Markov Structure Research Articles

Modelling the case for cost-effectiveness of interventions to improve medication adherence in patients with difficult to control asthma

Background Asthma is a prevalent non-communicable disease in high-income countries, affecting more than 10% of their populations. While often symptomatically mild it accounts for 2-3% of primary care appointments, 60,000 hospital admissions, and 1,200 deaths annually in England. Importantly, a significant proportion of these events are the result of poor adherence to prescribed and effective treatments, with 60% of hospital admissions attributed to suboptimal compliance. This study aims to support the development and commissioning of interventions by establishing the value case for improving medication adherence. Methods A probabilistic cohort decision model was developed with the aim of estimating the long-term health impacts and resultant costs to the healthcare system of different levels of population medication adherence for those with difficult-to-control asthma. The model applies a Markov structure based on the Global Initiative for Asthma (GINA) guidelines to define the level of asthma control. Informative parameters are drawn from existing published literature supplemented by expert input where required. Results Improved adherence is associated with reduced asthma exacerbations and better overall health of the cohort, measured in life years and quality-adjusted life years (QALYs). For instance, an educational intervention that increased adherence from 50% to 70% reduced exacerbations by 1.75 over 20 years, while increasing QALYs by 0.20, and reducing the healthcare costs by £989. Conclusions Significant economic and health benefits can be achieved with effective interventions to improve treatment adherence in asthma. This study provides a value case for developing and commissioning such interventions.

On random coefficient INAR processes with long memory

Abstract We consider random coefficient INAR(1) processes with a strongly dependent latent random coefficient process. It is shown that, in spite of its conditional Markovian structure, the unconditional process exhibits long-range dependence. Short-term prediction and estimation of parameters involved in the prediction are considered. Asymptotic rates of convergence are derived.

Prognostic Testing for Prostate Cancer-A Cost-Effectiveness Analysis Comparing a Prostatype P-Score Biomarker Approach to Standard Clinical Practice.

The Prostatype score (P-score) is a prognostic biomarker that integrates a three-gene (IGFBP3, F3, and VGLL3) signature derived from prostate biopsy samples, with key clinical parameters, including prostate-specific antigen (PSA) levels, Gleason grade, and tumor stage at diagnosis. The test has demonstrated superior predictive accuracy for prostate cancer outcomes compared with traditional risk categorization systems such as D'Amico. Notably, it reclassifies a higher proportion of patients into the low-risk category, making them eligible for active surveillance. This study assessed the cost-effectiveness of the P-score in comparison with D'Amico and the Swedish National Prostate Cancer Register (NPCR) risk categorization systems. A two-step decision analytic model was developed. The model consisted of a decision tree-informed Markov structure estimating the lifetime outcomes of 60-year-old men with diagnosed prostate cancer. Prostate cancer was classified as low-risk, intermediate-risk, or high-risk using either the P-score or D'Amico. Initial therapy was based on observed treatment patterns from the Swedish NPCR. Costs (SEK, year 2022) and quality-adjusted life years (QALYs) were estimated from a healthcare perspective and discounted at 3% per year; incremental cost-effectiveness ratio (ICER) was the primary outcome. The P-score led to cost savings and generated an additional 0.19 QALYs compared with D'Amico. The added costs of the genetic test and higher costs of active surveillance and radiotherapy were counterbalanced by savings from reduced costs of surgery, treatment-related side-effects, and metastatic disease. The gain in QALYs was primarily due to the avoidance of metastatic disease and a reduction in treatment-related side-effects. The results of this study suggest that the P-score is likely to be a cost-effective alternative to D'Amico for prognostic evaluation of newly diagnosed prostate cancer in Sweden and compared with NPCR when health-related quality of life was included.

