  The Adult Changes in Thought (ACT) study is a long-running prospective study
of incident all-cause dementia and Alzheimer's disease (AD). As the cohort
ages, death (a terminal event) is a prominent competing risk for AD (a
non-terminal event), although the reverse is not the case. As such, analyses of
data from ACT can be placed within the semi-competing risks framework. Central
to semi-competing risks, and in contrast to standard competing risks, is that
one can learn about the dependence structure between the two events. To-date,
however, most methods for semi-competing risks treat dependence as a nuisance
and not a potential source of new clinical knowledge. We propose a novel
regression-based framework that views the two time-to-event outcomes through
the lens of a longitudinal bivariate process on a partition of the time scale.
A key innovation of the framework is that dependence is represented in two
distinct forms, $\textit{local}$ and $\textit{global}$ dependence, both of
which have intuitive clinical interpretations. Estimation and inference are
performed via penalized maximum likelihood, and can accommodate right
censoring, left truncation and time-varying covariates. The framework is used
to investigate the role of gender and having $\ge$1 APOE-$\epsilon4$ allele on
the joint risk of AD and death.
