  A widely-used model for determining the long-term health impacts of public
health interventions, often called a "multistate lifetable", requires estimates
of incidence, case fatality, and sometimes also remission rates, for multiple
diseases by age and gender. Generally, direct data on both incidence and case
fatality are not available in every disease and setting. For example, we may
know population mortality and prevalence rather than case fatality and
incidence. This paper presents Bayesian continuous-time multistate models for
estimating transition rates between disease states based on incomplete data.
This builds on previous methods by using a formal statistical model with
transparent data-generating assumptions, while providing accessible software as
an R package. Rates for people of different ages and areas can be related
flexibly through splines or hierarchical models. Previous methods are also
extended to allow age-specific trends through calendar time. The model is used
to estimate case fatality for multiple diseases in the city regions of England,
based on incidence, prevalence and mortality data from the Global Burden of
Disease study. The estimates can be used to inform health impact models
relating to those diseases and areas. Different assumptions about rates are
compared, and we check the influence of different data sources.