Cost-Effectiveness of Voncento Prophylaxis Versus On-Demand Treatment in von Willebrand Disease in the United Kingdom.

von Willebrand factor (VWF) concentrates may be required for on-demand treatment (ODT) or long-term prophylaxis (LTP) in von Willebrand disease (VWD). This study assesses the cost-effectiveness of LTP compared with ODT in VWD patients treated with Voncento in the United Kingdom (UK). A Markov structure was developed to estimate quality-adjusted life years (QALYs) and costs of VWD treatment over a lifetime horizon. Treatment options included ODT or LTP. For both options, we assumed plasma-derived VWF/factor VIII (pdVWF/FVIII) 2.4:1 (Voncento) as the VWF product used. Clinical parameters were obtained from published literature and Voncento's summary characteristics. Utility weights were obtained from published literature. Costs (in 2021 GBP) and outcomes were discounted annually by 3.5%. Sensitivity analyses were conducted. Three baseline annual bleed rate (ABR) scenarios (11, 26.5 and 39.6) were considered. In the base-case analyses, Voncento LTP resulted in lower costs (-£831,206) and greater QALY (6.14) versus ODT. Savings were primarily due to reductions in product use required (-£529,571) and bleed-related other medical costs (-£301,352). Compared with ODT, LTP also resulted in 322.52 fewer major bleeds and 515.68 fewer minor bleeds over a lifetime horizon. Probabilistic sensitivity analyses showed dominance in 96.12% of simulations and cost-effectiveness in 97.68% of simulations. For the 39.6 ABR scenario, LTP was also dominant compared with ODT. Results suggest that Voncento LTP is more effective and cost-saving compared with ODT in the UK for VWD patients with higher ABR. Prophylaxis for patients with frequent bleeds is likely to be a cost-saving and effective strategy.

Multiple Myeloma in Italy: An Epidemiological Model by Treatment Line and Refractoriness Status

Multiple Myeloma in Italy: An Epidemiological Model by Treatment Line and Refractoriness Status

Statistical inference for lindley random walks with correlated increments

This paper studies statistical inference for a Lindley random walk model when the increment process driving the walk is strictly stationary. Lindley random walks govern customer waiting times in many queueing models and several natural and business processes, including snow depths, frozen soil depths, inventory quantities, etc. The probabilistic properties of a Lindley walk with time-correlated stationary changes are first reviewed. We provide a streamlined argument that the process has a proper limiting distribution when the mean of the incremental changes is negative, and that the Lindley process is strictly stationary when starting from this stationary distribution. Next, the Markov characteristics of the process are explored when the change process has a Markov structure of first or higher order. A derivation of the model's likelihood is given when the change process is a Gaussian autoregressive time series. An efficient particle filtering method for evaluating and optimizing the likelihood with Gaussian changes is then devised and studied via simulation.

Local geometry of NAE-SAT solutions in the condensation regime

AbstractThe local behavior of typical solutions of random constraint satisfaction problems (csp) describes many important phenomena including clustering thresholds, decay of correlations, and the behavior of message passing algorithms. When the constraint density is low, studying the planted model is a powerful technique for determining this local behavior which in many examples has a simple Markovian structure. The work of Coja-Oghlan, Kapetanopoulos, Müller (Comb Prob Comput 29:346-422, 2020) showed that for a wide class of models, this description applies up to the so-called condensation threshold. Understanding the local behavior after the condensation threshold is more complex due to long-range correlations. In this work, we revisit the random regular nae-sat model in the condensation regime and determine the local weak limit which describes a random solution around a typical variable. This limit exhibits a complicated non-Markovian structure arising from the space of solutions being dominated by a small number of large clusters. This is the first description of the local weak limit in the condensation regime for any sparse random csps in the one-step replica symmetry breaking (1rsb) class. Our result is non-asymptotic and characterizes the tight fluctuation $$O(n^{-1/2})$$ O ( n - 1 / 2 ) around the limit. Our proof is based on coupling the local neighborhoods of an infinite spin system, which encodes the structure of the clusters, to a broadcast model on trees whose channel is given by the 1rsb belief-propagation fixed point. We believe that our proof technique has broad applicability to random csps in the 1rsb class.

