Epidemiology

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L14_ConfoundingADA.pptx

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Interaction

In this, your last lesson, we’ll talk about a special type of confounding known as interaction.

Overview

Overview of Interaction

How to Detect Interaction

About Interaction

Secondary exposure obscures truth

E and E* interact

Synergistic

Antagonistic

As mentioned, interaction is a special type of confounding that obscures the truth about the primary exposure’s relationship to the disease of interest. Interaction is a biological phenomena that occurs when the effects of the primary exposure and secondary exposure act together to produce a much greater(synergistic) or much weaker (antagonistic) measure of effect than the mere sum of the two exposures..

Recall that with confounding, we want to control for (or eliminate) the effects of E* so as to get closer to the “truth” between E and D. With interaction, we do not want to do this because it isn’t the secondary exposure (E*) in and of itself that is obscuring the truth.

Because interaction is a biological phenomena, it should be appreciated and communicated if found.

Let’s look at an example.

Example

To determine the relationship between oral cancer and alcohol use, you conduct a ca-co study using 400 cases and 400 controls. Your data showed that 320 cases and 180 controls were alcohol drinkers. Because many drinkers smoke cigarettes, and there is an independent relationship between smoking and oral cancer, you measure for smoking status as well. Results show that among drinkers, 252 cases and 72 controls smoked. Of those who did not drink, 48 cases and 40 controls smoked.

So, your primary exposure of interest is………..

And your secondary exposure of interest is……..

f you said drinking and smoking in that order, then give yourself a hearty pat on the back. =)

Step 1: Set up Data Table for E and Calculate Crude OR

	Ca	Co	Total
E+ (Drinkers)	320	180	500
E- (Nondrinkers)	80	220	300
Total	400	400	800

Drinking is your primary E of interest, so calculate the OR for drinking and oral cancer after plugging these data into your 2x2 and calculate a crude OR.

OR crude = ad/bc

= (320 x 220) / (180 x 80)

=70,400/14,400

= 4.9

Step 2: Stratify E by E*

	ca	co	total
SMOKERS (E*+)
E+ (drinkers)	252	72	324
E- (nondrinkers)	48	40	88
Totals	300	112	412
NON-SMOKERS (E*-)
E+ (drinkers)	68	108	176
E- (nondrinkers)	32	180	212
Totals	100	288	388
Grand Total	400	400	8000

If you are unsure how I derived these numbers, please review the lesson on “confounding” where I walk you through the process.

Step 3: Calculate Strata-Specific ORs and compare to Crude OR

OR smoker = 2.9

OR nonsmoker = 3.5

Crude OR = 4.9

OR nonsmoker = (252 x 40)/ (72 x 48) = 10,080/3456 = 2.9

OR smoker = ((68 x 180) / (108 x 32) = 12,240/3456 = 3.5

So when we compare our E* s-s ORs to our crude OR, we notice a few things. First, we see that both strata differ from the crude. Second, we see that the general rule #1 for confounding is met because both s-s ORs are lower than the crude. We also note that the s-s ORs are not that similar; thus, general rule 2 for confounding states we shouldn’t try to adjust for E*. Instead, we suspect synergistic interaction, aka interaction. And we suspect it, we must investigate it. Let me show you how. =)

Step 4: Determine Excess Risk

	Column 1	Column 2	Column 3	Column 4	Column 5	Column 6
	Alcohol	Smoking	Ca	Co	OR	Excess Risk
Row 1
Row 2
Row 3
Row 4

To test for interaction, we create what is called an excess risk table. Yay! More tables!! An excess risk table allows us to determine if there really is a synergistic effect, by comparing each strata of E,E* to a referent.

I’m going to walk you through how the table is set up and calculated in the next several slides, but will also post a video as well on how to do this.

First, you set up the table as shown on the slide. It is VERY important to label each column explicitly, to keep yourself organized, as such

Column 1 = primary E

Column 2 = secondary E (E*)

Column 3 = D+ (cases)

Column 4 = D- (controls)

Column 5 = Odds Ratio

Column 6 = Excess risk

We will have 4 rows, which I will explain in the next slide

	Column 1	Column 2	Column 3	Column 4	Column 5	Column 6
	Alcohol	Smoking	Ca	Co	OR	Excess Risk
Row 1	No	No
Row 2	Yes	No
Row 3	No	Yes
Row 4	Yes	Yes

Columns 2 and 3 by Row

Here’s how to set up your rows:

Row 1 = E-, E*- (non drinker, non smoker)

Row 2 = E+, E*- (drinker, non smoker)

Row 3 = E-, E*= (non drinker, smoker)

Row 4 = E+, E*+ (smoker, drinker)

Row 1 must always be the unexposed on both Es and row 4 must always be the exposed on both Es. You can switch the order of rows 2 and 3 with no consequences…

Now, let’s plug in our numbers….

