Dynamic medication adherence modeling in primary prevention of cardiovascular disease: a Markov microsimulation methods application

Absorbing Markov chain model of PrEP drug adherence to estimate adherence decay rate and probability distribution in clinical trials

Pre-exposure prophylaxis (PrEP) is increasingly used to prevent the transmission of H.I.V. in at-risk populations. However, PrEP users may discontinue use of the medicine due to side effects, lower perceived risk, or other reasons. The usage metrics of 594 individuals was tracked over 350 days using the Wisepill electronic monitoring system. We model the PrEP drug adherence level using an absorbing Markov chain with a unique absorbing state. The transition matrix T obtained from the Wisepill data will have a trivial eigenvector (eigendistribution) associated with the first (i.e., largest) eigenvalue 1. The 2nd eigenvalue(s) then become important in determining the asymptotic behavior of the Markov chain, dictating how fast the Markov chain decays to the absorbing state. Under a fairly general assumption, we prove that the second positive eigenvalue is unique and the corresponding eigenvector will have nonnegative entries with exceptions at absorbing states. In addition, we define the asymptotic half life of the absorbing Markov chain directly from the 2nd eigenvalue. We then determine the 2nd eigenvalue of T and the asymptotic half life of the Markov chain, which turns out to be very close to the real half life of the Markov chain. Finally, we interpret the 2nd eigenvector as the relative probability distribution of X∞ with respect to the decay rate of the 2nd eigenvalue. By applying these methods to the Wisepill data, we estimate the half-life of population adherence to be 46 weeks. The bi-weekly decay rate observed in these data from 90 to 100 % adherence is 3 %. This work produces an estimate at which adherence falls over time, given no external intervention is applied. These results suggest an eigenvector-based approach to estimate adherence trends, as well as the timing of interventions to improve adherence.

Impact of adherence on the cost-effectiveness of apixaban and rivaroxaban in stroke prevention among patients with atrial fibrillation in the United States

OBJECTIVE

Despite the beneficial effects of DOACs, suboptimal adherence is widely documented, and real-world adherence is lower than in clinical trials. The objective of this study is to compare the cost-effectiveness of apixaban versus rivaroxaban for stroke prevention by incorporating real-world adherence from the US payer's perspective.

METHODS

We developed a Markov model with three health states to evaluate the total costs and quality-adjusted life years (QALY) at a willingness to pay threshold of $100,000. The population was a hypothetical cohort of 65-year-old patients with moderate to high stroke risk. The transition probabilities of healthy adherent, nonadherent, and stroke were obtained from a Medicare Advantage Plan. The utilities and costs were obtained from prior clinical studies. Deterministic and probabilistic sensitivity analyses were conducted.

RESULTS

Apixaban was cost-effective than rivaroxaban at a willingness to pay threshold of $100,000. Apixaban yielded an additional 0.12 QALYs at a cost of $1904.39, resulting in an incremental cost-effectiveness ratio (ICER) of $16,279.25 per QALY gained. The Monte Carlo simulations indicated that apixaban was cost-effective at 89.67% of simulations. The ICER results were impacted by the medical costs among nonadherent patients.

CONCLUSION

After incorporating adherence, apixaban 5 mg was a cost-effective alternative to rivaroxaban 20 mg for stroke prevention among elderly atrial fibrillation (AF) patients.

Cost-effectiveness of applying high-sensitivity troponin I to a score for cardiovascular risk prediction in asymptomatic population

INTRODUCTION

Risk stratification scores such as the European Systematic COronary Risk Evaluation (SCORE) are used to guide individuals on cardiovascular disease (CVD) prevention. Adding high-sensitivity troponin I (hsTnI) to such risk scores has the potential to improve accuracy of CVD prediction. We investigated how applying hsTnI in addition to SCORE may impact management, outcome, and cost-effectiveness.

