$200,000-433,000 annually for men with a confidence interval

that goes from 194,000 to 206,600

and so you can see now the estimate size will be different on the order of

$33,000 per year more for men than women.

The confidence intervals do not overlap but this comparison here is unadjusted,

it's the crude unadjusted association is

certainly possible that other characteristics differ between men and women that

are also related salary and that may still be a problem to be

fair but in terms of estimating

the actual comparable difference in the physicians we have,

it's important to take those into account.

So, what they did was they went ahead and adjusted for different factors

and then adjusted association between salaries in

biological sex adjusting for a specialty,

academic rank, leadership positions,

publications, and research time.

And what they found is after they did this,

the difference between men and women who were comparable in terms

of these other things attenuated a bit down to only order

$13,400 which is certainly less

than the unadjusted average difference of on the order of $33,000.

But nevertheless, this difference is still statistically significant and large so

even after accounting for differences between men and

women that may be related to salary there was still a gap.

A sizable gap albeit not as large as

what was originally shown in the unadjusted comparison.

So what they did essentially,

was they used the method called

multiple linear regression and we'll get to that in the next section but basically

they fit a simple logistic regression model where the outcome was

annual salary and the only predictor was sex and the slope for sex when coded was a

one for males and a zero for females was that

$32,764 difference in the unadjusted mean difference in salaries between men and women.

And when they fit a model that adjusted for these other things,

the resulting slope for sex was

$13,399 where sex was coded as one for males and zero to females.

Let's look at another example and think about what we

can expect in terms of confounding here.

This is the primary biliary cirrhosis trial data

randomized study where patients with primary biliary cirrhosis were

randomized to either receive the drug D Penicillin abbreviated as DPCA or a placebo.

We've looked at this many times and

the incidence rate ratio of death for these patients in the 12-plus year

follow-up period for the drug group placebo was 1.06 with

a confidence interval that span from 0.75 to 1.5.

So, extensively, it looked like there was no benefit of the drug.

Not only would we already have a heads up that

the drug would be a good thing because even if it were,

statistically different than the placebo it would

not be in the direction we were hoping for

because it would incur a higher risk of death but

ultimately the result wasn't statistically significant.

As if that would matter when we had

an estimated association that showed more deaths among the drug group.

But what we might want to ask is are we comparing comparable people in these two groups.

So, you may recall though that patients,

the 312 in the study were randomized to the DPCA the drug or the placebo group.

So, in a moment we're going to present the adjusted incidence rate ratio,

adjusted only for sex but we could do more adjustments if we wanted to,

adjusted for both sex and baseline bilirubin levels of the subjects in the study.

Let me ask you this, how do you expect this adjusted incidence rate ratio to

compare in value to the unadjusted estimate of 1.06 from the previous slide?

And you may want to pause here and think about this but let's think about

what the necessary and sufficient conditions are for

either sex or baseline bilirubin or both to be

confounders of the association between death and treatment.

So, let's look in order to be a confounder,

each of these would have to be related to both death,

the outcome of interest, and treatment.