Columns 3 & 4

	Column 1	Column 2	Column 3	Column 4	Column 5	Column 6
	Alcohol	Smoking	Ca	Co	OR	Excess Risk
Row 1	No	No	32	180
Row 2	Yes	No	68	108
Row 3	No	Yes	48	40
Row 4	Yes	Yes	252	72

	ca	co	total
SMOKERS (E*+)
E+ (drinkers)	252	72	324
E- (nondrinkers)	48	40	88
Totals	300	112	412
NON-SMOKERS (E*-)
E+ (drinkers)	68	108	176
E- (nondrinkers)	32	180	212
Totals	100	288	388
Grand Total	400	400	8000

To show you where I’m getting my numbers, I copied the data table from Step 2 and color coded the numbers. =)

Note: if you’ve set your stratified data up with the E*+ 2x2 table on top, then the Row 1 in your Excess Risk Table will be the last row in your data table and Row 4 will be the first.

Ok, now let’s get to the OR and Excess Risk columns….

Column 5: Compute Row ORs

	Column 1	Column 2	Column 3	Column 4	Column 5	Column 6
	Alcohol	Smoking	Ca	Co	OR	Excess Risk
Row 1	No	No	32 (c)	180 (d)	1 (null)
Row 2	Yes	No	68 (a)	108 (b)	3.5
Row 3	No	Yes	48 (a)	40 (b)	6.8
Row 4	Yes	Yes	252 (a)	72 (b)	19.7

When testing for interaction, we use row 1 as our referent. Because these people are “exposure free,” they -- in essence – represent the natural course of the D of interest, and thus are the null.

Calculating OR. As I noted above, the first row is the referent and therefore will always have the OR of 1 (because 1 is the null value of OR). The other rows are calculated like a normal OR, using the data from the referent row as cells C and D. The A and B cells come from the data in each specific row. We the calculate the OR as usual: OR = ad/bc …. So, in this example we have:

Row 2 = (68 x 180) / (108 x 32) = 12,240/3456 =3.5

Row 3 = (48 x 180) / (40 x 32) = 8640/1280 =6.8

Row 4 = (252 x 180) / (72 x 32) = 45,360/2304 = 19.7

Still with me?

Column 6: Subtract null from OR

	Column 1	Column 2	Column 3	Column 4	Column 5	Column 6
	Alcohol	Smoking	Ca	Co	OR	Excess Risk
Row 1	No	No	32 (c)	180 (d)	1 (null)	--
Row 2	Yes	No	68 (a)	108 (b)	3.5	2.5
Row 3	No	Yes	48 (a)	40 (b)	6.8	5.8
Row 4	Yes	Yes	252 (a)	72 (b)	19.7	18.7

Column 6 shows us how much risk there given the exposure(s) over what occurs naturally. Because Row 1 is the referent, this cell will be blank. For Rows 2 – 4, though, we subtract 1 from the OR values to determine the excess risk. Why? Because the null value of OR = 1; therefore anything above 1 is excess. =) To reiterate, Excess Risk = OR - 1

So:

Row 2 = 3.5 – 1 = 2.5

Row 3 = 6.8 – 1 = 5.8

Row 4 = 19.7 – 1 = 18.7

Now that our Excess Risk table is complete, let’s move on to step 5

Step 5: Make Interaction Determination

Additive Excess Risk = 8.3

Combined Excess Risk = 18.7

Excess Risk Ratio: 2.3

Recall, interaction is when variables act together to produce a much greater (synergistic) or much weaker (antagonistic) measure of effect than the mere sum of the two variables. Therefore, we want to compare the observed excess risk of the two individual Es summed (rows 2 and 3) to the observed excess risk of the two Es together (row 4)

Additive Excess Risk = Excess Risk of Row 2 + Excess Risk of Row 3 = 2.5 + 5.8 = 8.3

Combined Excess Risk = Excess Risk of Row 4 = 18.7

Next, compute how much greater (or lesser) the excess risk of the combined exposures (row 4) is compared to the summed (additive) excess risk of the individual exposures (Row 2 + Row 3). We do this by computing an excess risk ratio as such:

Excess Risk Ratio = Combined Excess Risk / Additive Risk = 18.7/8.3 = 2.3

Interpretation: Both variables acting together produce roughly 2.3 times greater excess risk than the variables produce additively.

Here’s the rule: If the combined excess risk (row 4) is more than twice the additive excess risk (row 2 + row 3), then we have interaction.

Now what?

So are we finished? Well, it depends… Because we detected interaction, and we never want to control for such a phenomena, we are finished. If, however, we don’t detect interaction, then we need to go back and control for confounding.

The reason we do this is because our stratified E* ORs differed from our crude E OR and our general rule #1 was met. Because it’s a judgement call on how different the E* ORs are from one another, we sometimes get it right by “eyeballing” and sometimes don’t. But because the math is so much fun to do, we really don’t care. =)