# 4.2 - Using Ratios to Compare Two Populations

A ratio may be used to convey the strength of an effect or association between two population groups or the relative 'risk' of the study (e.g. exposed) group compared to a comparison group (e.g. unexposed.). A ratio is not dependent on the prevalence of exposure among the study population.

Ratio
$$\dfrac{\text { Disease Frequency }(\text { Population } A)}{\text { Disease Frequency }(\text { Population } B)}$$

A ratio can be reported with upper and lower bounds. We will learn some formulas for these calculations in a later lesson.  When there is no significant difference between groups, the ratio will equal 1 and/or include 1 in its confidence interval.

## Ratio Calculations Section

### Risk Ratios

#### Cumulative incidence ratio

• More generally can be thought of as:
• Ratio of Disease Incidence= [A/(A+B)] / [C/(C+D)]
• In our pollution example, this would be [291/1351] / [232/1631] = 1.51.  Thus, participants from high-pollution cities are 1.51 times as likely as those from low-pollution cities to die.  This makes sense since we saw that the cumulative incidence of death was about 21% in the high pollution city, and 14% in the low-pollution cities.

#### Incidence rate ratio

• Follows the same general formula, but instead of comparing incidences, we are comparing incidence rates.  So first, we need to calculate the incidence rate in each city.
• High pollution city incidence rate of death = 291 deaths/ 17917 person-years, simplifies to 16.24 deaths per 1000 person-years
• Low pollution city incidence rate of death = 232 deaths/ 21618 person years, simplifies to 10.73 deaths per 1000 person years
• In our pollution example this would be (16.24/1000 person-years) / (10.72/1000 person-years) = 1.51

### Odds Ratio

• Exposure Odds Ratio [A/C] / [B/D] = [A*D] / [B*C]
• Disease Odds Ratio [A/B] / [C/D] = [A*D] / [B*C]
• Both simplify to the same OR
• In our pollution example, this would be 291*1399 / 1060*232 = 1.66.  Thus, participants from the high-pollution cities have 1.66 times higher odds of dying than those from low-pollution cities.