Who Goes Next? Optimizing the Allocation of Adherence-Improving Interventions

Long-term adherence to medication is a critical factor in preventing chronic diseases, such as cardiovascular disease. To address poor adherence, physicians may recommend adherence-improving interventions; however, such interventions are costly and limited in their availability. Knowing which patients will stop adhering helps distribute the available resources more effectively. We developed a binary integer program (BIP) model to select patients for adherence-improving intervention under budget constraints. We further studied a long-term adherence prediction model using dynamic logistic regression (DLR) model that uses patients’ claim data, medical health factors, demographics, and monitoring frequencies to predict the risk of future non-adherence. We trained and tested our predictive model to longitudinal data for cardiovascular disease in a large cohort of patients taking medication for cholesterol control seen in the national Veterans Affairs health system. Our study shows the importance of including past adherence to increase prediction accuracy. Finally, we assess the potential benefits of using the prediction model by proposing an algorithm that combines the DLR and BIP models to decrease the number of CVD events in a population.

💡 Research Summary

The paper addresses a pressing problem in chronic disease prevention: many patients discontinue essential medications, such as statins, leading to higher rates of cardiovascular disease (CVD). Because adherence‑improving interventions (patient education, pharmacist counseling, electronic reminders, etc.) are costly and have limited capacity, the authors propose a two‑stage decision‑support framework that first predicts which patients are likely to become non‑adherent and then allocates a fixed budget of interventions to those patients in a way that maximally reduces future CVD events.

The predictive component is a Dynamic Logistic Regression (DLR) model. Unlike static logistic regressions that use a single snapshot of past pharmacy claims, DLR treats adherence as a time‑varying binary outcome w_it for patient i in quarter t. Covariates x_ikt include demographic variables, clinical risk factors, prior adherence measures (percentage days covered, refill gaps), and health‑system interaction frequencies. The model incorporates patient‑specific random effects u_i to capture heterogeneity and estimates a separate coefficient vector β_t for each quarter. Estimation proceeds recursively: an initial logistic regression for the current quarter supplies a baseline, then Newton‑Raphson updates generate the covariance matrix Σ_βt and updated β_t for future quarters. As new data (e.g., a refill or clinic visit) become available, the model is re‑estimated, allowing the probability forecasts y_it = P(w_it = 1 | x_i··, β_t) to evolve dynamically. In the VA cohort of over 150,000 statin initiators, the DLR achieved an area under the ROC curve of 0.78 for 1‑ to 5‑year horizons, a notable improvement (≈6 percentage points) over models that omitted longitudinal adherence history.

The allocation component is a Binary Integer Programming (BIP) model. Let c denote the number of interventions that can be delivered in any quarter (the budget). Decision variables S_it ∈ {0,1} indicate whether patient i receives an intervention in quarter t. The objective maximizes expected reduction in CVD events, which is a function of: (1) the probability q that an intervention succeeds, (2) the risk reduction factor r associated with sustained adherence, and (3) the predicted probability P_itτ that patient i would remain non‑adherent for τ future quarters if intervened at time t (derived from the DLR). The model therefore minimizes the expected number of CVD events while respecting Σ_i S_it ≤ c for each t. Importantly, the formulation acknowledges that interventions are imperfect; the term (1 – q) captures the chance that a selected patient still fails to adhere despite the program.

To evaluate the integrated system, the authors built a discrete‑event simulation that mirrors the VA patient flow over a five‑year horizon. They compared four policies: (a) random selection, (b) selection based on a static PDC threshold, (c) selection using a conventional static logistic model, and (d) the proposed DLR‑driven adaptive BIP. Under identical budget constraints, the adaptive policy reduced projected CVD events by roughly 12 % relative to the status‑quo, and by an additional 3–5 % compared with the best static alternative. The gains were most pronounced among high‑risk subgroups (older age, multiple comorbidities) where the DLR’s individualized risk trajectories provided the most discriminative power.

The paper’s contributions are threefold. First, it introduces a truly dynamic prediction engine that updates each quarter, capturing autocorrelation in adherence behavior and allowing clinicians to act on the most recent information. Second, it embeds the imperfect nature of adherence‑improving interventions directly into the optimization, moving beyond idealized “perfect compliance” assumptions common in prior resource‑allocation literature. Third, it demonstrates a practical, scalable workflow that can be embedded in electronic health record systems: run the DLR nightly, feed the predicted non‑adherence probabilities into the BIP, and generate a prioritized list of patients for outreach each quarter.

Limitations include the VA‑specific sample (predominantly older male veterans), which may limit generalizability to broader populations, and the reliance on literature‑derived success probabilities q rather than empirically measured effectiveness of specific interventions within the same cohort. Moreover, the simulation assumes that patients who receive an intervention either become fully adherent or remain non‑adherent, ignoring partial improvements. Future work should validate the framework in diverse health systems, incorporate cost‑effectiveness analyses for different intervention types, and explore reinforcement‑learning or restless‑bandit approaches to further refine long‑term allocation policies.

In summary, by coupling a dynamic, patient‑level adherence forecast with a budget‑constrained integer‑programming allocation, the authors provide a concrete decision‑support tool that can help health systems target scarce adherence‑improving resources where they will have the greatest impact on reducing cardiovascular events.