It has been claimed that exposure to risk of road traffic accidents (usually conceptualized as mileage) is curvilinearly associated with crashes (i.e., the increase in number of crashes decreases with increased mileage). However, this effect has been criticized as mainly an artifact of self-reported data.
To test the proposition that self-reported accidents create part of the curvilinearity in data by under-reporting by high-accident drivers, self-reported and recorded collisions were plotted against hours of driving for bus drivers.
It was found that the recorded data differed from self-reported information at the high end of exposure, and had a more linear association with the exposure measure as compared to the self-reported data, thus supporting the hypothesis.
Part of the previously reported curvilinearity between accidents and exposure is apparently due to biased methods. Also, the interpretation of curvilinearity as an effect of exposure upon accidents was criticized as unfounded, as the causality may just as well go the other way.
The question of how exposure associates with crash involvement is far from resolved, and everyone who uses an exposure metric (mileage, time, induced) should be careful to investigate the exact properties of their variable before using it.