Markov Cohort State-Transition Model: A Multinomial Distribution Representation

HIGHLIGHTS

A Markov model simulates the average experience of a cohort of patients.Monte Carlo simulation, the standard approach for estimating the variance, is computationally expensive.A multinomial distribution provides an exact representation of a Markov model.Using the known formulas of a multinomial distribution, the mean and variance of a Markov model can be readily calculated.

CDX2 Biomarker Testing and Adjuvant Therapy for Stage II Colon Cancer: An Exploratory Cost-Effectiveness Analysis

OBJECTIVES

Adjuvant chemotherapy is not recommended for patients with average-risk stage II (T3N0) colon cancer. Nevertheless, a subgroup of these patients who are CDX2-negative might benefit from adjuvant chemotherapy. We evaluated the cost-effectiveness of testing for the absence of CDX2 expression followed by adjuvant chemotherapy (fluorouracil combined with oxaliplatin [FOLFOX]) for patients with stage II colon cancer.

METHODS

We developed a decision model to simulate a hypothetical cohort of 65-year-old patients with average-risk stage II colon cancer with 7.2% of these patients being CDX2-negative under 2 different interventions: (1) test for the absence of CDX2 expression followed by adjuvant chemotherapy for CDX2-negative patients and (2) no CDX2 testing and no adjuvant chemotherapy for any patient. We derived disease progression parameters, adjuvant chemotherapy effectiveness and utilities from published analyses, and cancer care costs from the Surveillance, Epidemiology, and End Results (SEER)-Medicare data. Sensitivity analyses were conducted.

RESULTS

Testing for CDX2 followed by FOLFOX for CDX2-negative patients had an incremental cost-effectiveness ratio of $5500/quality-adjusted life-years (QALYs) compared with no CDX2 testing and no FOLFOX (6.874 vs 6.838 discounted QALYs and $89 991 vs $89 797 discounted US dollar lifetime costs). In sensitivity analyses, considering a cost-effectiveness threshold of $100 000/QALY, testing for CDX2 followed by FOLFOX on CDX2-negative patients remains cost-effective for hazard ratios of <0.975 of the effectiveness of FOLFOX in CDX2-negative patients in reducing the rate of developing a metastatic recurrence.

CONCLUSIONS

Testing tumors of patients with stage II colon cancer for CDX2 and administration of adjuvant treatment to the subgroup found CDX2-negative is a cost-effective and high-value management strategy across a broad range of plausible assumptions.

Benefits and Harms of a Prevention Program for Iodine Deficiency Disorders: Predictions of the Decision-Analytic EUthyroid Model

Background: Iodine deficiency is one of the most prevalent causes of intellectual disability and can lead to impaired thyroid function and other iodine deficiency disorders (IDDs). Despite progress made on eradicating iodine deficiency in the last decades in Europe, IDDs are still prevalent. Currently, evidence-based information on the benefit/harm balance of IDD prevention in Europe is lacking. We developed a decision-analytic model and conducted a public health decision analysis for the long-term net benefit of a mandatory IDD prevention program for the German population with moderate iodine deficiency, as a case example for a European country. Methods: We developed a decision-analytic Markov model simulating the incidence and consequences of IDDs in the absence or presence of a mandatory IDD prevention program (iodine fortification of salt) in an open population with current demographic characteristics in Germany and with moderate ID. We collected data on the prevalence, incidence, mortality, and quality of life from European studies for all health states of the model. Our primary net-benefit outcome was quality-adjusted life years (QALYs) predicted over a period of 120 years. In addition, we calculated incremental life years and disease events over time. We performed a systematic and comprehensive uncertainty assessment using multiple deterministic one-way sensitivity analyses. Results: In the base-case analysis, the IDD prevention program is more beneficial than no prevention, both in terms of QALYs and life years. Health gains predicted for the open cohort over a time horizon of 120 years for the German population (82.2 million inhabitants) were 33 million QALYs and 5 million life years. Nevertheless, prevention is not beneficial for all individuals since it causes additional hyperthyroidism (2.7 million additional cases). Results for QALY gains were stable in sensitivity analyses. Conclusions: IDD prevention via mandatory iodine fortification of salt increases quality-adjusted life expectancy in a European population with moderate ID, and is therefore beneficial on a population level. However, further ethical aspects should be considered before implementing a mandatory IDD prevention program. Costs for IDD prevention and treatment should be determined to evaluate the cost effectiveness of IDD prevention.

