Let (h_{0}(t)) denote the hazard function when (mathbf{x}_{i}=mathbf{0}), and (S_{0}(t)=exp left(int_{0}^{t} h_{0}(u) d u ight)) be the

Let \(h_{0}(t)\) denote the hazard function when \(\mathbf{x}_{i}=\mathbf{0}\), and \(S_{0}(t)=\exp \left(\int_{0}^{t} h_{0}(u) d u\right)\) be the corresponding survival function. If \(h\left(t, \mathbf{x}_{i}\right)=\phi\left(\mathbf{x}_{i} ; \boldsymbol{\beta}\right) h_{0}(t)\), show \(S\left(t, \mathbf{x}_{i}\right)=\) \(S_{0}(t)^{\phi\left(\mathbf{x}_{i} ; \boldsymbol{\beta}\right)}\).