  We compare two multi-state modelling frameworks that can be used to represent
dates of events following hospital admission for people infected during an
epidemic. The methods are applied to data from people admitted to hospital with
COVID-19, to estimate the probability of admission to ICU, the probability of
death in hospital for patients before and after ICU admission, the lengths of
stay in hospital, and how all these vary with age and gender. One modelling
framework is based on defining transition-specific hazard functions for
competing risks. A less commonly used framework defines partially-latent
subpopulations who will experience each subsequent event, and uses a mixture
model to estimate the probability that an individual will experience each
event, and the distribution of the time to the event given that it occurs. We
compare the advantages and disadvantages of these two frameworks, in the
context of the COVID-19 example. The issues include the interpretation of the
model parameters, the computational efficiency of estimating the quantities of
interest, implementation in software and assessing goodness of fit. In the
example, we find that some groups appear to be at very low risk of some events,
in particular ICU admission, and these are best represented by using
"cure-rate" models to define transition-specific hazards. We provide
general-purpose software to implement all the models we describe in the
"flexsurv" R package, which allows arbitrarily-flexible distributions to be
used to represent the cause-specific hazards or times to events.