Cost-Effectiveness of Different Formats for Delivery of Cognitive Behavioral Therapy for Depression: A Systematic Review Based Economic Model

OBJECTIVES

Cognitive behavioral therapy (CBT) is an effective treatment for depression. Different CBT delivery formats (face-to-face [F2F], multimedia, and hybrid) and intensities have been used to expand access to the treatment. The aim of this study is to estimate the long-term cost-effectiveness of different CBT delivery modes.

METHODS

A decision-analytic model was developed to evaluate the cost-effectiveness of different CBT delivery modes and variations in intensity in comparison with treatment as usual (TAU). The model covered an average treatment period of 4 months with a 5-year follow-up period. The model was populated using a systematic review of randomized controlled trials and various sources from the literature.

RESULTS

Incremental cost-effectiveness ratios of treatments compared with the next best option after excluding all the dominated and extended dominated options are: £209/quality-adjusted life year (QALY) for 6 (sessions) × 30 (minutes) F2F-CBT versus TAU; £4 453/QALY for 8 × 30 F2F versus 6 × 30 F2F; £12 216/QALY for 8 × 60 F2F versus 8 × 30 F2F; and £43 072/QALY for 16 × 60 F2F versus 8 × 60 F2F. The treatment with the highest net monetary benefit for thresholds of £20 000 to £30 000/QALY was 8 × 30 F2F-CBT. Probabilistic sensitivity analysis illustrated 6 × 30 F2F-CBT had the highest probability (32.8%) of being cost-effective at £20 000/QALY; 16 × 60 F2F-CBT had the highest probability (31.0%) at £30 000/QALY.

CONCLUSIONS

All CBT delivery modes on top of TAU were found to be more cost-effective than TAU alone. Four F2F-CBT options (6 × 30, 8 × 30, 8 × 60, 16 × 60) are on the cost-effectiveness frontier. F2F-CBT with intensities of 6 × 30 and 16 × 60 had the highest probabilities of being cost-effective. The results, however, should be interpreted with caution owing to the high level of uncertainty.

Earlier Provision of Gastric Bypass Surgery in Canada Enhances Surgical Benefit and Leads to Cost and Comorbidity Reduction

Background: Effective provision of bariatric surgery for patients with obesity may be impeded by concerns of payers regarding costs or perceptions of patients who drop out of surgical programs after referral. Estimates of the cost and comorbidity impact of these inefficiencies in gastric bypass surgery in Canada are lacking but would aid in informing healthcare investment and resource allocation.

Objectives: To estimate total and relative public payer costs for surgery and comorbidities (diabetes, hypertension, and dyslipidemia) in a bariatric surgery population.

Methods: A decision analytic model for a 100-patient cohort in Canada (91% female, mean body mass index 49.2 kg/m², 50% diabetes, 66% hypertension, 59% dyslipidemia). Costs include surgery, surgical complications, and comorbidities over the 10-year post-referral period. Results are calculated as medians and 95% credibility intervals (CrIs) for a pathway with surgery at 1 year (“improved”) compared with surgery at 3.5 years (“standard”). Sensitivity analyses were performed to test independent contributions to results of shorter wait time, better post-surgical weight loss, and randomly sampled cohort demographics.

Results: Compared to standard care, the improved path was associated with reduction in patient-years of treatment for each of the three comorbidities, corresponding to a reduction of $1.1 (0.68–1.6) million, or 34% (26-41%) of total costs. Comorbidity treatment costs were 9.0- and 4.7-fold greater than surgical costs for the standard and improved pathways, respectively. Relative to non-surgical bariatric care, earlier surgery was associated with earlier return on surgical investment and 2-fold reduction in risk of prevalence of each comorbidity compared to delayed surgery.

Conclusions: Comorbidity costs represent a greater burden to payers than the costs of gastric bypass surgery. Investments may be worthwhile to reduce wait times and dropout rates and improve post-surgical weight loss outcomes to save overall costs and reduce patient comorbidity prevalence.

