Apples, Arsenic, and Risk - Part 15: 19% more...67 years...carry the 2...

Consumer Reports states in their January 2012 report on arsenic in apple juice:

The resulting analysis of almost 3,000 study participants found that those reporting apple-juice consumption had on average 19 percent greater levels of total urinary arsenic than those subjects who did not.

If the average total urinary arsenic [NHANES] for 12-18 year old's is 8.55 ug/L, Apple juice drinkers would be - on average - 19% higher than that, or 10.17 ug/L.

The "long-term low-level arsenic exposure" was calculated as follows:

We estimated long-term low-level exposure by multiplying current estimated arsenic levels by the number of years residing in current home.

So an 18 year old would have a long-term low-level arsenic exposure of 18 x 8.55 = 153.9 ug/L-year.

And the 18 year old apple juice drinker would have a long-term low-level arsenic exposure of 18 x 10.17 = 183.1 ug/L-year.

So if the unstandardized regression coefficient - B - results are as reported, these are the scores we would predict between the two groups, average & apple juice drinkers, over an 18 year exposure period.

I ran their data in an Excel spread sheet so I could see what the difference would be between the two scores.  That's found in the last column at the bottom.  Notice how not one of those tests has a decrease or increase in the score over one (1).

The question I have is this: If the linear regression calculates an unstandardized regression coefficient called "B," and that we interpret an unstandardized regression coefficient as follows:

For every metric unit change in the independent variable, the dependent variable changes by X units.

The change in score these researchers report is so small as to be of little value.  Yet what was reported in this paper was used by Consumer Reports to make the claim that low-levels of arsenic below the drinking water MCL of 10 ug/L presents "a chronic problem" "related to poor scores in language, memory, and other brain functions."

Consumer Reports is using the conclusion of this paper to support their claim that:

Mounting scientific evidence suggests that chronic exposure to arsenic and lead even at levels below water standards can result in serious health problems.

Is this the" mounting scientific evidence" they are using to support their claim that low-level exposure is related to poor scores in language, memory, and other brain functions?

Did the researchers from Texas Tech and the University of North Texas find that "long-term low-level exposure to arsenic was significantly associated with poorer scores?"

Yes.  And that's the problem that needs to be addressed.

Numbers mean something.  Those "Bs" reported are valid in supporting their conclusion:

Our findings suggest an association between low-level arsenic exposure and neuropsychological functioning, as originally hypothesized. Of particular interest is the association between long-term low-level arsenic exposure and neuropsychological functioning across a broader range of domains than current exposure. Our findings offer the first direct evidence that low level arsenic exposure, extrapolated from current arsenic levels and self report of duration in residence is associated with poorer neuropsychological functioning among community-dwelling adults and elders in the U.S.

They found an association and the statistics - the p-value - supports it.  But what did they really find?

Or, more importantly, did they see results that would support lowering the level of arsenic deemed safe?  Are their results strong enough to stop us from drinking apple juice?  Should we, on the basses of a -0.001 change in a score require apple juice providers to reduce the concentration of arsenic from and average of 4 ug/L to 3 ug/L?

Why did four researchers produce this paper, and why did it it get published in a peer review journal?  Because there is nothing wrong with it in terms of it meeting the standards for publishing.

It's valid, it's honest, it's conclusion is correct.  Unfortunately it does not support the claim of "mounting scientific evidence suggests that chronic exposure to arsenic and lead even at levels below water standards can result in serious health problems."

It shows something that means nothing.  And that right there leads Consumer Reports, Dr. Oz, and good ol' Chuck Norris down the path of requiring a change where one is not needed.

As our investigation found, when scientists and doctors do look, the connections they’ve found underscore the need to protect public health by reducing Americans’ exposure to this potent toxin.

Why is this a big deal?  Let me quote the Texas Commission on Environmental Quality (TCEQ) once again:

[I]f erring on the side of conservatism significantly overestimates risk or hazard and is not  fully  justified, then harm to public health may result from diverting public, industry, and government attention and resources away from chemicals which may represent more of a public health risk at environmental levels. (TCEQ)

Next Post: Apples, Arsenic, and Risk - Part 16: The Great and Powerful Oz

Apples, Arsenic, and Risk - Part 14: A poorer score of -0.001

Once more....

Consumer Reports claims in their January 2012 article on arsenic in apple juice:

Mounting scientific evidence suggests that chronic exposure to arsenic...even at levels below water standards can result in serious health problems.

