Relative Risk

Definition

Consider a $2\times 2$ Contingency Table

	Event	Non-event
Group 1	$n_{11}$	$n_{12}$	$n_{1.}$
Group 2	$n_{21}$	$n_{22}$	$n_{2.}$
	$n_{.1}$	$n_{.2}$	$n_{..}$

Point Estimation

The relative risk (RR) is estimated by $RR=\frac{\text{experimental event rate}}{\text{control event rate}}=\frac{n_{11}/n_{1.}}{n_{21}/n_{2.}}$

Confidence Interval

The confidence interval for relative risk is estimated by Delta Method. $\widehat{\mathrm{Var}}(\ln RR)=\frac{1}{n_{12}}(1-\frac{n_{11}}{n_{1.}})+\frac{1}{n_{21}}(1-\frac{n_{21}}{n_{2.}})$ The $100(1-\alpha )\%$ confidence interval for $RR$ is defined as $\exp [\ln RR\pm z_{\alpha /2}\sqrt{\widehat{\mathrm{Var}}(\ln RR)}]$

Facts

Relative risk must be used in Cohort Study or experimental study, can not be used for Case-Control Study.