Stochastic dual dynamic programming for optimal power flow problems under uncertainty

Planning in the power sector has to take into account the physical laws of alternating current (AC) power flows as well as uncertainty in the data of the problems, both of which greatly complicate optimal decision making. We propose a computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in AC power systems. Our approach uses recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian structure. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal policy of the stochastic AC-OPF problem as long as the SDP relaxations are tight. To test the practical viability of our approach, we set up a case study of a storage siting, sizing, and operations problem. We show that the convex SDP relaxation of the stochastic problem is usually tight and discuss ways to obtain near-optimal physically feasible solutions when this is not the case. The algorithm finds a physically feasible policy with an optimality gap of 3% and yields a significant added value of 27% over a rolling deterministic policy, which leads to overly optimistic policies and underinvestment in flexibility. This suggests that the common industry practice of assuming direct current and deterministic problems should be reevaluated by considering models that incorporate realistic AC flows and stochastic elements in the data as potentially more realistic alternatives.

Cost-effectiveness intervention thresholds for romosozumab and teriparatide in the treatment of osteoporosis in the UK.

To estimate the 10-year probability of a major osteoporotic fracture (MOF) at which sequential treatment with romosozumab or teriparatide followed by alendronate, compared with alendronate alone, becomes cost-effective in a UK setting. A microsimulation model with a Markov structure was used to simulate fractures, costs, and quality-adjusted life years (QALYs), in women receiving sequential treatment with either romosozumab or teriparatide followed by alendronate, compared with alendronate alone. Patients aged 50 to 90years with a recent MOF, hip or spine fracture were followed from the start of a 5-year treatment until the age of 100years or death. The analysis had a healthcare perspective. Efficacy of romosozumab, teriparatide and alendronate was derived from phase III randomised controlled trials. Resource use and unit costs were derived from the literature. Cost-effectiveness intervention threshold (CEIT), defined as the 10-year probability of a major osteoporotic fracture at which treatment becomes cost-effective, was compared with clinically appropriate intervention thresholds for bone-forming treatment in women with very high fracture risk as recommended by the UK National Osteoporosis Guideline Group (NOGG). The base case analysis showed that sequential romosozumab-to-alendronate treatment was cost-effective from a 10-year MOF probability of 18-35% and above depending on age and site of sentinel fracture at a willingness to pay (WTP) of £30,000. For teriparatide-to-alendronate, treatment was cost-effective at a 10-year MOF probability of 27-57%. The results were sensitive to pricing of the drugs but relatively insensitive to treatment duration, romosozumab persistence assumptions, and site of sentinel fracture. The CEITs for romosozumab-to-alendronate treatment were lower than the clinical thresholds from the age of 70years meaning that treatment could be considered both cost-effective and aligned with the NOGG treatment guidelines. By contrast, for teriparatide-to-alendronate the CEITs were higher than the clinical thresholds irrespective of age. However, cost-effective scenarios were found in the presence of strong clinical risk factors in addition to a recent sentinel fracture. The results of this study indicate that sequential romosozumab-to-alendronate or teriparatide-to-alendronate treatment can be a cost-effective treatment option for postmenopausal women at very high risk of fracture.

Portfolio and reinsurance optimization under unknown market price of risk

We investigate the optimal investment-and-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques, we convert the original optimization problem involving different filtrations into an equivalent stochastic control problem under the observation filtration, i.e. the so-called separated problem. The Markovian structure of the separated problem allows us to apply a classical approach to stochastic optimization based on the Hamilton–Jacobi–Bellman equation, and to provide explicit formulas for the value function and the optimal investment-and-reinsurance strategy. We finally discuss some comparisons between the optimal strategies pursued by a partially informed insurer and that followed by a fully informed insurer, and we evaluate the value of information using the idea of indifference pricing. These results are also supported by numerical experiments.

