# 4.3 - Using Differences to Compare Two Populations

Alternatively, differences can be calculated between the estimates for the two groups. The difference can be reported with a confidence interval that includes upper and lower bounds.  If the confidence interval includes 0, this indicates that there is no significant difference between the groups. If the interval does not include 0, there is an increased risk for one population compared to the other (or conversely, a decreased risk). The difference can convey an excess or decreased risk among the exposed group due to exposure, possibly an excess or decreased risk that would be removed if the exposure ends, a potential reduction in risk for exposed individuals, or the absolute risk of the exposure.

Differences: Disease Frequency(Population A) - Disease Frequency(Population B)

## Difference Calculations Section

### Risk Difference

#### Cumulative incidence difference

• More generally can be thought of as:
• Difference of Disease Incidence= [A/(A+B)]  -  [C/(C+D)]
• In our pollution example, this would be [291/1351]  -  [232/1631] = 21.5% - 14.2% = 7.3%.  Thus, participants from high-pollution cities have a 7.3% higher risk of death than participants from low-pollution cities.

#### Incidence rate difference

• In our pollution example, this would be (16.24/1000 person-years) - (10.72/1000 person-years) = 5.51/1000 person-years. Thus, there are 5.51 excess deaths per 1000 person-years among those in the high pollution city.  Alternatively, the number of deaths could be reduced by 5.51 per 1000 person-years, if the pollution level in the high-pollution city was reduced to that of the low-pollution city.

### Attributable Proportion among the Total Population (APt)

(Also known as population attributable risk (PAR))

The Attributable Proportion among the Total Population depends upon the prevalence of the exposure in the study population. This value is often used to convey implications for policy or regulations.

#### General Formula

• $$\mathrm{AP}_{\mathrm{t}}=\dfrac{\text { Risk(study population)-Risk(unexposed group) }}{\text { Risk(study population) }}$$

#### Cumulative incidence APt

• In our example this would be [(523/2982) - (232/1631)]/(523/2982) = 0.189.  Thus 18.9% of the deaths in the population are attributable to the high pollution levels, and thus would be eliminated if the pollution levels were reduced.

#### Incidence rate APt

• First, we need to calculate the incidence rate in the entire population.  This would be the sum of all the deaths (1430) divided by the sum of all the person-years (111076) = 12.87 deaths per 1000 person-years.
• In our example, this would be [(12.87/1000 person-years - 10.73/1000 person-years)] / (12.87/1000 person-years) = 0.166.  Thus 16.6% of the deaths in the population are attributable to the high pollution levels, and thus would be eliminated if the pollution levels were reduced.