The Markov True and Error (MARTER) model (Birnbaum & Wan, 2020) has three components: a risky decision making model with one or more parameters, a Markov model that describes stochastic variation of parameters over time, and a true and error (TE) model that describes probabilistic relations between true preferences and overt responses. In this study, we simulated data according to 57 generating models that either did or did not satisfy the assumptions of the True and Error fitting model, that either did or did not satisfy the error independence assumptions, that either did or did not satisfy transitivity, and that had various patterns of error rates. A key assumption in the TE fitting model is that a person’s true preferences do not change in the short time within a session; that is, preference reversals between two responses by the same person to two presentations of the same choice problem in the same brief session are due to random error. In a set of 48 simulations, data generating models either satisfied this assumption or they implemented a systematic violation, in which true preferences could change within sessions. We used the true and error (TE) fitting model to analyze the simulated data, and we found that it did a good job of distinguishing transitive from intransitive models and in estimating parameters not only when the generating model satisfied the model assumptions, but also when model assumptions were violated in this way. When the generating model violated the assumptions, statistical tests of the TE fitting models correctly detected the violations. Even when the data contained violations of the TE model, the parameter estimates representing probabilities of true preference patterns were surprisingly accurate, except for error rates, which were inflated by model violations. In a second set of simulations, the generating model either had error rates that were or were not independent of true preferences and transitivity either was or was not satisfied. It was found again that the TE analysis was able to detect the violations of the fitting model, and the analysis correctly identified whether the data had been generated by a transitive or intransitive process; however, in this case, estimated incidence of a preference pattern was reduced if that preference pattern had a higher error rate. Overall, the violations could be detected and did not affect the ability of the TE analysis to discriminate between transitive and intransitive processes.

This paper describes a theory of the variability of risky choice that describes empirical properties of choice data, including sequential effects and systematic violations of response independence. The Markov True and Error (MARTER) model represents the formation and fluctuation of true preferences produced by stochastic variation of parameters over time, which produces changing true preference patterns. This model includes a probabilistic association between true preferences and overt responses due to random error. Computer programs have been developed to simulate data according to this model, to fit data to the TE model, and to test and analyze violations of iid (independent and identical distributions) that are predicted by the model. Data simulated from MARTER models show properties that are characteristic of real data, including violations of iid similar to those observed in previous empirical research. This paper also illustrates how methods based on analysis of binary response proportions do not and in many cases cannot correctly diagnose what model was used to generate the data. The MARTER model is extremely general and neutral with respect to models of risky decision making. For example, the transitive transfer of attention exchange (TAX) model and intransitive Lexicographic Semiorder (LS) models can both be represented as special cases of MARTER, and they can be tested against each other, even when binary choice proportions cannot discriminate which model was used to simulate the data. Software to simulate data according to this model, and to fit data to this model, to test this model, and to compare special case theories are included or linked to this article.

An aircraft wing is the carrier of imaging payload (interferometric synthetic aperture radar (SAR) or array SAR) of a high-resolution aerial remote sensing system, and high-precision estimation of wing deformation is the key. There are two main traditional modelling methods for wing deformation, namely stochastic theory modelling and material mechanics modelling only dealing with single disturbance, of which the model parameters are derived from empirical values. Aiming at the complex multi-source disturbance of an aircraft wing, this paper separately probes the influence of external disturbance (air disturbance) and internal disturbance (engine vibration) based on the real-time observation of sensors and classifies the wing deformation on the basis of auto-regressive (AR) modelling for parameter identification. With the authentic flight data of a certain types of aircraft, the experimental analysis shows that the wing deformation under the influence of engine vibration is the 14th-order AR model, and the wing deformation under the influence of turbulence is the fifth-order AR model. Meanwhile, this paper also provides an experimental verification idea for the wing deflection modelling built on the second- or third-order Markov model.

Objectives: Earlier treatment of publicly funded patients may achieve health gains that justify the additional costs of reducing waiting times. This study reports on the cost-effectiveness of implementing a private contracting model to meet alternative maximum waiting time targets for publicly funded patients undergoing total knee replacement surgery in Australia.

Methods: A linked decision tree and cohort Markov model was developed and populated and validated using secondary data sources to represent the pathways, costs, and quality adjusted life-years (QALYs) gained of non-urgent patients with alternative waiting times for total knee replacement surgery to a maximum age of 100 years.

Results: Assuming public waiting times are reduced through the purchase of private services, additional QALYs are gained at an incremental cost of less than $40,000. Value could be increased if lower private prices could be negotiated. Results are also sensitive to the rate of deterioration in function while waiting for surgery and the impact of functional status at the time of surgery on postsurgery outcomes.

