>> Because adding potential confounding variables towards statistical model can
help us to gain a deeper understanding of the relationship between variables or
lead us to rethink an association.
It's important to learn about statistical tools that will allow us to examine
multiple variables simultaneously, that is look at more than two or
three variables at the same time.
The general purpose of multi variant modeling techniques, such as multiple
regression and logistic regression is to learn more about the relationship
between several explanatory variables and one response variable.
>> These regression procedures are very widely used in research.
In general, they allow us to ask and hopefully answer the question,
what is the best predictor of?
And does variable A or variable B confound the relationship between my
explanatory variable of interest and my response variable?
>> For example, educational researchers
might want to learn about the best predictors of success in high school.
Sociologists may wanna find out which of the multiple social indicators
best predict whether or
not a new immigrant group will adapt to their new country of residence.
Biologists may want to find out which factors, such as temperature or
barometric pressure or humidity best predict caterpillar reproduction.
So how can multivariate models help us to evaluate the presence or
absence of confounding or lurking variables?
Since the difficulty arises because of the lurking variables values being
tied in with those of the explanatory variable, one way to attempt to
unravel the true nature of the relationship between explanatory and
response variables is to separate out the effects of the lurking variable.
>> You may have already identified a significant relationship between
your explanatory and response variables.
And now want to think about whether this is a real relationship or if instead,
the relationship is confounded by one or more lurking variables.
>> For example, here's a graphical association between birth order and
number of cases of down syndrome per 100,000 live births.
As you can see, it looks like a linear association where the first born
in a family has the lowest likelihood of having down syndrome.
With later birth order up to a fifth born child,
there's increased risk of being born with down syndrome.
This is a statistically significant association when
analyzed via a chi square test of independence with birth
order as the categorical explanatory variable in the presence or
absence of down syndrome as the two level categorical response variable.
Another statistically significant relationship is
the association between maternal age at a child's birth and
the likelihood that the child will have down syndrome.
You can see here that babies of younger women up to about the age of 29 or
30 to 34 have really low rates of down syndrome.
Among mothers age 35 to 39 and older, you see the rates are clearly higher.
>> Remember, in the case of the confounding variable the observed
association with the response variable should be attributed to the confounder
rather than the explanatory variable.
We test for confounders by including these third variables or fourth or
fifth in our statistical modules that may explain the association of interest.
>> In these examples, it's possible that the association between a child's
birth order and risk for down syndrome could be confounded by maternal age.
Alternately, the association between maternal age and
down syndrome might be confounded by birth order or both birth order and
maternal age might independently predict the likelihood of
a diagnosis of down syndrome after controlling for each other.
Here's a graph that answers this question by showing that maternal age confounds
the relationship between birth rank and down syndrome and that it's really
maternal age rather than birth rank, that's associated with Down Syndrome.
Here, you see birth order along the horizontal axis.
The maternal age groups are along the z-axis.
Then on the y-axis, we have cases of down syndrome per 100,000 live births.
If we look across birth order separately for each maternal age group,
we see that there really is no difference in rates of downs syndrome by birth order.
In other words, once we control for the age of the mother that is examine
the rates of down syndrome across birth order but one maternal age group
at a time, there's no association between birth order and down syndrome.
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If we look at rates of down syndrome across maternal age for
each individual birth order we see an upward trend as maternal aging, Increases.
So if you look across these colors,
this is a great graphical representation where we see that it isn't
birth order that is associated with down syndrome, it's maternal age.
In other words, once we control for birth order,
there's still an association between maternal age and down syndrome.
Birth order does not confound the relationship between maternal age and
Down Syndrome.
The relationship holds even after controlling for birth order.