Equilibrium states for hyperbolic potentials via inducing schemes *

In a context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding measures. This generalizes a result due to Ramos and Viana, where analytical methods are used for maps with no critical sets. The strategy here consists in using a finite number of inducing schemes with a Markov structure in infinitely many symbols to code the dynamics, to obtain an equilibrium state for the associated symbolic dynamics and then projecting it to obtain an equilibrium state for the original map. We apply our results to the important class of multidimensional Viana maps.

A Bayesian hierarchical hidden Markov model for clustering and gene selection: Application to kidney cancer gene expression data.

We introduce a Bayesian approach for biclustering that accounts for the prior functional dependence between genes using hidden Markov models (HMMs). We utilize biological knowledge gathered from gene ontologies and the hidden Markov structure to capture the potential coexpression of neighboring genes. Our interpretable model-based clustering characterized each cluster of samples by three groups of features: overexpressed, underexpressed, and irrelevant features. The proposed methods have been implemented in an R package and are used to analyze both the simulated data and The Cancer Genome Atlas kidney cancerdata.

Cost-effectiveness of sotagliflozin for the treatment of patients with diabetes and recent worsening heart failure.

Aim: To assesses the cost-effectiveness of sotagliflozin for the treatment of patients hospitalized with heart failure and comorbid diabetes. Materials & methods: Ade novo cost-effectiveness model with a Markov structure was created for patients hospitalized for heart failure with comorbid diabetes. Outcomes of interest included hospital readmissions, emergency department visits and all-cause mortality measured over a 30-year time horizon. Baseline event frequencies were derived from published real-world data studies; sotagliflozin's efficacy was estimated from SOLOIST-WHF. Health benefits were calculated quality-adjusted life years (QALYs). Costs included pharmaceutical costs, rehospitalization, emergency room visits and adverse events. Economic value was measured using the incremental cost-effectiveness ratio (ICER). Results: Sotagliflozin use decreased annualized rehospitalization rates by 34.5% (0.228 vs 0.348, difference: -0.120), annualized emergency department visits by 40.0% (0.091 vs 0.153, difference: -0.061) and annualized mortality by 18.0% (0.298 vs 0.363, difference: -0.065) relative to standard of care, resulting in a net gain in QAYs of 0.425 for sotagliflozin versus standard of care. Incremental costs using sotagliflozin increased by $19,374 over a 30-year time horizon of the patient, driven largely by increased pharmaceutical cost. Estimated ICER for sotagliflozin relative to standard of care was $45,596 per QALY. Conclusion: Sotagliflozin is a cost-effective addition to standard of care for patients hospitalized with heart failure and comorbid diabetes.

Early-stage hepatocellular carcinoma screening in patients with chronic hepatitis B in China: a cost-effectiveness analysis.

Aim: To evaluate the cost-effectiveness of seven screening strategies for chronic hepatitis B (CHB) patients in China. Methods: A discrete event simulation model combining a decision tree and Markov structure was developed to simulate a CHB cohort aged ≥40years on a lifetime horizon and evaluate the costs and health outcomes (quality-adjusted life years [QALYs] gained) of ultrasonography (US), alpha-fetoprotein (AFP), protein induced by vitamin K absence-II (PIVKA-II), AFP+US, AFP+PIVKA-II, GAAD (a diagnostic algorithm based on gender and age combined with results of AFP and PIVKA-II) and GAAD+US. Epidemiologic, clinical performance, utility and cost data were obtained from the literature, expert interviews and real-world data. Uncertainties on key parameters were explored through deterministic and probabilistic sensitivity analyses (DSA and PSA). Results: Compared with other strategies, GAAD+US detected the most HCC patients at early stage, and GAAD was the screening strategy with the lowest average cost per HCC case diagnosed. Using 3× China's 2022 GDP per capita ($38,233.34) as the threshold, the three strategies of US, GAAD and GAAD+US formed a cost-effectiveness frontier. Screening with US, GAAD, or GAAD+US was associated with costs of $6110.46, $7622.05 and $8636.32, and QALYs of 13.18, 13.48 and 13.52, respectively. The ICER of GAAD over US was $4993.39/QALY and the ICER of GAAD+US over GAAD was $26,691.45/QALY, which was less than 3× GDP per capita. Both DSA and PSA proved the stability of the results. Conclusion: GAAD+US was the most cost-effective strategy for early HCC diagnosis among CHB patients which could be considered as the liver cancer screening scheme for the high-risk population in China.

