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One of the most significant barriers to medication treatment is patients'non-adherence to a prescribed medication regimen. The extent of the impact ofpoor adherence on resulting health measures is often unknown, and typicalanalyses ignore the time-varying nature of adherence. This paper develops amodeling framework for longitudinally recorded health measures modeled as afunction 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-dynamiccovariates such as baseline health characteristics. Given the inefficienciesusing standard inferential procedures for DLMs associated with infrequent andirregularly recorded response data, we develop an approach that relies onfactoring the posterior density into a product of two terms; a marginalposterior density for the non-dynamic parameters, and a multivariate normalposterior density of the dynamic parameters conditional on the non-dynamicones. This factorization leads to a two-stage process for inference in whichthe non-dynamic parameters can be inferred separately from the time-varyingparameters. We demonstrate the application of this model to the time-varyingeffect of anti-hypertensive medication on blood pressure levels from a cohortof patients diagnosed with hypertension. Our model results are compared to onesin which adherence is incorporated through non-dynamic summaries.

Measuring Effects of Medication Adherence on Time-Varying Health Outcomes using Bayesian Dynamic Linear Models