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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