Arsenic in Rice: Part 4 - Slope Factor...one more time!

I have written about the good ol' Slope Factor a number of times.  It is how we look at the risk from exposure to chemicals we view as carcinogens.  Carcinogens are where we have painted ourselves in the corner by claiming:

In contrast, the Federal SDWA sets an MCL goal of “zero” for carcinogens. (NJ)

You cannot have zero, so why even bring it up?  All it does is sets the stage for lower and lower exposure limits because zero becomes the goal.

If the cornerstone of the science of toxicology is accepting the premise that there is a "range of exposures from zero to some finite value can be tolerated by the organism with essentially no chance of expression of the toxic effect," then zero is just as relevant to protecting public health as some other number.  The quest is to find that number and set that as the threshold.

New Jersey has set the threshold at 5 ppb which it claims is "the most protective level within the constraints of medical, scientific and technological feasibility" for protecting public health from and "excess lifetime risk of lung and bladder cancer"

From my last post, we learned that 5 ppb is a threshold that was derived because of technological feasibility. In other words, ain't no way to treat water for arsenic to get it below that concentration.

The real number they wanted to see was 0.003 ppb which would give them an excess risk of one in one million excess cancers in a 70 year lifetime.

Now that we know those two values, 0.003 and 0.000001 (one in one million) we can calculate the slope factor they used in their calculation.

To do this we will use the method developed by California's EPA (CalEPA) for determining the "no significant risk level" (NSRL) for Proposition 65 "Known to the State of California to Cause Cancer" notifications.

Source

California uses a lifetime cancer risk at or below one in one hundred thousand (10-5 or 0.00001).  New Jersey sets the risk at or below one in one million (10-6 or 0.000001).  New Jersey law in this case aims to be more protective since zero is a non-attainable number.

What we need to do now is find the Cancer Slope, which CalEPA calls the qhuman.  The qhuman is a value described in terms of  (mg/kg-day)-1.

To get this value, we will need to convert our 0.003 ppb (which is in μg/L) to the amount in milligrams (mg).

So...if there are 1000 μg in a mg, the μg is 1000 times smaller than a mg.  Which makes 0.003 μg equivalent to 0.000003 mg.

Here is where it gets a bit confusing.  That number that New Jersey came up with, that's for a safe level of arsenic in drinking water for a life time excess cancer risk of one in one million.  A lifetime is 70 years and the amount of drinking water we consume is calculated on 2 liters a day.  So, the total amount of arsenic that would be consumed over a lifetime is 0.006 μg.

In other words, if a 70 kg person drank two liters of water a day, they would consume a total of 0.006 μg of arsenic from that water.  At that total amount, the drinking water would pose no more than one additional bladder or lung cancer in one million folks drinking the same water.

The key then is to keep the total arsenic from drinking water to at or below 0.006 μg or 0.000006 mg.

That total concentration is based on the potency of the carcinogen we are looking at.  That potency is called the slope factor and is a "theoretical estimate for humans" which CalEPA calls the qhuman which is in (mg/kg-day)-1.

Math time!

Using the CalEPA formula, I calculated the qhuman (Slope Factor) that was used by New Jersey to come up with the 0.003 μg/L for drinking water to give a lifetime cancer risk of one in one million excess bladder/lung cancers.

By my calculation, the qhuman (Slope Factor) = 11.6  (mg/kg-day)-1

That Slope Factor is consistent with the one the one the EPA uses for their male bladder cancer lifetime incidence estimate:

Table 5-3 Male Bladder Cancer Lifetime Incidence Estimate.xls

So now that we have the Slope Factor, we can look at the theoretical risk at different concentrations, such as 5 ppb and 10 ppb.

Next Post: Arsenic in Rice:  Part 5 - What Does "Most Protective" mean in New Jersey?

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