Table 1.

Summary of variance expressions of marginal relative risk with the modified Poisson regression.

Working correlation	mi = m?	Known mi	Expression of κ
Independence	Yes	–	$\frac{1+(m-1)\rho }{m}$
Independence	No	Yes	$\frac{n{\sum }_{i=1}^n{m}_i\left\{1+\left(m_i-1\right)\rho \right\}}{{\left({\sum }_{i=1}^n{m}_i\right)}^2}$
Independence	No	No	$\frac{1+\left\{\left(1+C{V}^2\right)\overline{m}-1\right\}\rho }{\overline{m}}$
Exchangeable	Yes	–	$\frac{1+(m-1)\rho }{m}$
Exchangeable	No	Yes	${\left(\frac{1}{n}\sum _{i=1}^n\frac{m_i}{1+\left(m_i-1\right)\rho }\right)}^{-1}$
Exchangeable	No	No	${\left(\frac{\overline{m}}{1+(\overline{m}-1)\rho )}\right)}^{-1}{\left\{1-{\text{CV}}^2\frac{\overline{m}\rho (1-\rho )}{{\left\{1+(\overline{m}-1)\rho \right\}}^2}\right\}}^{-1}$

Note: The general variance expression is σ² = κ × {(1 − P₁)/πP₁ + (1 − P₀)/(1 − π)P₀}.