A comparison of partitioned survival analysis and state transition multi-state modelling approaches using a case study in oncology

AIMS

To construct and compare a partitioned-survival analysis (PartSA) and a semi-Markov multi-state model (MSM) to investigate differences in estimated cost effectiveness of a novel cancer treatment from a UK perspective.

MATERIALS AND METHODS

Data from a cohort of late-stage cancer patients (N > 700) enrolled within a randomized, controlled trial were used to populate both modelling approaches. The statistical software R was used to fit parametric survival models to overall survival (OS) and progression-free survival (PFS) data to inform the PartSA (package "flexsurv"). The package "mstate" was used to estimate the MSM transitions (permitted transitions: (T1) "progression-free" to "dead", (T2) "post-progression" to "death", and (T3) "pre-progression" to "post-progression"). Key costs included were treatment-related (initial, subsequent, and concomitant), adverse events, hospitalizations and monitoring. Utilities were stratified by progression. Outcomes were discounted at 3.5% per annum over a 15-year time horizon.

RESULTS

The PartSA and MSM approaches estimated incremental cost-effectiveness ratios (ICERs) of £342,474 and £411,574, respectively. Scenario analyses exploring alternative parametric forms provided incremental discounted life-year estimates that ranged from +0.15 to +0.33 for the PartSA approach, compared with -0.13 to +0.23 for the MSM approach. This variation was reflected in the range of ICERs. The PartSA produced ICERs between £234,829 and £522,963, whereas MSM results were more variable and included instances where the intervention was dominated and ICERs above £7 million (caused by very small incremental QALYs).

LIMITATIONS AND CONCLUSIONS

Structural uncertainty in economic modelling is rarely explored due to time and resource limitations. This comparison of structural approaches indicates that the choice of structure may have a profound impact on cost-effectiveness results. This highlights the importance of carefully considered model conceptualization, and the need for further research to ascertain when it may be most appropriate to use each approach.

Generating evidence to inform health technology assessment of treatments for SLE: a systematic review of decision-analytic model-based economic evaluations

This study aimed to understand and appraise the approaches taken to handle the complexities of a multisystem disease in published decision-analytic model-based economic evaluations of treatments for SLE. A systematic review was conducted to identify all published model-based economic evaluations of treatments for SLE. Treatments that were considered for inclusion comprised antimalarial agents, immunosuppressive therapies, and biologics including rituximab and belimumab. Medline and Embase were searched electronically from inception until September 2018. Titles and abstracts were screened against the inclusion criteria by two reviewers; agreement between reviewers was calculated according to Cohen’s κ. Predefined data extraction tables were used to extract the key features, structural assumptions and data sources of input parameters from each economic evaluation. The completeness of reporting for the methods of each economic evaluation was appraised according to the Consolidated Health Economic Evaluation Reporting Standards (CHEERS) statement. Six decision-analytic model-based economic evaluations were identified. The studies included azathioprine (n=4), mycophenolate mofetil (n=3), cyclophosphamide (n=2) and belimumab (n=1) as relevant comparator treatments; no economic evaluation estimated the relative cost-effectiveness of rituximab. Six items of the CHEERS statement were reported incompletely across the sample: target population, choice of comparators, measurement and valuation of preference-based outcomes, estimation of resource use and costs, choice of model, and the characterisation of heterogeneity. Complexity in the diagnosis, management and progression of disease can make decision-analytic model-based economic evaluations of treatments for SLE a challenge to undertake. The findings from this study can be used to improve the relevance of model-based economic evaluations in SLE and as an agenda for research to inform future health technology assessment and decision-making.

Brazilian Analytical Decision Model for Cardiovascular Disease: An Adaptation of the Scottish Cardiovascular Disease Policy Model

INTRODUCTION

Despite the significant impact of cardiovascular disease (CVD), there is not yet an analytical decision tool for assessing efficiency of interventions to prevent primary CVD events in Brazil. Therefore, we sought to adapt a Scottish CVD Policy Model to be used in the proposed population.

METHODS

Calibration consisted of identifying multiplicative factors for linear predictors of existing survival analysis models to produce predictions that closely match observed data (Life-table and Brazilian cohort study). Target data were life expectancy (LE) and cumulative incidence of coronary heart disease (CHD), cerebrovascular disease (CBVD), fatal CVD and fatal non-CVD. Root-Mean-Square-Error (RMSE) was used to estimate differences between predictions and observations. Acceptance criteria were defined as a fit of less than one year for LE and 1% for cumulative incidence. Male and female models were built separately.

