= Solution
Let $T_i=1$ denote Progabide and $T_i=0$ placebo; write $a_i$ for age and $b_i$ for baseline count. The fitted <Poisson regression> specifies independent
$$
Y_i\sim\operatorname{Poisson}(\mu_i),\qquad\eta_i=\log\mu_i=\beta_0+\beta_Aa_i+\beta_TT_i+\beta_Bb_i+\beta_{TB}T_ib_i.
$$
Its <log-likelihood> is
$$
\ell(\beta)=\sum_{i=1}^{107}\{Y_i\eta_i-e^{\eta_i}-\log(Y_i!)\}.
$$
The coefficient table in the original PDF, whose TeX transcription is truncated, gives the <maximum-likelihood estimates>
$$
\boxed{(\widehat\beta_0,\widehat\beta_A,\widehat\beta_T,\widehat\beta_B,\widehat\beta_{TB})=(1.1215275,0.0090311,-0.3592068,0.0186824,0.0008682).}
$$
For the <treatment interaction contrast in a Poisson regression>, the baseline slope of the log mean is $0.0186824$ on placebo and $0.0195506$ on Progabide. At fixed age and baseline $b$, the fitted drug-to-placebo mean ratio is $\exp(-0.3592068+0.0008682b)$. Increasing baseline by one multiplies that ratio by $e^{0.0008682}\approx1.0008686$. Thus the <interaction term> describes how the treatment ratio changes with baseline, rather than a uniform additive change in seizure counts. The displayed call makes clear that the source's `summary(model1)` line is an object-name typo for the epilepsy fit.
Back to article page
