### Article

## Impact of between-area and within-area exposure variability on pure specification bias in ecological studies

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Published: | September 14, 2004 |
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### Outline

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#### Introduction

In epidemiology, ecological studies are usually carried out if individual data for disease risk estimation are missing. Under these conditions, exposure, disease and covariables are analysed as being properties of groups of individuals, rather than as properties of single individuals. This causes methodical problems which may yield considerable bias in risk estimation [Ref. 1].

One of these problems arises when there is non-constant within-group exposure. In this case, a risk model appropriate at the individual level can be applied at the group level without bias only if the model is linear [Ref. 2]. However, other risk models are common in epidemiology. Applying a multiplicative one, which is the obvious choice [Ref. 2] in analysing rare diseases, the so-called pure specification bias may occur [Ref. 1].

It is well known that within-area variability has a major impact on the amount of pure specification bias. Moreover, Salway and Wakefield [Ref. 3] claim that also the between-area to within-area variance ratio of exposure plays an important role in ecological studies. They argue that pure specification bias will be reduced if the between-area to within-area variance ratio is large. However, this has not been shown in any systematic way.

#### Method

We performed a simulation study to investigate the impact of the ratio of the between-area and the within-area variance on pure specification bias. We simulated data for groups with equal and different numbers of individuals. For each person exposure was generated from lognormal distributions based on a preset distribution with different values for means and variances. Cases were generated assuming a logistic model using realistic values for the risk coefficient.

#### Results

In contrast to the assumption of Salway and Wakefield [Ref. 3], the results of our simulations indicate that it cannot be concluded that a high value of the between-area to within-area variance ratio yield small pure specification bias in general. That means even if the between-area variance is large compared to the within-area variance the use of ecological studies might be hampered by this bias. Therefore, also in situations where on the one hand exposure depends on the distance to a responsible event and on the other hand individuals who live in the same area have rather similar exposure, pure specifiaction bias can occur. One example is radiation exposure due to the Chernobyl accident. However, for fixed between-area variability pure specification bias is the smaller the smaller the within-area variability.

#### Discussion

Although a high value of the between-area to within-area variance ratio does not yield small pure specification bias in general, there are situations when this relationship is true. However, it is not clear under which circumstances this can happen. Therefore, further simulation studies are needed to investigate in which situations a high value of the ratio will result in a small pure specification bias.

### References

- 1.
- Greenland S. Divergent biases in ecological and individual-level studies. Statist. Med. 1992; 11: 1209-1223.
- 2.
- Wakefield J, Salway R. A statistical framework for ecological and aggregate studies. J. R. Statist. Soc. 2001; 164(1): 119-137.
- 3.
- Salway R, Wakefield J. A comparison of approaches to ecological inference in epidemiology, political science and sociology. www.cbrss.harvard.edu/events/ eic/nov/wakefieldsalway.ps. 2003.