RESULTS

The original model underestimated LE (RMSE=2.85 for men and 1.91 for women), CHD and CBVD for women (RMSE=0.044 and 0.041, respectively). The calibration process identified multiplicative factors to reach acceptance criteria for the four target data mentioned above (RMSE=0.61, 0.21, 0.016 and 0.017, respectively). Over prediction was identified only for CHD events in men (RMSE=0.031) being further calibrated (RMSE=0.008). All other target data met the acceptance criteria. Overall, the calibrated model predicts properly to individuals aging 35-80 years old, diabetics or not, smokers or not, with or without family history of CVD, and presenting at least one of the risk factors uncontrolled: Systolic Blood Pressure, Total Cholesterol or HDL-Cholesterol.

DISCUSSION

This is the first decision analytic model capable of assessing efficiency of interventions that prevent primary CVD events in Brazil. In future research, independent external validation should be carried out to corroborate the reliability of the model outputs.

Where are we at with model-based economic evaluations of interventions for dementia? a systematic review and quality assessment

ABSTRACTObjective:To identify, review, and critically appraise model-based economic evaluations of all types of interventions for people with dementia and their carers.

DESIGN

A systematic literature search was undertaken to identify model-based evaluations of dementia interventions. A critical appraisal of included studies was carried out using guidance on good practice methods for decision-analytic models in health technology assessment, with a focus on model structure, data, and model consistency.

SETTING

Interventions for people with dementia and their carers, across prevention, diagnostic, treatment, and disease management.

RESULTS

We identified 67 studies, with 43 evaluating pharmacological products, 19 covering prevention or diagnostic strategies, and 5 studies reporting non-pharmacological interventions. The majority of studies use Markov models with a simple structure to represent dementia symptoms and disease progression. Half of all studies reported taking a societal perspective, with the other half adopting a third-party payer perspective. Most studies follow good practices in modeling, particularly related to the decision problem description, perspective, model structure, and data inputs. Many studies perform poorly in areas related to the reporting of pre-modeling analyses, justifying data inputs, evaluating data quality, considering alternative modeling options, validating models, and assessing uncertainty.

CONCLUSIONS

There is a growing literature on the model-based evaluations of interventions for dementia. The literature predominantly reports on pharmaceutical interventions for Alzheimer's disease, but there is a growing literature for dementia prevention and non-pharmacological interventions. Our findings demonstrate that decision-makers need to critically appraise and understand the model-based evaluations and their limitations to ensure they are used, interpreted, and applied appropriately.

Early warning systems for the management of chronic heart failure: a systematic literature review of cost-effectiveness models

INTRODUCTION

Describing the general and methodological characteristics of decision-analytical models used in the economic evaluation of early warning systems for the management of chronic heart failure patients and performing a quality assessment of their methodological characteristics is expected to provide concise and useful insight to inform the future development of decision-analytical models in the field of heart failure management.

AREAS COVERED

The literature on decision-analytical models for the economic evaluation of early warning systems for the management of chronic heart failure patients was systematically reviewed. Nine electronic databases were searched through the combination of synonyms for heart failure and sensitive filters for cost-effectiveness and early warning systems.

EXPERT COMMENTARY

The retrieved models show some variability with regards to their general study characteristics. Overall, they display satisfactory methodological quality, even though some points could be improved, namely on the consideration and discussion of any competing theories regarding model structure and disease progression, identification of key parameters and the use of expert opinion, and uncertainty analyses. A comprehensive definition of early warning systems and further research under this label should be pursued. To improve the transparency of economic evaluation publications, authors should make available detailed technical information regarding the published models.

An economic analysis of tolvaptan compared with fluid restriction among hospitalized patients with hyponatremia

OBJECTIVE

The vasopressin-receptor antagonist tolvaptan is used for the treatment of hyponatremia (HN) in hospitalized patients with congestive heart failure (CHF) or syndrome of inappropriate antidiuretic hormone secretion (SIADH). The objective of this economic modeling study was to assess the potential cost and health outcomes associated with tolvaptan in comparison with fluid restriction (FR).

