= Two-group Poisson ratio conditional likelihood
{c}
{title2=$Y_1\mid(Y_0+Y_1=m)\sim\operatorname{Bin}(m,e^\beta/(1+e^\beta))$}
For independent aggregate <Poisson distributions> with means $n\lambda$ and $n\lambda e^\beta$, conditioning on the total eliminates $\lambda$. <Independent Poisson conditioning> gives the displayed <binomial distribution>. Its <conditional likelihood> is proportional to $e^{\beta Y_1}(1+e^\beta)^{-m}$, also the <profile likelihood> after maximizing over the unrestricted positive baseline rate. Unequal exposures replace the binomial success probability by $n_1e^\beta/(n_0+n_1e^\beta)$.
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