Using the PreventS trial data, our objective is to estimate the average effect of a Health Wellness Coaching intervention on improvement of cardiovascular health at 9 months post randomization and in each of 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 general causal framework to identify and estimate the 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 implement our causal framework through Bayesian models. We also propose general 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. Model non-identifiability is a major problem in estimation of unmeasured confounders. 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 posterior solutions are produced and they are contradictory. The random intercept outcome models that only adjust for unmeasured confounding in the outcome distribution are proposed as a good surrogate causal model in the presence of unmeasured confounding. No multiple posterior solutions are found from the random intercept outcome models, but the random intercept outcome models need further development.There is evidence that the Health Wellness Coaching intervention is beneficial to cardiovascular health at 9 months post randomization. On average, completing one Health Wellness Coaching 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, but due to sensitivity of Bayesian models, these changes may become smaller or statistically insignificant. On average, completing one Health Wellness Coaching session increases the 5-year cardiovascular disease risk score recalculated with PREDICT by 0.00 (-0.03, 0.02), with little sensitivity of Bayesian models, which indicates completing one Health Wellness Coaching session does not change the 5-year cardiovascular disease risk score recalculated with PREDICT on average. There is also evidence from a random intercept model that based on the Life's Simple Seven total score, the Health Wellness Coaching intervention has a larger beneficial effect on cardiovascular health during 3 months 3 4 post randomization than in either of two consecutive 3-month periods between 3 and 9 months post randomization. During 3 months post randomization, attending one HWC session reduces the LS7 outcome by 0.10 (-0.14, 0.35) on average. Between 3 and 6 months post randomization, attending one HWC session reduces the LS7 outcome by 0.02 (-0.36, 0.40) on average. Between 6 and 9 months post rand...