Example 122: Relative Risk and 95% CI of CVD Events Associated With Hypertension and Elevated LDLCholesterol Section
The tables below provide incidence densities and 95% confidence intervals for persons with various risk factors (hypertension (HTN) specifically, and elevated LDL cholesterol, and the combination of these two risk factors) for three different outcomes: acute myocardial infarction (Acute MI), incident coronary heart disease (CHD), and fatal coronary heart disease (Fatal CHD).
Risk Factors  Acute MI (501 events) 
CHD (959 events) 
Fatal CHD (146 events) 

HTN  1.95 (1.61,2.36)  1.90 (1.65,2.18)  3.45 (2.35,5.05) 
Elevated LDLC  1.70 (1.40,2.06)  1.65 (1.44,1.90)  1.38 (0.97,1.95) 
Adjusted for age, sex, ethnicity, education, smoking status, BMI, and diabetes.
Multiplicative interaction between HTN and Elevated LDLC was not significant at p < 0.10 level.
Adjusted* Incidence Density (10,000 personyears) and 95% CI of CHD Associated With Hypertension and ElevatedLDLCholesterol
Risk Factors  Acute MI  Incident CHD  Fatal CHD 

Without HTN and Elevated LDLC.  23.3 (18.6, 29.3)  41.8(35.3, 49.7)  4.1 (2.3,7.5) 
HTN  38.7 (30.0, 49.9)  85.2 (71.5, 101.5)  19.5 (13.2, 28.8) 
Elevated LDLC  35.3 (29.9, 41.8)  72.7 (64.5, 81.8)  7.9 (5.4, 11.6) 
HTN and Elevated LDLC  73.7 (62.5, 86.9)  133.8 (118.3, 151.4)  23.8 (17.3, 32.6) 
Test†P Value  0.005  0.122  0.922 
* Adjusted for age, sex, ethnicity, education, smoking status, BMI, and diabetes.
† Significant test of additive interaction (observed risk due to HTN and elevated LDL vs. expected risk due to both risk factors) using an additive model.
We can see that 23.3 is the rate expressed in number per 10,000 person years of acute MI for those persons without either hypertension or an elevated LDL cholesterol level. This is our baseline group. They have a low rate of 23.34 acute MI. For those with hypertension the rate increases to 38.7. For those with an elevated LDL cholesterol the rate goes up to a 35.3. For those with both factors the rate is 73.7.
These results have already been adjusted for age, sex, and the city, education, smoking status, BMI, and diabetes, the covariates in this model.
You can test the significance of the additive interaction here. If you add 38.7 and 35.3 together you come up very close to 73.7 (74.0). This suggests that these two factors work together in an additive model. There is no biologic synergy between these two risk factors, they work independently of each other. Hypertension and elevated LDL cholesterol do not work synergistically to produce coronary heart disease.
Can you have more than two interaction effects? How about three, four or more?
Yes, you can but it is better keep the model simple. Each time you test an interaction, there should be a fully expressed model. Therefore, if you have two factors than there is only one interaction. If you have three factors there are many more interactions and you need to check each of these. The number of interactions will increase very rapidly; confusion takes away from the conclusions.
Here is one more way to look at these data:
Adjusted Incidence Density (10,000 personyears) and 95% CI of OR for MI Associated With Hypertension and Elevated LDLChol.
Risk Factors 
Acute MI


Without HTN and Elevated LDLC. 
23.3 (18.6, 29.3)

HTN 
38.7 (30.0, 49.9)

Elevated LDLC 
35.3 (29.9, 41.8)

HTN and Elevated LDLC 
73.7 (62.5, 86.9)

Test†P Value 
0.005

 Incidence Density (ID) from background is 23.
 ID due to HTN is 16, (3923).
 ID due to elevated LDLC is 12, (3523).
 Observed ID due to HTN & elevated LDLC is 51, (7423).
 Expected ID due to HTN & elevated LDLC is 28, (16+12).
 Test: 28 vs. 51
The incidence density for those with neither of the risk factors, is 23. The incidence density due to hypertension is the difference between these two, 39  23, or 16. Therefore, the increased incidence density is 16. The presence of hypertension increases the incidence density by 16 per 10,000 personyears. If we look at those with just elevated LDL cholesterol we see the increase is 12 per 10,000 personyears, 35  23.
Putting these together the value is 73. If we take the difference between the rate for both exposures versus no exposures, 74  23 equals 51. We expect to 16 and 12 here, our expected incidence density. However, we are looking at an observed incidence density of 51.
The whole is larger than the sum of parts.
The observed disease rate due to the combination of these two risk factors is significantly higher than that expected if these two risk factors act only additively.
Finally, we can also express this as a percentage.
Excess Risk Due to Interaction:
The excess risk is 23 (5128), the percent excess risk is 31% (23/74).
We said that the excess risk was 23, which is 31% of 74, the total rate. Therefore, 31% risk of developing acute MI among people with both hypertension and elevated LDLC was attributable to the synergistic interaction of these two risk factors.
Congratulations! You have completed reading the Lesson Material for Week 13.