A 2011 study examined the long-term effects of low-level exposure on more than 300 rural Texans whose groundwater was estimated to have arsenic at median levels below the federal drinking-water standard.

It found that exposure was related to poor scores in language, memory, and other brain functions.

What I want you to focus on is "even at levels below water standards" and "exposure was related to poor scores in language, memory, and other brain functions."

In my last post I looked at these two claims by the studies authors:

1. Current estimated groundwater arsenic exposure level was significantly associated with poorer scores in language, visuospatial skills, and executive functioning. 
2. Current arsenic exposure significantly classified cognitive dysfunction. 

In this post I want to look at their conclusion for what the term "long-term low-level arsenic exposure:"

We estimated long-term low-level exposure by multiplying current estimated arsenic levels by the number of years residing in current home.

I'm not going to make an argument as to whether or not that that's a valid methodology.  I don't need to.  The B(SE) they report in Table 3 tell me there is nothing to be concerned about:

Source

Once again, I'm no linear regression expert or statistical astute person.  What I know about something is what I have been taught and what is consistently discussed.  I may be wrong on how to interpret those B(SE) scores, but I don't think I am. (Comments are on - feel free to skool' me)

Here is what the Google says about an "unstandardized regression coefficient" - "B":

To interpret an unstandardized regression coefficient: for every metric unit change in the independent variable, the dependent variable changes by X units. For instance, if income is the dependent variable, and years of education is one of the independent variables, and the unstandardized regression coefficient for education is 3,000, then this would mean that for very additional year of education a respondent has, their income increases by $3,000.00 (controlling for the other independent variables in the equation). (1)

and...

As you may remember, in a linear regression model the estimated raw or unstandardized regression coefficient for a predictor variable (referred to as B) is interpreted as the change in the predicted value of the dependent variable for a one unit increase in the predictor variable. Thus a B coefficient of 1.0 would indicate that for every unit increase in the predictor, the predicted value of the dependent variable also increases by one unit. In the common case where there are two or more correlated predictors in the model, the B coefficient is known as a partial regression coefficient, and it represents the predicted change in the dependent variable when that predictor is increased by one unit while holding all other predictors constant. (2)

Let's take the example in the first blurb.

"if income is the dependent variable" will now become "if RBANS Visuopatial score is the dependent variable."

"years of education is one of the independent variables" will now become "long-term low-level arsenic exposure is one of the independent variables."

"and the unstandardized regression coefficient for education is 3,000" will now become "and the unstandardized regression coefficient for  RBANS Visuopatial  is -0.001"

"then this would mean....."

"that for very additional ug/L-year of arsenic a rural Texan is exposed to, their  RBANS Visuopatial score decreases by 0.001 (controlling for the other independent variables in the equation)

Please tell me I am wrong in how this is to be interpreted.  Please don't tell me that these four researchers from Texas Tech and the University of North Texas reported that:

However, we can assert that those individuals who have resided for long periods of time in regions that have historically low levels of arsenic in groundwater supplies are at increased risk for cognitive dysfunction.

...based on unstandardized regression coefficient - B - results as follows:

• MMSE: −0.003
• CLOX 2: −0.001
• FAS: −0.012
• RBANS Language: −0.005
• TMTA:  0.034
• EXIT: 0.006
• RBANS Immediate Memory: −0.010

How does a change in score of -0.003 for each ug/L-year arsenic exposure constitute an "increased risk for cognitive dysfunction?"

Let me do some math...."long-term low-level arsenic exposure:"

We estimated long-term low-level exposure by multiplying current estimated arsenic levels by the number of years residing in current home.

So the ug/L-year = Estimated Arsenic Level x Number of Years in Home...Looking at Table 2....

Source

So....240.15 / 6.33 = 37 years...nah, that can't be right.  972.83 / 15.26 = 63 years.  I'm not sure how they calculated that number of 240.15.  If the highest range was 972.83 ug/L-years and the highest arsenic range was 15.26 ug/L that would mean 63 years of exposure in the same house.  That's possible, I guess, especially for a rural community.

The unstandardized regression coefficient states the for every metric unit change in the independent variable, the dependent variable changes by X units.  So the "X" units we are talking about is the score.  What I don't know is the unit change we could use to calculate that predicted score.

The long-term arsenic range is 2.87 - 972.83 ug/L-years.  I'll assume that the unit change is one ug/L-year.  This would equate to a difference of 972.83 - 2.87 = 969.96 units of change.

