  This proposal is motivated by an analysis of the English Longitudinal Study
of Ageing (ELSA), which aims to investigate the role of loneliness in
explaining the negative impact of hearing loss on dementia. The methodological
challenges that complicate this mediation analysis include the use of a
time-to-event endpoint subject to competing risks, as well as the presence of
feedback relationships between the mediator and confounders that are both
repeatedly measured over time. To account for these challenges, we introduce
natural effect proportional (cause-specific) hazard models. These extend
marginal structural proportional (cause-specific) hazard models to enable
effect decomposition. We show that under certain causal assumptions, the
path-specific direct and indirect effects indexing this model are identifiable
from the observed data. We next propose an inverse probability weighting
approach to estimate these effects. On the ELSA data, this approach reveals
little evidence that the total efect of hearing loss on dementia is mediated
through the feeling of loneliness, with a non-statistically significant
indirect effect equal to 1.012 (hazard ratio (HR) scale; 95% confidence
interval (CI) 0.986 to 1.053).
