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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Apples, Arsenic, and Risk - Part 3: EPA's Black Diamond Cancer Slope

Basically, what we want to know is how much gosh darn arsenic in my drinking water, apple juice, or grape juice is "safe?"  Heck, we know it's in there, in fact with arsenic it's darn near in everything we consume.

For now, the amount of arsenic in our drinking water we consider "safe" is 10 ug/L or 10 ppb (parts per billion).  That daily exposure to the human population (including sensitive subgroups) is likely to be without an appreciable risk of deleterious effects during a lifetime (70 years) of drinking water with 10 ppb arsenic in it.

Yet Consumer Reports tells its readers that "water with 10 ppb of arsenic, the excess cancer risk is one in 500" and Dr. Nachman with Johns Hopkins claims that the current 10 ppb standard for drinking water is "unprotective." (1)

So, which is it?  Is the new EPA proposal based on mortality data from Morales et al. (2000) for the dose-response assessment for the final draft SFo correct, or are we protected from deleterious effects during a lifetime with the current RfD and 10 ppb for drinking water?

It comes down to how much stock you put in the data used to calculate the numbers used in your model.

In my first post on this topic I showed how the CalEPA determines the concentration of a carcinogen which "pose no significant risk" for cancer under California's Proposition 65 regulation.

That's important to understand here, because if there is "no significant risk" of cancer at a particular concentration of a carcinogen, how can we also state, as Consumer Reports does, that EPA assumes there's actually no "safe" level of exposure?"

This is where it gets complicated, and here is where we lose the public.

Back to the question: How much gosh darn arsenic in my drinking water, apple juice, or grape juice is "safe?"

The reason I spend time researching and writing on this stuff is because we as environmental and public health professionals do a terrible job of quantifying risk so that the average person can answer the most basic of questions: Is this stuff in my food & drink going to harm me?  Is the contamination in, or around me, going to harm me or my kids?  Is it safe?

The amount of arsenic Consumer Reports states that will result in one additional cancer in 500 is 10 ppb, which is the amount or arsenic in drinking water that EPA states will not result in an appreciable risk of deleterious effects during a lifetime.

Neither of these statements can be true at the same time.  And for either one to be true, we must have confidence in the data used to calculate the risk.  Ultimate truth in determining a "safe" level of arsenic will never be known, so the best we can do is look at the concentration of arsenic in the drinking water that our current method of determining risk supports.

Either EPA's proposed slope factor is the way to go, or the current model supporting 10 ppb in drinking water is valid.

Forget "less is better" - that's a given - but it plays no part in accepting one model's conclusion over another.

An excess of one additional cancer in 500, as Consumer Reports informs its readers, results from drinking water with 10 ppb arsenic.  This is based on a simple calculation:

([mg/day] * SFo) / 70 kg = risk (CalEPA)

For calculating how much arsenic in drinking water that "pose no significant risk," the EPA uses the concept of "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. (2)

A bit of confusion takes place here.  What is a significant risk?  For carcinogens, CalEPA uses a "no significant risk level (NSRL) associated with a lifetime cancer risk of 10-5" - or one additional cancer in 100,000.  EPA, as you can see above, bases cancer risk on one additional cancer in 1,000,000 (10-6).

What's all this mean?  Based on the formula above, the [mg/day] calculated for "no significant risk"will be less for the EPA then for California's Proposition 65.

If less is better, wouldn't we want to go with the EPA's one in a million rather the CalEPA's one in 100,000?  Well of course, you know, less is better, right?

This is where it gets really confusing, not to mention difficult to communicate.  That one additional cancer in 100,000 or 1,000,000 is a probability, which is how we describe risk associated with carcinogens.

For example, the probability of you winning the Texas Lottery is 1 in 25,827,165 (3).  Does this mean you will win at least once if you play 25,827,165 different times?  No.  Same with "getting" cancer from drinking water with 10 ppb arsenic.

There is a difference here, though, with the lottery each play has the potential to win since six numbers will be drawn.  For exposure, the carcinogen may cause damage, or it may not.  Then, if it does cause damage, the body may repair that damage, or it may not.  Consequently, the more exposure the more chance for damage to occur.  This then is followed by repair.  Cancer is the result of damage (causing abnormal and unregulated growth of cells) that is not repaired and is then able to grow and spread (metastasis).

Cancer risk is based on the idea that if we know there is a concentration where we see cancer produced, then some concentration less than that will produce cancer at a diminishing rate.  That's not how carcinogens work in the body, but its the best we have - that's why it's known as a "theoretical potency factor."

The cancer slope factor "SFo" for arsenic that the EPA wants to use is based on the idea that there is a dose-response for carcinogens as there is for non-carcinogens.

In order for the Unit Risk that calculates the excess cancer risk per one microgram (1 ug) of arsenic per liter of drinking water to be valid, the cancer slope factor must be valid, that is, can we accept the potency of arsenic causing cancer based on a theoretical value derived from assuming that there is a dose-response for cancer?

It's the best toxicologist have to tell us what "safe" is.  So let's assume that the premise of a theoretical potency is correct based on the slope factor derived from a dose-response curve for a particular carcinogen, like arsenic.  How that potency is derived is based on the slope as it relates to dose and response.

What is the "slope"?  Same definition here as it has in math:

The slope of a line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line. (4)

The steeper the dose-response line, the more potent the carcinogen.  All of this is theoretical, of course, because it assumes you can get a straight line for your dose-response data.  

Source

Cancer does not work that way, so you have to assume a straight line based on extrapolating a straight line from the data points you do have - which is predicated on the idea that there is a dose-response relationship at both the high and low dose.

Source

So 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 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.

When Consumer Reports tells their readers:

For known human carcinogens such as inorganic arsenic, the EPA assumes there's actually no "safe" level of exposure, so it normally sets exposure limits that include a margin of safety to ideally allow for only one additional case of cancer in a million people, or at worst, no more than one in 10,000. For water with 10 ppb of arsenic, the excess cancer risk is one in 500.

consumer Reports and their researchers are telling us that EPA's cancer potency for arsenic, the theoretical slope factor - SFo - has been derived correctly.

In order for one excess cancer risk in 500 for 10 ppb arsenic in drinking water to be valid, the slope factor must be correctly extrapolated from the dose-response curve for the cancer in question.

Has it?

Next Post: Apples, Arsenic, and Risk - Part 4: The TCEQ tells the EPA, Phooey!


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