If we take that number - 969.96 and multiply it by the B values reported as "significantly associated with poorer scores" we would expect the following score changes for a person exposed to 15.26 ug/L of arsenic for 67 years:

• MMSE: −0.003 x 969.96 = -2.9
• CLOX 2: −0.001 x 969.96 = -0.96
• FAS: −0.012  x 969.96 = -11.6
• RBANS Language: −0.005  x 969.96 = -4.8
• TMTA:  0.034  x 969.96 = 32.9
• EXIT: 0.006  x 969.96 = 5.8
• RBANS Immediate Memory: −0.010  x 969.96 =  -9.6

I'm not sure that a unit of change is calculated like that, but based on a worst case scenario, and from what the Google tells me about how an "unstandardized regression coefficient" works, that's the changes in scores I would predict for a 67 year long exposure to 15.26 ug/L of arsenic.

What would we predict for a person who consumes apple juice for 67 years?


Next Post: Apples, Arsenic, and Risk - Part 15: 19% more...67 years...carry the 2...


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Apples, Arsenic, and Risk - Part 13: How much is "19 percent higher levels?"

My last post had me looking at a study Consumer Reports states in their January 2012 report on arsenic in apple juice that:

A study published in 2011 in the International Journal of Environmental Research and Public Health examined the long-term effects of low-level exposure on more than 300 rural Texans whose groundwater was estimated to have arsenic at median levels below the federal drinking-water standard. It found that exposure was related to poor scores in language, memory, and other brain functions.

This study used linear regression to:

Examine the potential association between current and long-term arsenic exposure and detailed neuropsychological functioning in a sample of rural-dwelling adults and elders.

What we know so far is this:

• Linear regression models were created using raw neuropsychological test scores as outcome variables and either current or long-term arsenic exposure estimates as predictor variables.
• Linear regression is when you want to predict values of one variable, given values of another variable.

So what we can see from Table 3:

Source

Is that when the current arsenic level increases by one unit, the  "RBANS Language scores" decrease by 0.458 (controlling for the other independent variables in the equation).  That's the prediction of their linear regression model for RBANS Language Scores [−0.458 (p = 0.008)].

For the 13 tests administered, the study found that current GIS-based groundwater arsenic exposure was significantly related to poorer scores for three of the tests:

• RBANS Language scores B(SE) = −0.458 (0.171), p = 0.008
• Visuospatial skills CLOX2, B(SE) = −0.118 (0.060), p = 0.048
• Executive functioning CLOX1 B(SE) = −0.225 (0.080), p = 0.005

So for the sake of argument (and to give me something to write about) let's say that this model is predictive as the authors claim.  How much "poorer" would the scores be for children who drink apple juice?

According to Consumer Reports:

The resulting [NHANES] analysis of almost 3,000 study participants found that those reporting apple-juice consumption had on average 19 percent greater levels of total urinary arsenic than those subjects who did not.

Interesting....remember this table from NHANES:

Source

The mean and (95% CL) for kids 6-11 years old is 7.08 (5.68-8.84).

With that, we can calculate how much "19% more total urinary arsenic" would be for 6-11 year old kids who drink apple juice.

Do some math...carry the 2....7.08 x 1.19 = 8.43 ug/L

So apple juice drinking 6-11 year old kids have 1.35 ug/L more arsenic.  If the linear regression model in this study is correct, we would predict their scores to decrease as follows.  The "B" represents the slope of the regression line--the amount of change in Y due to a change of 1 unit of X:

• RBANS Language scores: -0.618
• Visuospatial skills CLOX2: -0.159
• Executive functioning CLOX1: -0.304

Is that decrease in score a concern?  Look at the standard deviations for the test results in Table 2.  (CLOX means are not listed by the authors, I am assuming their range is similar to the other tests)

Source

For RBANS Language the standard deviation is 5.46 points.  Our little apple juice drinkers would see a decrease in their scores of 0.618.

"But"...you say..."the results might understate the correlation between juice consumption and urinary arsenic levels because NHANES urinary data exclude children younger than 6, who tend to be big juice drinkers."

Let's up the arsenic to that found in males; 9.50 ug/L.  19% more...carry the 2...9.50 x 1.19 = 11.3 ug/L

So...2.25 ug/L more arsenic...or 2.25 units...2.25 x -0.458 = 1.03 points lower for RBANS Language.  That's assuming their model holds true.   Look at the range of results they got; 8 - 42.  Would a decrease of one point indicate a concern?  Is this what Consumer Reports means when they state:

"Mounting scientific evidence suggests that chronic exposure to arsenic...even at levels below water standards can result in serious health problems."

