Fig. 1

Two hypothetical relationships of hearing impairment to cumulative noise exposure in four cities. Units for noise exposure and hearing impairment have been specified arbitrarily for ease of presentation. Data for each city are distinguished by the shading of data points. A and B Depict the same hypothetical dataset. In A, only cluster-specific regression lines are indicated, while in B summary regression lines have been added for the full dataset a) when clustering is ignored (dotted red line), and b) after adjustment for clustering (solid blue line). C Shows a second dataset in which the relationship of hearing impairment to cumulative noise exposure in each city is as in A and B, but distribution of noise exposures is the same in each city. Again, the dotted red line represents the summary regression line when clustering is ignored, and the solid blue line, that after adjustment for clustering