So, the previous section we talked about the potential impact of

confounding and at least one example said one way to handle it,

is to break out and measure

separate estimates of the association for different levels of the confounder.

For example, when we looked at the relationship between

disease and smoking separately for males and females.

But if there's similar associations in

those respective levels of the confounder, so for example,

we saw positive associations between smoking disease in both males and females,

wouldn't it be nice to pull

those consistent estimates across

different levels in the confounder into one overall estimate.

And that's what we're going to talk about here now,

something called unadjusted estimate.

Look, in this section,

we'll talk about the presentation of such estimates,

the interpretation, and their utility in ceci confounding.

And then the next section will give us

a conceptual overview of the idea behind adjustment.

So, for this section,

I'd like you to come out understanding how to interpret

estimates of association that have been adjusted to

control for confounder and compare and contrast

the comparisons being made by unadjusted and adjusted association estimates.

So, adjustment is a method for making

comparable comparisons between groups in

the presence of a confounder or confounding variables.

We will discuss the basics of the mechanics behind

adjustment in the next section but here,

we'll focus on how to interpret them.

So, again recall the results from

our first fictitious study that we did in the previous section,

the study that was done to investigate the association between

smoking and certain disease outcome in male and female adults.

And we saw when we looked at everyone in

one two-by-two table looking at the relationship between smoking disease,

the relative risk of disease for smokers to non-smokers

was slightly less than one or 0.93.

But we saw that this is being influenced by the difference in

sex distributions among smokers and non-smokers,

smokers were more likely to be male,

and males were less likely to have disease.

So, the relative risks that we looked at compares all smokers to all non-smokers.

That relative risk of 0.93,

it did not take any other factors into account.

So, such an estimate is called an unadjusted or crude estimated association.

In this case, the unadjusted or crude estimated association between disease and smoking.

Adjustment provides a mechanism for estimating

the outcome exposure relationship after removing

the potential distortion or negation that comes

from a confounder or multiple confounders.

In the fictional example,

for example the relationship between disease and smoking can be adjusted for sex.

And so since I made up this example,

I had access to all the raw data,

so even though this isn't based on a real scenario,

there is data to represent this.

So, frequently what you'll see in journal articles and we'll explore

this again in more detail in the multiple regression sections,

the bridge presentation of results from non-randomized study will include

a table that shows side by side unadjusted and adjusted measures of association.

So, one one this may manifest itself if our primary concern is about disease and smoking,

we might have a table that looks like this.

We'll show the relative risk of disease and now I've added

95 percent confidence intervals and these can be

computed and we'll discuss that idea in the next section as well.

All I'm showing here is the relative risk of disease for smokers to non-smokers.

In the second column here,

it's the crude or unadjusted and so the setup declares

non-smokers to be the reference group and the implication is that this relative risk of

0.93 is a comparison of the relative risk of disease for smokers to

the reference of nonsmokers with a confidence interval of 0.68 to 1.27.

When we do the adjustment and adjust only for sex,

the relative risk comparing smokers to non-smokers goes up, it's now 1.57.

You can think of it, and we'll talk more about this in the next section,

it's sort of a weighted average between

the sex-specific relative risks we saw for smokers to non-smokers,

the 1.8 for males and the 1.5 for females.

So, this unadjusted relative risk, this 0.93,

compares the risk of disease for all smokers compared to

all non-smokers in the sample regardless of sex or any other characteristic and is,

hence, the estimates the comparisons of

all smokers to non-smokers in the population sample.

This adjusted estimated relative risk of 1.57,

this compares the risk of disease for smokers to

non-smokers of the same sex in the sample and hence

estimates the comparison of smokers to non-smokers of

the same sex in the population sample.

So, this 1.57 is the estimated relative risk of disease for male smokers to

male non-smokers and for female smokers to female non-smokers.

So, as long as we're comparing males to males or females to females,

the relative risk adjusted for sex differences between smokers and non-smokers of

disease is 1.57 for smokers to non-smokers in both sexes.

So, as long as we're comparing individuals of the same sex,

whether be female smokers to female non-smokers or male smokers to male non-smokers,

the relative risk of disease for smokers to non-smokers is 1.57,

it's the same for males and females.

The unadjusted and adjusted associations can be compared both numerically

and qualitatively to assess confounding by at least some of the adjustors.

In this case we've only adjusted for one thing, sex.

And we can see the estimated association goes from something close to the null of one,

so something substantially larger than one.

So, I would say there is some confounding in these data.

From a statistical standpoint,

one could argue that once we account for the uncertainty in the estimates,

there's some crossover in the confidence intervals here,

so it's not clear whether these are statistically distinguishable.

And if they weren't,

then from a statistical standpoint,

this would just be sampling variability.

But generally speaking, I'm willing to say that since the estimate change by

such a large amount and

these confidence intervals are a function of sample size as well as other things,

I would go ahead and say there was some evidence of confounding in this data

given that the adjusted is qualitatively different than the unadjusted.

Let's go back to our observational study that we looked at to

examine the association between arm circumference in Nepalese children.

And again, it was a 150 randomly selected children,

age zero to 12 months who had arm circumference,

weight, and height measured.

So, what I want to look at here and I'm going to compare in this table

the unadjusted and adjusted associations

between arm circumference in both height and weight.

In this situation, let's see what we got,

let's focus on height first and foremost.

So, what we have here are

the regression slopes from models with arm circumference as the outcome.

So in this row,

we have regression slopes for height,

so this first model here is from a regression that

relates y hat is arm circumference and there some intercept,

I don't remember what it is offhand,

but the slope for height was positive.