But all that's for the current arsenic level.  Let's look at what they found when they ran the linear regression with long-term arsenic - ug/L-years.


Next Post: Apples, Arsenic, and Risk - Part 14: A poorer score of -0.001

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Apples, Arsenic, and Risk - Part 12: Correlation does not imply causation

In my last post I asked the question:

What about Consumer Reports telling its readers about a 2011study in the International Journal of Environmental Research and Public Health that examined the long-term effects of low-level exposure on more than 300 rural Texans whose groundwater?

Consumer Reports claims in their January 2012 article on arsenic in apple juice that these Texans were estimated to have exposure to arsenic at median levels below the MCL and when tested showed poor scores in language, memory, and other brain functions.

That brings me to asking this question: will "low-levels" of arsenic, as was found in the apple juice samples tested by Consumer Reports lead adversely affect those that consume apple juice?  Here is what they state at the beginning of their report:

Mounting scientific evidence suggests that chronic exposure to arsenic...even at levels below water standards can result in serious health problems.

I've looked at cancer, hyperkeratosis, and type 2 diabetes, that leaves this one last study on chronic exposure to look at.  Will this support their claim that levels below the MCL can result is serious health problems?

Here is what Consumer Reports tells their readers about this 2011 study:

It found that exposure was related to poor scores in language, memory, and other brain functions.

Here is what that paper concludes:

The results of the study showed that GIS-based groundwater arsenic exposure (current and long-term) was significantly related to poorer scores in language, visuospatial skills, and executive functioning. Additionally, long-term low-level exposure to arsenic was significantly correlated to poorer scores in global cognition, processing speed and immediate memory.

"Significantly related" and "significantly correlated."

Two things to keep in mind here:

1. The term "significantly" is in reference to statistics.  That is, it is unlikely to have occurred by chance.  Not significant as in "sufficiently great or important to be worthy of attention."
2. The term "correlated" means a statistical measurement of the relationship between two variables.

So "significantly correlated" means a relationship between two variables that is unlikely to have occurred by chance.

Rule number one about correlations:  They do not imply causation!!!

Source

...and so it goes with low-levels of arsenic in our our apple juice and water.

Let's look at the table of results:

Source

I am by no means a statistician, nor am I really that versed to expertly explain "unstandardized regression coefficient" as it is derived from a "linear regression" model.  For more info on this see 1, 2, 3, or 4.

What I do understand about this table is this:

Linear regression models were created using raw neuropsychological test scores as outcome variables and either current or long-term arsenic exposure estimates as predictor variables.

So....

Simple linear regression is when you want to predict values of one variable, given values of another variable.

The purpose of regression analysis is to come up with an equation of a line that fits through that cluster of points with the minimal amount of deviations from the line. The deviation of the points from the line is called "error."

Once you have this regression equation, if you knew a person's Long-term or current arsenic level of exposure, you could then predict their score on one of the  neuropsychological tests administered.

The data in Table 3 is reported for:

B = unstandardized regression coefficient.

So...

B coefficients are interpreted as the amount of change in the dependent variable (Y) that is associated with a change in one unit of the independent variable (X).

All B coefficients are unstandardized, which means that the magnitude of their values is relative to the means and standard deviations of the independent and dependent variables in the equation.

It represents the slope of the regression line--the amount of change in Y due to a change of 1 unit of X.

The unstandardized coefficients are used for actually making a prediction, using the independent variables as they were measured.  For example, if a variable is in dollars, the unstandardized coefficient is in dollars, if a variable is in inches, it is in inches.

What Table 3 tells us is this:

If "RBANS Language scores" is the dependent variable, and "current arsenic level" is one of the independent variables, and the unstandardized regression coefficient (B) for  "RBANS Language scores"  is −0.458 (p = 0.008), then this would mean that for every additional ug/L of arsenic exposed to, there would be a decrease of 0.458 in the RBANS Language scores  (controlling for the other independent variables in the equation).

Remember, correlation does not imply causation.  In other words, it may not be the arsenic that drops the score but something else going on.  For example, there was an increase in polio cases correlated to the amount of ice cream sold.  Ice cream was not the cause of polio, polio cases increased in the summer as did sales of ice cream.

But let's say that this model is predictive, as the authors claim:

Groundwater arsenic exposure (current and long-term) was significantly related to poorer scores in language, visuospatial skills, and executive functioning.

What "serious health problems" - or in this case - how much "poorer" would the scores be for children who drink apple juice?

Next post: Apples, Arsenic, and Risk - Part 13: How much is "19 percent higher levels?"


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