Measuring effects of medication adherence on time-varying health outcomes using Bayesian dynamic linear models

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 article develops a modeling framework for longitudinally recorded health measures modeled as a function of time-varying medication adherence. 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. Standard inferential procedures for DLMs are inefficient when faced 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 antihypertensive medication on blood pressure levels for a cohort of patients diagnosed with hypertension. Our model results are compared to ones in which adherence is incorporated through non-dynamic summaries.