METHODS

A decision-analytic model was developed to estimate potential cost and health outcomes associated with tolvaptan compared with FR among hospitalized CHF and SIADH patients with severe HN (serum sodium [SS] levels < 125 mEq/L). The model, which was populated with data from the published literature, assumes that response to treatment influences hospital length of stay, probability of an intensive care unit (ICU) admission, and probability of a 30-day all-cause hospital readmission. One-way and probabilistic sensitivity analyses (PSAs) assessed the influence of parameter uncertainty on model results.

RESULTS

Model results suggest that, among hospitalized CHF patients with severe HN, the use of tolvaptan compared with FR may lead to reductions of 7.2% and 4.6% in ICU admissions and 30-day readmissions, respectively. Compared with FR, tolvaptan may result in total cost-savings of $156 per hospitalized CHF patient. Among hospitalized SIADH patients with severe HN, the model suggested reductions of 14.6% and 5.1% in ICU admissions and 30-day readmissions, respectively. Compared with FR, tolvaptan may result in total cost-savings of $135 per hospitalized SIADH patient. PSAs found that the probabilities of net cost-savings from the use of tolvaptan compared with FR were 64% and 59% among patients with severe HN with CHF and SIADH, respectively.

CONCLUSIONS

Decision-analytic modeling based on published data for hospitalized CHF and SIADH patients with severe HN, indicates that tolvaptan compared with FR has the potential to improve health outcomes and produce cost-savings that more than offset the cost of tolvaptan.

Cost-effectiveness of the sequential application of tyrosine kinase inhibitors for the treatment of chronic myeloid leukemia

Several tyrosine kinase inhibitors (TKIs) are approved for chronic myeloid leukemia (CML) therapy. We evaluated the long-term cost-effectiveness of seven sequential therapy regimens for CML in Austria. A cost-effectiveness analysis was performed using a state-transition Markov model. As model parameters, we used published trial data, clinical, epidemiological and economic data from the Austrian CML registry and national databases. We performed a cohort simulation over a life-long time-horizon from a societal perspective. Nilotinib without second-line TKI yielded an incremental cost-utility ratio of 121,400 €/quality-adjusted life year (QALY) compared to imatinib without second-line TKI after imatinib failure. Imatinib followed by nilotinib after failure resulted in 131,100 €/QALY compared to nilotinib without second-line TKI. Nilotinib followed by dasatinib yielded 152,400 €/QALY compared to imatinib followed by nilotinib after failure. Remaining strategies were dominated. The sequential application of TKIs is standard-of-care, and thus, our analysis points toward imatinib followed by nilotinib as the most cost-effective strategy.

Optimizing the position and use of omalizumab for severe persistent allergic asthma using cost-effectiveness analysis

BACKGROUND

There has been some controversy on whether the costs of omalizumab outweigh its benefits for severe persistent allergic asthma.

OBJECTIVES

This study aimed to resolve the uncertainties and limitations of previous analyses and establish the cost-effectiveness of omalizumab under the list price and Patient Access Scheme (PAS) discounted price for the UK National Health Service.

METHODS

A decision-analytic model was developed to evaluate the long-term cost-effectiveness of omalizumab under the perspective of the National Health Service. Outcomes were expressed as quality-adjusted life-years (QALYs). Patient subgroups were defined post hoc on the basis of data collected in clinical trials: previous hospitalization, on maintenance oral corticosteroids, and three or more previous exacerbations.

RESULTS

The incremental cost-effectiveness ratio varied from £30,109 to £57,557 per QALY gained depending on the population considered using the PAS price; incremental cost-effectiveness ratios were over a third higher using the list price. Omalizumab is likely to be cost-effective at the threshold of £30,000 per QALY gained in the severe subgroups if the improvement in health-related quality of life from omalizumab is mapped from an asthma-specific measure to the EuroQol five-dimensional questionnaire (vs. the EuroQol five-dimensional questionnaire directly collected from patients) or asthma mortality refers to death after hospitalization from asthma (vs. asthma-mortality risk in the community).

CONCLUSIONS

Although the cost-effectiveness of omalizumab is more favorable under the PAS price, it represents good value for money only in severe subgroups and under optimistic assumptions regarding asthma mortality and improvement in health-related quality of life. For these reasons, omalizumab should be carefully targeted to ensure value for money.

