Tuesday, May 14, 2013

Actuarial Risk versus the Risk Estimated from Our Chemical Exposure

Actuarial Risk is very different from the risk to human health that we estimate from chemical exposure.    Indeed, actuarial risk is pretty straightforward.   It is simply the historical risk of an activity with the assumption that the present and near future will be like the past.  Let's look at the risk of traffic accidents. About 35,000 American died in traffic accidents in 2010 (the last year I could easily find with complete data).  One might predict from this that about that many would died again in 2011 and 2012.   Given a 75 year lifetime this is a lifetime risk of about 1 in 150.   In reality this risk, for a number of reasons that I will not go into, has come down steadily in the last 40 years or so.  This actual risk was about 1/65 in 1969.

This is actuarial risk and given the numbers it is easy to calculate and from year to year is pretty accurate for systems that change slowly.  Insurance companies rely heavily on this to set premiums in a effort to be competitive and to assure that they will remain profitable.

The estimated risk from our exposure to chemicals is not calculated in this manner and is not nearly as accurate. Indeed, most of the time it is not calculated at all.  But forgive me, I am getting ahead of myself. The very important topic of calculating the risk to exposure to non-carcinogenic chemical will be a matter for another blog.  Here I will talk about the calculated or estimated human risk of getting cancer from exposure to a chemical suspected to cause cancer at least in animals.   The standard manner of testing a chemical for its ability to cause cancer is to expose separate groups of animals (perhaps 20-50 rats or mice in each group) to high levels of the chemical for a majority of their lifetime (typically 2 years) with the highest dose designed to be so toxic as to be the highest dose the animals can tolerate without quickly dying from it.  This is called the Maximum Tolerated Dose (MTD) for the highest group and then perhaps 2 or 3 groups at fractions of this dose with the hope that a least the lowest dose will result in a No Observed Adverse Effect Level (NOAEL).    At the end of the study the animals are killed and surgically examined very carefully by a pathologist for any signs of cancer in their tissues.   Say that 10 out of 20 in the MTD group got a certain tumor then the response would be 50%.     Typically the lower dose groups will, as expected, give lower response rates and the NOAEL will have a response rate that is indistinguishable from control rats that were treated the same but without exposure to the chemical.  In reality the NOAEL dose would have resulted in 3-20% response if a much larger number of rats than 20-50 had been tested.

Now comes the magic.   We are not interested in an exposure that gives 10% or even 1% risk.  This is simply too high.   We want to know what the exposure is that results in a risk of 1 in a million or 1 in 100,000 for members of the general public. For workers we often look upon a much higher risk  as "not unacceptable" but we are sticking here in our example with the general public .   In order to estimate this level of risk one needs to apply a mathematical model to fit the data and do what is known as low dose extrapolation based on the model.   The problem is that there are many models that fit the known data but give very different estimated exposures for 1 in 1,000,000 risk.   As a result the estimated risk at any exposure that people might actually be exposed to can vary by a hundred or even more than a thousand fold.   The EPA has adopted a model that it uses to do this extrapolation but it can be argued that this model and indeed all the other models are arguments without data.   We simply do not know what is happening to human tissues as a result of any low exposure level nor do we know the actual risk posed at these low levels.  The risk predicted by these models at these environmentally relevant exposures are not actual risk they are putative risk.

A model-predicted risk of 1 in 1,000,000 for the pesticides in the salads we eat does not mean that one in million (between 300-350 folks in the US) will get cancer in their lifetime from eating their salad.   The number may be zero or even a negative number (i.e., protection from cancer) depending on which model one uses for low dose extrapolation.   I know it may be intriguing but I am also leaving negative risk at low dose as another topic for a future blog.  Its enough here to remember that the putative cancer risk assessment  from chemical exposure is putative and not actual risk and as such full of uncertainty.


  1. I am reminded of a quip by Eli Richter, M.D.:

    Q: "What is the definition of a Public Health Disaster?"

    A: "An effect large enough for an epidemiologist to measure."

  2. Dear JSY,

    Certainly true of the past and, to an extent, the present and cause for real concern. Given better models of retrospective exposure and better diagnostic tools perhaps we can do a better job in the future.

  3. Thanks Mike. A good explanation of the difference between actuarial and putative risk.

    Phil Lewis