# Comparing Risk Among Two or More Exposure Groups

In a previous module we saw that we can measure disease frequency (cumulative incidence, incidence rate, or prevalence) by identifying the number of cases in the numerator and the population (people or person-time) in the denominator. Knowing the level of disease frequency in a single group, however, does not tell us whether membership in that group increases, decreases, or has no effect on risk. We can measure the cumulative incidence of twin (or higher multiple) births among women who use fertility treatment but we can't draw any preliminary conclusion without knowing the incidence of similar births among women who didn't use such treatment. Thus, identifying the causes of disease in epidemiology inherently involves comparison between groups of people who differ by exposure. This difference could be qualitative (yes/no), such as whether one did or did not consume a certain food at a restaurant on a specific evening, or quantitative (higher/lower), such as differences in the amount of carbohydrates consumed in one's diet. By measuring and comparing the incidence of the outcome of interest in two or more groups categorized by extent of exposure, we can begin to assess whether there is an association between exposure and outcome.

Because many potential causes fit more into the quantitative rather than qualitative category, a more general way to conceptualize comparisons is to think of the category of interest (the category hypothesized to be associated with disease) as the "index" category and the category that serves as the comparison as the "reference" category. You will often see this usage.

## Data Summary

The format in which the data for different groups can be summarized is very simple and is the same regardless of the measure of disease frequency. A generic template is shown in the figure: exposure status (in this case, yes/no) is indicated in rows, and the outcome status for each exposure category is shown in the columns.

Consider the following example regarding the management of Hodgkin lymphoma, a cancer of the lymphatic system. Years ago when a patient was diagnosed with Hodgkin Disease, they would frequently undergo a surgical procedure called a "staging laparotomy." The purpose of the staging laparotomy was to determine the extent to which the cancer had spread, because this was important information for determining the patient's prognosis and optimizing treatment. At times, the surgeons performing this procedure would also remove the patient's appendix, not because it was inflamed; it was done "incidentally" in order to ensure that the patient never had to worry about getting appendicitis. However, performing an appendectomy requires transecting it, and this has the potential to contaminate the abdomen and the wound edges with bacteria normally contained inside the appendix. Some surgeons felt that doing this "incidental appendectomy" did the patient a favor by ensuring that they would never get appendicitis, but others felt that it meant unnecessarily increasing the patient's risk of getting a post-operative wound infection by spreading around the bacteria that was once inside the appendix. To address this, the surgeons at a large hospital performed a retrospective cohort study. They began by going through the hospital's medical records to identify all subjects who had had a "staging laparotomy performed for Hodgkin." They then reviewed the medical record and looked at the operative report to determine whether the patient had an incidental appendectomy or not. They then reviewed the progress notes, the laboratory reports, the nurses notes, and the discharge summary to determine whether the patient had developed a wound infection during the week after surgery. The investigators reviewed the records of 210 patients who had undergone the staging procedure and found that 131 had also had an incidental appendectomy, while the other 79 had not. The data from that study are summarized in the table below. The numbers in the second and third columns indicate the number of subjects who did or did not develop a post-operative wound infection among those who had the incidental appendectomy (in the "Yes" row) and those who did not have the incidental appendectomy (in the "No" row). For example, the upper left cell indicates that seven of the subjects who had an incidental appendectomy (the exposure of interest) subsequently developed a wound infection. The upper right cell indicates that the other 124 subjects who had an incidental appendectomy did NOT develop a wound infection.

 Had Incidental Appendectomy? Wound Infection No Wound Infection Total Yes 7 124 131 No 1 78 79

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## Two by Two Tables (2x2) or Contingency Tables

There is no fixed convention for setting up a 2x2 (also known as contingency) table. However, when you use these tables to compute measures of association there is a distinct advantage to setting them up the same way all the time. If you don't, you can get confused when calculating measures of association. While you should set up your tables consistently, be aware that others may organize their tables differently, so be careful. I always put the exposure groups in rows with the row labels to the left, and I put the exposed (or most exposed) group on the top row. Outcome status is listed in the vertical columns; those with the outcome are listed in the left column.

Note also that contingency tables can accommodate more than two exposure groups just adding additional rows as illustrated on page 4 of this module. .

## Options for Comparing Disease Frequencies

The fundamental methods for comparing the frequency of disease (or health events in general) are to:

1. Calculate a ratio of the two measures of disease frequency (by dividing one by the other) or
2. Calculate the difference between the two measures by subtraction.