Notes, Vaupel, Manton, Stallard 1979, failty model

Reading notes on Vaupel, Manton, Stallard 1979, Demography, The impact of heterogeneity in individual frailty on the dynamics of mortality.

This is really a classic paper to study the effect of heterogeneity on aging.

VMS79 defined frailty $z$ as $\mu(z) = z \mu$, where $mu$ is the mortality rate (termed force of mortality in the paper).

VMS79 used a gamma distribution to model frailty. They found that frailty among the survivors at age $x$ is gamma distributed with the same shape parameter $k$ at birth. The second parameter is
$\lamda(x) = \lambda + H(x)$.