  Using the PreventS trial data, our objective is to estimate average effects
of a Health Wellness Coaching (HWC) intervention on improvement of
cardiovascular health at 9 months post randomization and in three consecutive
3-month periods over 9 months post randomization. Conventional approaches,
including instrumental variable models, are not applicable in the presence of
multiple correlated multivalued exposures and unmeasured confounding. We
propose a causal framework and its Bayesian modelling procedures to identify
and estimate average effects of one or multiple multivalued exposures on one
outcome in the presence of unmeasured confounding, noncompliance and missing
data, in a two-arm randomized trial. We also propose estimation methods of
unmeasured confounders, where the exposure and outcome distributions are
conditional on unmeasured confounders and then unmeasured confounders are
imputed as completely missing variables. Several types of model
non-identifiability and possible solutions are described. There is a risk that
estimation methods of unmeasured confounders can fail when multiple
contradictory posterior solutions are produced. The random intercept outcome
models that only adjust for unmeasured confounding in the outcome distribution
are proposed as a good surrogate causal model in this case, and they need
further development.
  There is evidence that the HWC intervention is beneficial to cardiovascular
health at 9 months post randomization. On average, completing one HWC session
improves the Life's Simple Seven total score by 0.16 (0.09, 0.22) and reduces
systolic blood pressure by 0.54 (0.19, 0.90) mm Hg. There is also evidence that
the HWC intervention has a larger beneficial effect on cardiovascular health
during 3 months post randomization. There is no clear evidence that the HWC
intervention benefits or harms mental health. The complete abstract is in the
article.