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

BACKGROUND

Real-world patients' medication adherence is lower than that of clinical trial patients. Hence, the effectiveness of medications in routine practice may differ.

OBJECTIVES

The study objective was to compare the outcomes of an adherence-naive versus a dynamic adherence modeling framework using the case of statins for the primary prevention of cardiovascular (CV) disease.

METHODS

Statin adherence was categorized into three state-transition groups on the basis of an epidemiological cohort study. Yearly adherence transitions were incorporated into a Markov microsimulation using TreeAge software. Tracker variables were used to store adherence transitions, which were used to adjust probabilities of CV events over the patient's lifetime. Microsimulation loops "random walks" estimated the average accrued quality-adjusted life-years (QALYs) and CV events. For each 1,000-patient microsimulations, 10,000 outer loops were performed to reflect second-order uncertainty.

RESULTS

The adherence-naive model estimated 0.14 CV events avoided per person, whereas the dynamic adherence model estimated 0.08 CV events avoided per person. Using the adherence-naive model, we found that statin therapy resulted in 0.40 QALYs gained over the lifetime horizon on average per person while the dynamic adherence model estimated 0.22 incremental QALYs gained. Subgroup analysis revealed that maintaining high adherence in year 2 resulted in 0.23 incremental QALYs gained as compared with 0.16 incremental QALYs gained when adherence dropped to the lowest level.

CONCLUSIONS

A dynamic adherence Markov microsimulation model reveals risk reduction and effectiveness that are lower than with an adherence-naive model, and reflective of real-world practice. Such a model may highlight the value of improving or maintaining good adherence.

Medical decision analysis for first-line therapy of chronic myeloid leukemia

Several tyrosine kinase inhibitors (TKIs) are approved for the treatment of chronic myeloid leukemia (CML). Our goal was to develop a clinical decision-analytic model for evaluation of the long-term effectiveness of different therapy regimens. We developed a Markov cohort model with a lifelong time horizon for first-line treatment with imatinib, dasatinib or nilotinib. Seven strategies including combinations of TKIs, chemotherapy and stem cell transplant were evaluated. The model was parameterized using published trial data, the Austrian CML registry and practice patterns estimated by experts. Health outcomes evaluated were life-years (LYs) and quality-adjusted LYs (QALYs). Based on our decision analysis, dasatinib following nilotinib failure was the most effective treatment in terms of LYs (19.8 LYs) and QALYs (16.1 QALYs). Sensitivity analyses showed that the ranking of strategies was mostly influenced by the duration of first- and second-line therapies. Our results may support decision-making regarding the sequential application of TKIs.

Simulation model for cost estimation of integrated care concepts of heart failure patients

BACKGROUND

As a direct result of the population growing older the total number of chronic illnesses increases. The future expenditure for care of chronically ill patients is an ever-present challenge for the health care system. New solutions based on integrated care or the inclusion of telemedical systems in the treatment procedure can be essential for reducing the future financial burden. Therefore a detailed economic model was developed, which enables the comparison of health and cost outcomes for conventional medical care and different integrated care concepts in heart failure treatment.

METHODS

F0r modelling, the discrete event technique was used. The model takes outpatient care as well as inpatient care into account to estimate the total occurring costs. It enables the treatment of patients by a physician, a specialist or a clinical ambulance for the simulation of the outpatient care. For inpatient care the model considers the total-costs of the hospitalization and rate of re-admission and furthermore the costs which occur because of special medical treatments or necessary stay at intensive care units. To rate the severity of symptoms patients can be classified using NYHA groups. To outline some of the potential model results, two scenarios have been simulated to compare both methods of care regarding overall costs.

RESULTS

The developed simulation model allows comparing health and cost outcomes of different integrated care concepts for the treatment of heart failure patients. Additionally to the simulation of standard outpatient and inpatient care procedures in Austria the approach of a telemedical monitoring system for heart failure patients was implemented in this economic model. With the simulated scenarios it could be shown that under the given simulation parameters the telemedical system can lead to cost savings of up to 8% within the first three years.

CONCLUSIONS

The developed model represents a comprehensive tool, which opens a wide field of possible simulation scenarios for the treatment of heart failure patients with special focus on overall cost estimations and reimbursement strategies. The simulated scenarios show that telemedical care has the potential of improved health outcomes and economic benefits.