hen <code>fit</code> is a <code>glm</code> object.</p>
<p>Let <span class="math inline">\(e_{0} = \exp(-\beta_{0} - \beta_{1} z_{0} - \boldsymbol{\beta}^{T}_{2:p} \mathbf{X})\)</span> and <span class="math inline">\(e_{1} = \exp (-\beta_{0} - \beta_{1} z_{1} - \boldsymbol{\beta}^{T}_{2:p} \mathbf{X})\)</span>.</p>
<p><span class="math display">\[\frac{\partial g(\boldsymbol{\beta})}{\partial \beta_{0}} =  \frac{- e_{1} + e_{0}}{(1 + e_{1})^2 } = \frac{e_{0}(1 - \exp(-\beta_{1}(z_{1} - z_{0}) ) ) }{(1 + e_{1