# Incidence Rate Ratios and Incidence Rate Differences

For cohort studies with ongoing, periodic individual follow-up, we can determine the "time at risk," which enables us to compute and compare incidence rates.

We can summarize the findings with another contingency table with the general form shown in the table below. Again, "a", "b", "c", and "d" represent the number of subjects in each category, and P-Ye and P-Yu represent the total person-years of disease-free observation time in the exposed and unexposed subjects, respectively.

Diseased Not Diseased Person-Time
Exposed a b P-Ye
Unexposed c d P-Yu

Incidence rate in the exposed group:     IRe = a/ P-Ye
Incidence rate in the unexposed group: IRu = c/ P-Yu

Consider the following example from the Nurses' Health Study which studied a large cohort of nurses for many years. The contingency table below summarizes data for a study looking at the association between body mass index (BMI) and development of a non-fatal myocardial infarction. No data is shown for subjects who did not have a myocardial infarction, because for each exposure group we only need the number who had an infarction and the total person-years of disease-free observation.

BMI

MI

No MI

Person-Years

>30

85

-

99,573

25-29.9

67

-

148,541

20-24.9

113

-

349,960

<20

41

-

177,356

These data can be used to calculate incidence rates per 100,000 person-years, the incidence rate ratio, and the incidence rate difference per 100,000 person-years as shown in the table below.

BMI

IR per 100,000 P-Y

IR Ratio

IR Difference

per 100,000 person-yrs.

>30

85.4

3.7

62.3

25-29.9

45.1

2.0

22.0

20-24.9

32

1.5

12.9

<20

23.1

-

-

See if you can replicate these calculations from the contingency table above.

If we compare the incidence rate in the heaviest to the leanest women:

Incidence rate ratio = IRR = (85.4/100,000 PY) / (23.1/100,000 PY) = 85.4/23.1 = 3.7

Interpretation: Women with BMI > 30 had 3.7 times the rate of having a non-fatal myocardial infarction compared to women with BMI < 20 during the study period.

And

Incidence rate difference = IRD = 85.4/100,000-23.1/100,000 = 62/100,000 PY

Interpretation: Among the heaviest women there were 62 excess cases of non-fatal MI per 100,000 person-years of follow-up that could be attributed to their excess weight during this study period.

This suggests, for example, that if we followed another 50,000 women with BMI > 30 for 2 years we might expect 62 excess non-fatal myocardial infarctions due to their weight(since 50,000 persons with complete follow-up for 2 years would provide 100,000 person-years of follow-up). Or one could prevent 62 non-fatal myocardial infarctions by getting them to reduce their weight.