Conclusions: More evidence on the value of expanded capacity or new models of care may inform new funding models to support such investments and reduced prices for new technologies, leading to more efficient and sustainable publicly funded healthcare systems.

Pelvic inflammatory disease (PID) and more specifically salpingitis (visually confirmed inflammation) is the primary cause of tubal factor infertility and is an important risk factor for ectopic pregnancy. The risk of these outcomes increases following repeated episodes of PID. We developed a homogenous discrete-time Markov model for the distribution of PID history in the UK. We used a Bayesian framework to fully propagate parameter uncertainty into the model outputs. We estimated the model parameters from routine data, prospective studies, and other sources. We estimated that for women aged 35–44 years, 33·6% and 16·1% have experienced at least one episode of PID and salpingitis, respectively (diagnosed or not) and 10·7% have experienced one salpingitis and no further PID episodes, 3·7% one salpingitis and one further PID episode, and 1·7% one salpingitis and ⩾2 further PID episodes. Results are consistent with numerous external data sources, but not all. Studies of the proportion of PID that is diagnosed, and the proportion of PIDs that are salpingitis together with the severity distribution in different diagnostic settings and of overlap between routine data sources of PID would be valuable.

We examine U.S. monetary policies from 1973 to 2014 with the Taylor rule as a benchmark by utilizing a k-state Markov regime-switching model in which the number and the periods of the regimes are endogenously determined. The model relates the federal funds rate to real time output gaps and inflation forecast. It endogenously identifies the periods of Taylor rule regime and discretionary regimes, consistent with the U.S. experience. The Taylor rule regime also coincides with periods of lower variability in inflation and in real GDP growth.

Objectives: Real-time virtual sonography (RVS) is a promising navigation technique for percutaneous radiofrequency ablation (RFA) treatment, especially in ablating nodules poorly visualized on conventional ultrasonography (US). However, its cost-effectiveness has not been established. The purpose of this study is to evaluate the cost-effectiveness of RVS navigated RFA (RVS-RFA) relative to US guided RFA (US-RFA) in patients with small hepatocellular carcinoma (HCC) in China, from the modified societal perspective.

Methods: A state-transition Markov model was created using TreeAge Pro™ 2012. The parameters used in the model, including natural history of HCC patients, procedure efficacy and related costs, were obtained from a systematic search of literature through PubMed, EMBASE, and Science Citation Index databases. The simulated cohort was patients with solitary, small HCC (<3 cm in diameter) and Child-Pugh class A or B, whose tumors are poorly visualized in B-mode US but clearly detectable by CT or MRI.

Results: In this cohort of difficult cases, RVS-RFA was a preferred strategy saving 2,467 CNY ($392) throughout the patient's life while gaining additional 1.4 QALYs compared with conventional US guidance. The results were sensitive to the efficacy of US-RFA and RVS-RFA including complete ablation rate and local recurrence rate, the median survival for patients with progressive HCC, the probability of performing RFA for recurrent HCC, and the cost of RVS navigation, disposable needle or hospitalization.

Conclusions: RVS-RFA is a dominant strategy for patients with small HCC unidentifiable in B-mode US, in terms of cost savings and QALYs gained, relative to the conventional US-guided method.

Objectives: A recent randomized, controlled trial in chronic heart failure patients showed that NT-proBNP-guided, intensive patient management (BMC) on top of multidisciplinary care reduced all-cause mortality and heart failure hospitalizations compared with multidisciplinary care (MC) or usual care (UC). We now performed a cost-utility analysis of these interventions from a payer's perspective.

Methods: Costs related to hospitalizations, ambulatory physician and nurse visits, and NT-proBNP testing for the three management strategies were acquired for both Austria (€) and Canada ($) and combined with the survival and quality of life data from the clinical trial for cost-effectiveness analysis. Data on long-term survival, costs, and quality-adjusted life-years (QALY) were extrapolated for a 20-year time horizon using a Markov model, which simulated the progression of disease through beta-blocker use, hospitalizations, and mortality.

Results: BMC was the most cost-effective strategy as it was dominant (cost-saving with improved health outcome) over both MC and UC based on both Austrian and Canadian costs. Incremental cost-effectiveness ratios for MC relative to UC were €3,746 and $5,554 per QALY gained for Austrian and Canadian costs, respectively. The probabilities for BMC being the most cost-effective strategy were 92 percent at a threshold value of Austrian €40,000 and 93 percent at a threshold value of Canadian $50,000.

