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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