2.3 Relative risk, odds ratio and hazard ratio

Some useful epidemiology background. E.g.

Epidemiologists often use relative measures of effect, such as relative risk or odds ratio. These calculations give a quantified measure of the risk of getting a disease or other health outcome given an exposure to a risk factor. This is shown below. First we can define a simple example where there are some cases of disease (D) who have been exposed to the risk factor (DE) and other cases who were not (DN). We may also know the number of people who were exposed but remained healthy (HE) and the number of healthy people who were not exposed (HN). The total exposed can be represented as NE and the total not exposed as NN.

	Diseased	Healthy	Row_totals
Exposed	DE	HE	NE
Not exposed	DN	HN	NN

The relative risk is the risk of disease given exposure calculated as the ratio of risks:

\[\begin{equation} RR = \frac{\frac{DE}{NE}}{\frac{DN}{NN}} \end{equation}\]

The odds ratio is the ratio of the odds:

OR = (DE/HE) / (DN/HN)

We will summarise the material from the appendix of

Hanigan, I.C., Geromboux, C., Horsley, J., Phelan, S., Jegasothy, E., Heathcote, K. and Morgan, G.G. (2020). Environmental health indicators for selected environmental hazards in New South Wales. Human Health and Social Impacts (HHSI) Node and the NSW Department of Planning, Industry and Environment (DPIE). https://cloudstor.aarnet.edu.au/plus/s/BUkjIIsJC3VTqmO DOI:10.17605/OSF.IO/YJ98D