METHODS

Characteristics of 72,190 apparently healthy individuals from the Biomarker for Cardiovascular Risk Assessment in Europe (BiomarCaRE) project were included into a discrete-event simulation comparing two strategies for assessing CVD risk. The standard strategy reflecting current practice employed SCORE (SCORE); the alternative strategy involved adding hsTnI information for further stratifying SCORE risk categories (S-SCORE). Individuals were followed over ten years from baseline examination to CVD event, death or end of follow-up. The model tracked the occurrence of events and calculated direct costs of screening, prevention, and treatment from a European health system perspective. Cost-effectiveness was expressed as incremental cost-effectiveness ratio (ICER) in € per quality-adjusted life year (QALYs) gained during 10 years of follow-up. Outputs were validated against observed rates, and results were tested in deterministic and probabilistic sensitivity analyses.

RESULTS

S-SCORE yielded a change in management for 10.0% of individuals, and a reduction in CVD events (4.85% vs. 5.38%, p<0.001) and mortality (6.80% vs. 7.04%, p<0.001). S-SCORE led to 23 (95%CI: 20-26) additional event-free years and 7 (95%CI: 5-9) additional QALYs per 1,000 subjects screened, and resulted in a relative risk reduction for CVD of 9.9% (95%CI: 7.3-13.5%) with a number needed to screen to prevent one event of 183 (95%CI: 172 to 203). S-SCORE increased costs per subject by 187€ (95%CI: 177 € to 196 €), leading to an ICER of 27,440€/QALY gained. Sensitivity analysis was performed with eligibility for treatment being the most sensitive.

CONCLUSION

Adding a person's hsTnI value to SCORE can impact clinical decision making and eventually improves QALYs and is cost-effective compared to CVD prevention strategies using SCORE alone. Stratifying SCORE risk classes for hsTnI would likely offer cost-effective alternatives, particularly when targeting higher risk groups.

Effectiveness and cost-effectiveness of an intervention to improve Initial Medication Adherence to treatments for cardiovascular diseases and diabetes in primary care: study protocol for a pragmatic cluster randomised controlled trial and economic model (the IMA-cRCT study)

BACKGROUND

Between 2 and 43% of patients who receive a new prescription in PC do not initiate their treatments. Non-initiation is associated with poorer clinical outcomes, more sick leave and higher costs to the healthcare system. Existing evidence suggests that shared decision-making positively impacts medication initiation. The IMA-cRCT assesses the effectiveness of the IMA intervention in improving adherence and clinical parameters compared to usual care in patients with a new treatment for cardiovascular disease and diabetes prescribed in PC, and its cost-effectiveness, through a cRCT and economic modelling.

METHODS

The IMA intervention is a shared decision-making intervention based on the Theoretical Model of Non-initiation. A cRCT will be conducted in 24 PC teams in Catalonia (Spain), randomly assigned to the intervention group (1:1), and community pharmacies in the catchment areas of the intervention PC teams. Healthcare professionals in the intervention group will apply the intervention to all patients who receive a new prescription for cardiovascular disease or diabetes treatment (no other prescription from the same pharmacological group in the previous 6 months). All the study variables will be collected from real-world databases for the 12 months before and after receiving a new prescription. Effectiveness analyses will assess impact on initiation, secondary adherence, cardiovascular risk, clinical parameters and cardiovascular events. Cost-effectiveness analyses will be conducted as part of the cRCT from a healthcare and societal perspective in terms of extra cost per cardiovascular risk reduction and improved adherence; all analyses will be clustered. Economic models will be built to assess the long-term cost-effectiveness of the IMA intervention, in terms of extra cost for gains in QALY and life expectancy, using clinical trial data and data from previous studies.

DISCUSSION

The IMA-cRCT represents an innovative approach to the design and evaluation of behavioural interventions that use the principles of complex interventions, pragmatic trials and implementation research. This study will provide evidence on the IMA intervention and on a new methodology for developing and evaluating complex interventions. The results of the study will be disseminated among stakeholders to facilitate its transferability to clinical practice.

TRIAL REGISTRATION

ClinicalTrials.gov, NCT05026775 . Registered 30th August 2021.

