Irreversible three-state disease model

An irreversible three-state continuous-time multi-state model permits only $1\to 2\to 3$, with state 3 absorbing. For constant rates $\lambda =q_{12}$ and $\mu =q_{23}$,At equal rates use $p_{12}(t)=\lambda t{e}^{-\lambda t}$. A panel-observed multi-state likelihood uses these transition probabilities, allowing unobserved intermediate visits between examinations.

A frozen-age approximation holds an age covariate constant at the start of each observation interval, allowing homogeneous transition probabilities to enter a panel-observed multi-state likelihood. It approximates a model with continuously changing age. Reciprocal rate calibration of mean waiting times is exact for a fixed-age exponential distribution, but not for a continuously ageing Gompertz distribution.