Economic evaluation of first-line cryoballoon ablation versus antiarrhythmic drug therapy for the treatment of paroxysmal atrial fibrillation from an English National Health Service perspective

IntroductionThree recent randomised controlled trials have demonstrated that pulmonary vein isolation as an initial rhythm control strategy with cryoablation reduces atrial arrhythmia recurrence in patients with symptomatic paroxysmal atrial fibrillation...

Comparative effectiveness and cost-effectiveness of natalizumab and fingolimod in rapidly evolving severe relapsing-remitting multiple sclerosis in the United Kingdom

Aim To evaluate the real-world comparative effectiveness and the cost-effectiveness, from a UK National Health Service perspective, of natalizumab versus fingolimod in patients with rapidly evolving severe relapsing-remitting multiple sclerosis (RES-RRMS). Methods Real-world data from the MSBase Registry were obtained for patients with RES-RRMS who were previously either naive to disease-modifying therapies or had been treated with interferon-based therapies, glatiramer acetate, dimethyl fumarate, or teriflunomide (collectively known as BRACETD). Matched cohorts were selected by 3-way multinomial propensity score matching, and the annualized relapse rate (ARR) and 6-month–confirmed disability worsening (CDW6M) and improvement (CDI6M) were compared between treatment groups. Comparative effectiveness results were used in a cost-effectiveness model comparing natalizumab and fingolimod, using an established Markov structure over a lifetime horizon with health states based on the Expanded Disability Status Scale. Additional model data sources included the UK MS Survey 2015, published literature, and publicly available sources. Results In the comparative effectiveness analysis, we found a significantly lower ARR for patients starting natalizumab compared with fingolimod (rate ratio [RR] = 0.65; 95% confidence interval [CI], 0.57–0.73) or BRACETD (RR = 0.46; 95% CI, 0.42–0.53). Similarly, CDI6M was higher for patients starting natalizumab compared with fingolimod (hazard ratio [HR] = 1.25; 95% CI, 1.01–1.55) and BRACETD (HR = 1.46; 95% CI, 1.16–1.85). In patients starting fingolimod, we found a lower ARR (RR = 0.72; 95% CI, 0.65–0.80) compared with starting BRACETD, but no difference in CDI6M (HR = 1.17; 95% CI, 0.91–1.50). Differences in CDW6M were not found between the treatment groups. In the base-case cost-effectiveness analysis, natalizumab dominated fingolimod (0.302 higher quality-adjusted life-years [QALYs] and £17,141 lower predicted lifetime costs). Similar cost-effectiveness results were observed across sensitivity analyses. Conclusions This MSBase Registry analysis suggests that natalizumab improves clinical outcomes when compared with fingolimod, which translates to higher QALYs and lower costs in UK patients with RES-RRMS.

The convergence rate of the equilibrium measure for the hybrid LQG Mean Field Game

In this work, we study the convergence rate of the N-player Linear-Quadratic-Gaussian (LQG) game with a Markov chain common noise towards its asymptotic Mean Field Game. By postulating a Markovian structure via two auxiliary processes for the first and second moments of the Mean Field Game equilibrium and applying the fixed point condition in Mean Field Game, we first provide the characterization of the equilibrium measure in Mean Field Game with a finite-dimensional Riccati system of ODEs. Additionally, with an explicit coupling of the optimal trajectory of the N-player game driven by N dimensional Brownian motion and Mean Field Game counterpart driven by one-dimensional Brownian motion, we obtain the convergence rate O(N−1/2) with respect to 2-Wasserstein distance.

Health economic analysis of the integrated cognitive assessment tool to aid dementia diagnosis in the United Kingdom.

