e gamma hyperprior on <span class="math inline">\(\sigma^2\)</span>.</p>
<p>We observe <span class="math inline">\(x_i\)</span> responses in <span class="math inline">\(n_i\)</span> patients in disease sub-type <span class="math inline">\(i\)</span>. The rate of response in subtype <span class="math inline">\(i\)</span> is modelled as <span class="math inline">\(p_i = \text{logit}^{-1}(\rho_i)\)</span>. Each <span class="math inline">\(x_i\)</span> is assumed to be binomially distributed with success parame