Treatment interaction contrast in a Poisson regression
= Treatment interaction contrast in a Poisson regression
In a <Poisson regression> with $\log\mu=\beta_0+\beta_TT+\beta_Bb+\beta_{TB}Tb$, the treatment <logarithm> of the mean ratio at baseline $b$ is $\beta_T+b\beta_{TB}$. The main treatment coefficient tests the contrast at $b=0$. An overall no-treatment test requires both $\beta_T=0$ and $\beta_{TB}=0$, with their joint <covariance matrix> for a <Wald test>.