  One of the most significant barriers to medication treatment is patients'
non-adherence to a prescribed medication regimen. The extent of the impact of
poor adherence on resulting health measures is often unknown, and typical
analyses ignore the time-varying nature of adherence. This paper develops a
modeling framework for longitudinally recorded health measures modeled as a
function of time-varying medication adherence or other time-varying covariates.
Our framework, which relies on normal Bayesian dynamic linear models (DLMs),
accounts for time-varying covariates such as adherence and non-dynamic
covariates such as baseline health characteristics. Given the inefficiencies
using standard inferential procedures for DLMs associated with infrequent and
irregularly recorded response data, we develop an approach that relies on
factoring the posterior density into a product of two terms; a marginal
posterior density for the non-dynamic parameters, and a multivariate normal
posterior density of the dynamic parameters conditional on the non-dynamic
ones. This factorization leads to a two-stage process for inference in which
the non-dynamic parameters can be inferred separately from the time-varying
parameters. We demonstrate the application of this model to the time-varying
effect of anti-hypertensive medication on blood pressure levels from a cohort
of patients diagnosed with hypertension. Our model results are compared to ones
in which adherence is incorporated through non-dynamic summaries.
