Poisson Rate Analysis

Incidence Rate:

$$IR = \frac{\text{Events}}{\text{Person-time}}$$

Rate Ratio (IRR):

$$IRR = \frac{IR_1}{IR_2} = \frac{d_1/T_1}{d_2/T_2}$$

95% CI for rate (exact):

$$CI = \left[\frac{\chi^2_{\alpha/2, 2d}}{2T}, \frac{\chi^2_{1-\alpha/2, 2(d+1)}}{2T}\right]$$

Where:

• d = number of events
• T = person-time at risk
• $\chi^2$ = chi-square distribution