4.2 - Using Ratios to Compare Two Populations
4.2 - Using Ratios to Compare Two PopulationsA 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
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.