Statistical analysis of one-compartment pharmacokinetic models with drug adherence

Pharmacokinetics is a scientific branch of pharmacology that describes the time course of drug concentration within a living organism and helps the scientific decision-making of potential drug candidates. However, the classical pharmacokinetic models with the eliminations of zero-order, first-order and saturated Michaelis-Menten processes, assume that patients perfectly follow drug regimens during drug treatment, and the significant factor of patients' drug adherence is not taken into account. In this study, therefore, considering the random change of dosage at the fixed dosing time interval, we reformulate the classical deterministic one-compartment pharmacokinetic models to the framework of stochastic, and analyze their qualitative properties including the expectation and variance of the drug concentration, existence of limit drug distribution, and the stochastic properties such as transience and recurrence. In addition, we carry out sensitivity analysis of drug adherence-related parameters to the key values like expectation and variance, especially for the impact on the lowest and highest steady state drug concentrations (i.e. the therapeutic window). Our findings can provide an important theoretical guidance for the variability of drug concentration and help the optimal design of medication regimens. Moreover, The developed models in this paper can support for the potential study of the impact of drug adherence on long-term treatment for chronic diseases like HIV, by integrating disease models and the stochastic PK models.

Incorporating adherence in cost-effectiveness analyses of asthma: a systematic review

Aims: Non-adherence is associated with poor clinical outcomes among patients with asthma. While cost-effectiveness analysis (CEA) is increasingly used to inform value assessment of the interventions, most do not take into account adherence in the analyses. This study aims to: (1) Understand the extent of studies considering adherence as part of the economic analyses, and (2) summarize the methods of incorporating adherence in the economic models. Materials and methods: A literature search was performed from the inception to February 2018 using four databases: PubMed, EMBASE, NHS EED, and the Tufts CEA registry. Decision model-based CEA of asthma were identified. Outcomes of interest were the number of studies incorporating adherence in the economic models, and the incorporating methods. All data were extracted using a standardized data collection form. Results: From 1,587 articles, 23 studies were decision model-based CEA of asthma, of which four CEA (17.4%) incorporated adherence in the analyses. Only the method of incorporating adherence by adjusting treatment effectiveness according to adherence levels was demonstrated in this review. Two approaches were used to derive the associations between adherence and effectiveness. The first approach was to apply a mathematical formula, developed by an expert panel, and the second was to extrapolate the associations from previous published studies. The adherence-adjusted effectiveness was then incorporated in the economic models. Conclusions: A very low number of CEA of asthma incorporated adherence in the analyses. All the CEA adjusted treatment effectiveness according to adherence levels, applied to the economic models.

Beyond Adherence Thresholds: A Simulation Study of the Optimal Classification of Longitudinal Adherence Trajectories From Medication Refill Histories

Background: The description of adherence based on medication refill histories relies on the estimation of continuous medication availability (CMA) during an observation period. Thresholds to distinguish adherence from non-adherence typically refer to an aggregated value across the entire observation period, disregarding differences in adherence over time. Sliding windows to divide the observation period into smaller portions, estimating adherence for these increments, and classify individuals with similar trajectories into clusters can retain this temporal information. Optimal methods to estimate adherence trajectories to identify underlying patterns have not yet been established. This simulation study aimed to provide guidance for future studies by analyzing the effect of different longitudinal adherence estimates, sliding window parameters, and sample characteristics on the performance of a longitudinal clustering algorithm.

Methods: We generated samples of 250–25,000 individuals with one of six longitudinal refill patterns over a 2-year period. We used two longitudinal CMA estimates (LCMA1 and LCMA2) and their dichotomized variants (with a threshold of 80%) to create adherence trajectories. LCMA1 assumes full adherence until the supply ends while LCMA2 assumes constant adherence between refills. We assessed scenarios with different LCMA estimates and sliding window parameters for 350 independent samples. Individual trajectories were clustered with kml, an implementation of k-means for longitudinal data in R. We compared performance between the four LCMA estimates using the adjusted Rand Index (cARI).

Results: Cluster analysis with LCMA2 outperformed other estimates in overall performance, correct identification of groups, and classification accuracy, irrespective of sliding window parameters. Pairwise comparison between LCMA estimates showed a relative cARI-advantage of 0.12–0.22 (p < 0.001) for LCMA2. Sample size did not affect overall performance.

