the same example. We will fill in the number of cases within each cell for each group. For instance, in group 1, there were 20 cases in 7,000 person-years of being at-risk.
Then we can calculate the rates per 100,000PY for each exposure level in each group as:

$$\text { Rate per } 100,000 \mathrm{PY}=\left(\dfrac{\text { #of cases }}{\text { total person-years }}\right) * 100,000 \mathrm{PY}$$
Exposure Group 1 Group 2 Group 3
Cases PY

Rate/
100,000
PY

Cases PY Rate/
100,000
PY
Cases PY Rate/
100,000
PY
Exposed (x=1) 20 7000 286 20 10000 200 20 13000 154
Unexposed (x=0) 13 13000 100 10 10000 100 7 7000 100
Total 33 20000 165 30 20000 150 27 20000 135
Exposure Rate   35%     50%     65%

Next, we can calculate the Rate Difference and Rate Ratio within each group as

$$\text { Rate Difference }=\text { Rate }_{\text {Exposed }}-\text { Rate }_{\text {Unexposed }}$$

$$\text { Rate Ratio }=\dfrac{\text { Rate }_{\text {Exposed }}}{\text { Rate }_{\text {Unexposed }}}$$

Exposure Group 1 Group 2 Group 3
Cases PY

Rate/
100,000
PY

Cases PY Rate/
100,000
PY
Cases PY Rate/
100,000
PY
Exposed (x=1) 20 7000 286 20 10000 200 20 13000 154
Unexposed (x=0) 13 13000 100 10 10000 100 7 7000 100
Total 33 20000 165 30 20000 150 27 20000 135
Exposure Rate   35%     50%     65%

Rate Difference 186     100     54
Rate Ratio 2.86     2.00     1.54

When we look at each group separately, we see that exposure is related to a higher rate of disease!

So, we would conclude that exposure increases the risk of this outcome, which is the opposite of what we concluded previously! We also observe that the rate of disease among the non-exposed was the same for all groups. Across groups, the rate of disease among the exposed was higher than the unexposed, but the rate seems to vary among the exposed groups.

Recall, that when we used the group-level (ecological) data we saw that this exposure appeared to be protective. HOWEVER, given the individual-level data, exposure appears to increase the risk of disease! This is an example of an ecological fallacy (or ecological bias)... using group-level data to support an individual pathway.

Can an ecological study produce results without ecological bias? Yes, under certain conditions...

If the rate difference is the same - If the rate difference is the same across the groups, there will be no ecological fallacy.