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Before it can be determined in any quantitative way what risk exists, it is necessary to determine whether ANY risk (hazard) exists.  This is usually done through a systematic evaluation of the available human and animal studies.
Explanation:  For asbestos exposure and lung cancer, for example, there is evidence that INDUSTRIAL PROCESS affects the slope of the risk.  Thus, those employed in asbestos mining and milling had measureable, but shallow risk (lower risk at highest exposures), while those who made asbestos textiles had highest risks.
If the black line intersecting zero is “correct”, there is theoretically some “risk” at any level of exposure (although the probability of that risk may be effectively none at zero).  This is almost a convention in cancer risk assessment, but may be wrong if the GREEN line is correct, which suggests that there is ZERO theoretical risk below the exposure at which the green line intersects the X (exposure) axis.
The problem is thus that the studies do not actually identify any points which are low on the dose level; whether human or (especially) animal.  The resulting PROJECTIONS may be largely either guesswork, convention (as in the linear no-threshold model), or both.
Remember that this is called Risk MANAGEMENT by EPA but Risk CHARACTERIZATION by many others.  Since management is a whole other ballgame, I prefer characterization:  this is simply a mathematical modelling of risk.
This is an example from Camus et al. in which in an ecological study it was shown that the numbers of expected lung cancers around a chrysotile mine among a female population were grossly overestimated when the actual estimated exposures were plugged into one particular risk assessment model (the one developed by Nicholson for EPA in 1986).
A similar, preliminary analysis of mesothelioma risk applied in the same way comes to the same conclusions.
This slide strictly for the mathematically unchallenged! 
The “plausible range” should not be confused with a confidence interval; it was simply estimated by an expert panel and the authors that the estimates of exposure, based on many sources, COULD have a range this wide dependent on many factors.  To put these numbers in context, remember that it is generally accepted that asbestosis risk does not exist below 25 to 50 fibre-years (f/ml years).
Although difficult to interpret, this slide indicates that the EPA predicted rate based on the midpoint of the “plausible” exposures would have predicted a hundred-fold more cases of this disease in this population (or thirty-fold if the risk assessment had been limited to the high-tremolite Thetford-Mines area).
Moving to a NEW TOPIC:  This is not part of “risk assessment” but some observers object to classical risk assessment activities in that they feel these do not adequately take this “precautionary principle” into account (although clearly they could, and often do, if enough of a margin of safety is provided).
These authors find that there are advantages to scientists in applying the precautionary principle, IF certain aspects of that principle are understood at the outset.
Restating the general principles; the quote is from the RIO 1992 document.