Apples, Arsenic, and Risk - Part 5: Calculating one in 500

I want to look at how Consumer Reports is able to claim that:

For water with 10 ppb of arsenic, the excess cancer risk is one in 500.

 How was that risk calculated, and most importantly, is it valid?

In my last couple of posts I have tried to explain how cancer risk is determined to answer the question of what amount of arsenic in my drinking water, apple juice, or grape juice is considered "safe?"  Ignoring less is better, how does the process work?

For chemicals that are known or suspected to be carcinogens, we use a potency factor which is the slope of the dose-response curve.  The EPA takes this potency and incorporates it into what they refer to as a "Unit Risk."

Unit Risk: The upper-bound excess lifetime cancer risk estimated to result from continuous exposure to an agent at a concentration of 1 µg/L in water, or 1 µg/m3 in air. The interpretation of unit risk would be as follows: if unit risk = 2 × 10-6 per µg/L, 2 excess cancer cases (upper bound estimate) are expected to develop per 1,000,000 people if exposed daily for a lifetime to 1 µg of the chemical per liter of drinking water. (1)

To calculate the Unit Risk, you need the cancer slope factor - potency - SFo.  Not to beat a dead horse here, but the  slope you calculate is going to be based on this hypothetical line you derive from the dose and the occurrence of cancer you have seen in your studies.

That hypothetical line is critical in determining the slope.  That slope represents the potency.  The potency will calculate the Unit Risk.  The Unit Risk will tell us the excess cancer cases (upper bound estimate) that are expected to develop per 1,000,000 people if exposed daily for a lifetime to 1 µg of the chemical per liter of drinking water.

The EPA is proposing to change the IRIS Toxicological Review of Inorganic Arsenic (Cancer) by increasing the slope factor - potency - by 17 fold.  Here is an example of how this cancer potency affects the cancer risk described.

Let's look at how the EPA looks at arsenic and bladder cancer in males.  This information comes from an Excel spreadsheet that can be downloaded from the IRIS web site.

The oral cancer slope factor (CSF or SFo) the EPA uses for its "Male Bladder Cancer Model Outputs" is:

11.2 mg/kg-day

If the average male weighs 70 kg and drinks 2 liters of water per day, the liters per kg drinking water intake will be calculated as follows:

2.0 L / 70 kg = 0.029 L/kg-day

To calculate the Unit Risk per ug/L, the cancer slope factor (CSF or SFo) is multiplied by 0.001 to go from mg to ug.

0.001 x 11.2 mg/kg-day = 0.0112 ug/kg-day.

...it is then multiplied by the L/kg-day:

0.0112 ug/kg-day x 0.029 L/kg-day = 0.00032 ug/L or 3.2E-04 = Unit Risk

The Unit Risk for Male Bladder Cancer for arsenic is 3.2E-04 ug/L

So how do we use that Unit Risk?

Well, for starters, we can use it to calculate the Lifetime Risk of arsenic in drinking water at 10 ug/L:
10 ug x 0.00032 ug/L = 0.0032 or 3.2E-3 Lifetime Incidence.

What's that mean?

If the cancer slope factor is correct, we will see 3 excess cancers in 1000 if exposed daily for a lifetime to 10 µg of arsenic per liter of drinking water.

So how much arsenic in drinking water would not present a significant risk for cancer?  What amount could we live with and still consider the water to be "safe?"

For that, the EPA has to decide what is significant.  Is it one in a million?  One in 100,000?  One in 10,000?  For a significant risk, the calculations used in the proposed IRIS document for arsenic use a "water concentration for a 10-4 incidence risk" - or one in 10,000.  The amount of arsenic in drinking water that is considered "safe" is the amount that will estimate a one in 10,000 lifetime risk.

To calculate the amount of arsenic in drinking water that will see a one in 10,000 lifetime risk, the EPA multiplies the cancer slope factor (CSF or SFo) by 0.0001 (1 in 10,000)

0.00032 x 0.0001 = 0.32 ug/L

There you have it.  To reduce the risk of male bladder cancer we need to consume no more than 0.32 ug/L of arsenic based on a 70 kg males drinking 2 liters per day for 70 years.  At that concentration, 0.32 ug/L, we should see no more than one additional male bladder cancers per 10,000.

Using the CalEPA method, we would come up with the same risk.  Using their formula, ([mg/day] * SFo) / 70 kg = risk, and the amount consumed, 0.32 ug/L = 0.00032 mg/L in a 70kg adult who drinks two liters of water per day (0.00032 x 2 = 0.00064 mg/L....we get:

([0.0064] x 11.2) / 70 = 0.000102 = 1.02E-04 or one in 10,000

And what does the proposed SFo model predict for excess male bladder cancers at the current MCL of 10 ug/L?  Three additional male bladder cancers per 1000, or about one in 330.

For those "lifetime risks" to me valid, the cancer slope factor (CSF or SFo) must be valid.  You saw in my last post that the TCEQ thinks the EPA has erred in how they calculated the slope factor.  You may also remember that the proposed cancer slope factor they want to use is 17 times higher than the one they use now.  They want to take it from a potency of 1.5 mg/kg-day to 25.7 per mg/kg-day.  The CSF used for male bladder cancer was 11.2 mg/kg-day and that gave use a male bladder cancer incidence of one per 300!

The question now becomes: how representative is that upper bound limit of risk that has been calculated?

Should we accept Consumer Reports excess cancer risk is one in 500 for 10 ug/L of arsenic in drinking water?

I bet the TCEQ has something to say about that as well.


Next post: Apples, Arsenic, and Risk - Part 6: Theory and Reality


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