Conclusion: The choice of LCMA estimate and sliding window parameters has a major impact on the performance of a clustering algorithm to identify distinct longitudinal adherence trajectories. We recommend (a) to assume constant adherence between refills, (b) to avoid dichotomization based on a threshold, and (c) to explore optimal sliding windows parameters in simulation studies or selecting shorter non-overlapping windows for the identification of different adherence patterns from medication refill data.

Using a dynamic adherence Markov model to assess the efficiency of Respiratory Medication Therapy Adherence Clinic (RMTAC) on asthma patients in Malaysia

Background

Respiratory Medication Therapy Adherence Clinic (RMTAC) is an initiative by the Ministry of Health (MOH) Malaysia to improve patients’ medication adherence, as an adjunct to the usual physician care (UC). This study aimed to evaluate the cost-effectiveness of combined strategy of RMTAC and UC (RMTAC + UC) vs. UC alone in asthma patients, from the MOH Malaysia perspective.

Methods

A lifetime horizon dynamic adherence Markov model with monthly cycle was developed, for quality-adjusted life year (QALY) gained and hospitalization averted outcomes. Transition probabilities of composite asthma control and medication adherence, utilities, costs, and mortality rates due to all causes were measured from local data sources. Effectiveness, exacerbation rates, and asthma mortality rates were taken from non-local data sources. One-way sensitivity analysis (SA) was conducted for assessing parameter uncertainties, whereas probabilistic SA (PSA) was conducted on a different set of utilities and effectiveness data. Costs were adjusted to 2014 US dollars ($). Both costs and benefits were discounted at a 3% rate annually.

Results

RMTAC + UC was found to be a dominant alternative compared to UC alone; $− 13,639.40 ($− 109,556.90 to $104,445.54) per QALY gained and $− 428.93 ($− 521.27 to ($− 328.69)) per hospitalization averted. These results were found to be robust against changes in all parameters except utilities in the one-way SA, and for both scenarios in PSA.

Conclusions

RMTAC + UC is more effective and yet cheaper than UC alone, from the MOH perspective. For the benefit of both MOH and patients, RMTAC is thus recommended to be remained, and expanded to more healthcare settings where possible.

Electronic supplementary material

The online version of this article (10.1186/s12962-018-0156-1) contains supplementary material, which is available to authorized users.

Comparison of the flexible parametric survival model and Cox model in estimating Markov transition probabilities using real-world data

BACKGROUND AND OBJECTIVE

Markov micro-simulation models are being increasingly used in health economic evaluations. An important feature of the Markov micro-simulation model is its ability to consider transition probabilities of heterogeneous subgroups with different risk profiles. A survival analysis is generally performed to accurately estimate the transition probabilities associated with the risk profiles. This study aimed to apply a flexible parametric survival model (FPSM) to estimate individual transition probabilities.

MATERIALS AND METHODS

The data were obtained from a cohort study investigating ischemic stroke outcomes in Western China. In total, 585 subjects were included in the analysis. To explore the goodness of fit of the FPSM, we compared the estimated hazard ratios and baseline cumulative hazards, both of which are necessary to the calculate individual transition probabilities, and the Markov micro-simulation models constructed using the FPSM and Cox model to determine the validity of the two Markov micro-simulation models and cost-effectiveness results.

RESULTS

The flexible parametric proportional hazards model produced hazard ratio and baseline cumulative hazard estimates that were similar to those obtained using the Cox proportional hazards model. The simulated cumulative incidence of recurrent ischemic stroke and 5-years cost-effectiveness of Incremental cost-effectiveness Ratios (ICERs) were also similar using the two approaches. A discrepancy in the results was evident between the 5-years cost-effectiveness and the 10-years cost-effectiveness of ICERs, which were approximately 0.9 million (China Yuan) and 0.5 million (China Yuan), respectively.

CONCLUSIONS

The flexible parametric survival model represents a good approach for estimating individual transition probabilities for a Markov micro-simulation model.