The aim of this study was to develop a comprehensive economic evaluation of the integrated cognitive assessment (ICA) tool compared with standard cognitive tests when used for dementia screening in primary care and for initial patient triage in memory clinics. ICA was compared with standard of care comprising a mixture of cognitive assessment tools over a lifetime horizon and employing the UK health and social care perspective. The model combined a decision tree to capture the initial outcomes of the cognitive testing with a Markov structure that estimated long-term outcomes of people with dementia. Quality of life outcomes were quantified using quality-adjusted life years (QALYs), and the economic benefits were assessed using net monetary benefit (NMB). Both costs and QALYs were discounted at 3.5% per annum and cost-effectiveness was assessed using a threshold of £20,000 per QALY gained. ICA dominated standard cognitive assessment tools in both the primary care and memory clinic settings. Introduction of the ICA tool was estimated to result in a lifetime cost saving of approximately £123 and £226 per person in primary care and memory clinics, respectively. QALY gains associated with early diagnosis were modest (0.0016 in primary care and 0.0027 in memory clinic). The net monetary benefit (NMB) of ICA introduction was estimated at £154 in primary care and £281 in the memory clinic settings. Introduction of ICA as a tool to screen primary care patients for dementia and perform initial triage in memory clinics could be cost saving to the UK public health and social care payer.

An economic evaluation of first-line cryoballoon ablation vs antiarrhythmic drug therapy for the treatment of paroxysmal atrial fibrillation from a U.S. Medicare perspective.

Three recent randomized controlled trials have demonstrated that, as an initial rhythm control strategy, first-line cryoballoon ablation (cryoablation) reduces atrial arrhythmia recurrence compared with antiarrhythmic drugs (AADs) in patients with symptomatic paroxysmal atrial fibrillation (PAF). The study sought to evaluate the cost-effectiveness of first-line cryoablation compared with first-line AADs for treating symptomatic PAF from a U.S. Medicare payer perspective. Individual patient-level data from 703 participants with PAF enrolled into the Cryo-FIRST (NCT01803438), STOP AF First (NCT03118518), and EARLY-AF (NCT02825979) trials were used to derive parameters for the cost-effectiveness model. The cost-effectiveness model used a hybrid decision tree and Markov structure. The decision tree had a 1-year time horizon and was used to inform the initial health state allocation in the first cycleof the Markov model. The Markov model used a 40-year time horizon (3-month cycle length). Health benefits were expressed in quality-adjusted life years (QALYs). Costs and benefits were discounted at 3% per year. Cryoablation was estimated to yield higher QALYs (+0.17) and higher costs (+$4274) per patient over a 40-year time horizon than AADs. Ultimately, this produced an average incremental cost-effectiveness ratio of $24,637 per QALY gained. Independent of initial treatment, individuals were expected to receive ∼1.2 ablations over a lifetime. There was a 45% relative reduction in time spent in atrial fibrillation health states for those initially treated with cryoablation compared with AADs. Initial rhythm control with first-line cryoballoon ablation is highly cost-effective compared with first-line AADs from a U.S. Medicare payer perspective.

Seemingly Unrelated Multi-State Processes: A Bayesian Semiparametric Approach

Many applications in medical statistics and other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In this context, multi-state models are a popular statistical technique, in particular when the exact transition times are not observed. The key quantities of interest are the transition rates, capturing the instantaneous risk of moving from one state to another. The main contribution of this work is to propose a joint semiparametric model for several possibly related multi-state processes (Seemingly Unrelated Multi-State, SUMS, processes), assuming a Markov structure for the transitions over time. The dependence between different processes is captured by specifying a joint prior distribution on the transition rates of each process. In this case, we assume a flexible distribution, which allows for clustering of the individuals, overdispersion and outliers. Moreover, we employ a graph structure to describe the dependence among processes, exploiting tools from the Gaussian Graphical model literature. It is also possible to include covariate effects. We use our approach to model disease progression in mental health. Posterior inference is performed through a specially devised MCMC algorithm.