= Cure model
{title2=$S(t)=\pi+(1-\pi)S_*(t)$}
A <cure model> mixes an individual class with identically zero <hazard function> and a susceptible class with <survivor function> $S_*$. For $0\leq\pi<1$, its representation as a <proportional frailty model> with $\mathbb E U=1$ is $U=0$ with probability $\pi$ and $U=1/(1-\pi)$ otherwise, with <baseline hazard> $h_0=(1-\pi)h_*$. The frailty law is a mixture of two <Dirac measures>, rather than an ordinary density. Its <Laplace transform> evaluated at $H_0$ gives the displayed <survivor function>. The limiting survival equals $\pi$ when $S_*(t)\to0$; otherwise the plateau also includes susceptible individuals who never experience the event.
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