Conclusions: NT-proBNP-guided, intensive HF patient management in addition to multidisciplinary care not only reduces death and hospitalization but also proves to be cost-effective.

Objectives: Cardiac resynchronization therapy (CRT) has recently been shown to reduce both mid-term and long-term mortality in patients with mild heart failure. Although proven effective, it is unclear whether CRT is cost-effective in low and middle-income countries (LMIC). Therefore, we set out to analyze the cost-effectiveness of CRT in Argentina in patients with New York Heart Association (NYHA) functional class (FC) I or II heart failure (HF). We chose to compare patients receiving optimal medical treatment (OMT) and CRT with those patients receiving only OMT.

Methods: We constructed a Markov model with a cohort simulation, and a life-time horizon to assess costs, life-years, and quality-adjusted life-year (QALY) gained as a result of treatment with both CRT and OMT from an Argentine third party payer perspective. We included patients who met the following criteria: left ventricular ejection fraction (LVEF) ≤ 40 percent, sinus rhythm with a QRS ≥ 120 msec, and NYHA FC I-II HF. The results were expressed as cost per life-year and QALY gained in international dollars (ID$) for the year 2009.

Results: For the base case analysis performed, we started at a fixed age of 65. After applying a 3 percent annual discount rate, the incremental cost-effectiveness ratio (ICER) was 38.005 ID$ per year of life gained and 34.185 ID$ per QALY gained.

Conclusions: Long-term treatment with CRT appears to be cost-effective in Argentina compared with patients treated solely with OMT. Similar analysis should be performed to determine if this treatment option is cost-effective in other LMIC.

We apply the known formulae of the RESTART problem to Markov models of software (and many other) systems, and derive new equations. We show how checkpoints might be included, with their resultant performance under RESTART. The result is a complete procedure for finding the mean, variance, and tail behavior of the job completion time as a function of the failure rate. We also provide a detailed example.

This is the third in a series of three papers. In the first paper we describe a comprehensive stochastic model of an individual's lifetime that includes diagnosis with ischaemic heart disease and stroke and also the development of the major risk factors for these conditions. The second paper discusses in some detail models for changes in body mass index (BMI) and also the effects of these changes, in particular the current trend towards increasing prevalence of obesity, on diabetes, cardiovascular diseases and expected future lifetime. This paper is devoted to the following applications of the model described in the first paper:

(a) quantifying the effects of smoking and of changes in smoking habits, and,

(b) quantifying the effects of treatment with statins (drugs designed to lower cholesterol).

This is the second in a series of three papers. In the first paper we describe a comprehensive stochastic model of an individual's lifetime that includes diagnosis with ischaemic heart disease and stroke and also the development of the major risk factors for these conditions. The third paper is devoted to some applications of this model.

In this paper we discuss the effect of BMI on diabetes, heart disease and mortality and we use data from the Framingham Heart Study and the Health Survey for England to develop stochastic models for changes in an individual's BMI. Some of these models incorporate time trends leading to increasing prevalence of obesity. We then use these models to investigate how future expected lifetime and future expected healthy lifetime depend on BMI.

Our conclusions are that if the prevalence of obesity increases, even to an extreme degree, then the prevalence of diabetes and hypertension in the population will increase, possibly to a significant extent, but the prevalence of heart disease and stroke will increase by a much smaller amount and the effect on expected future lifetime will be small.

We construct a stochastic model of an individual's lifetime that includes diagnosis with ischaemic heart disease and stroke and also the development of the major risk factors for these conditions: hypercholesterolaemia, hypertension, diabetes and obesity. Smoking, another major risk factor, is treated deterministically. Mathematically, the model is a continuous time, finite state space Markov process, with the individual's age playing the rôle of time. The model is parameterised using data from the Framingham Heart Study, with parameter values adjusted so that the model is appropriate for UK conditions in the early 21st century. The model has been designed so that it can be used to quantify the effects of:

(i) trends, in particular increasing prevalence of obesity.

(ii) changes in behaviour, in particular smoking patterns, and

(iii) treatments, in particular statins for hypercholesterolaemia.

These applications are covered in two accompanying papers.

Objectives: The method of choice for bariatric surgery remains controversial. The aim of this study was to compare the outcome of laparoscopic Roux-en-Y gastric bypass (L-RYGB) versus laparoscopic adjustable gastric banding (LAGB) using quality-adjusted life-years (QALYs).

Methods: We developed a Markov model of the quality of life and survival of L-RYGB and LAGB in obese patients. Using census data, we estimated the probability of dying and quality of life for each year of each cohort.

Results: For all cohorts, L-RYGB offers the highest advantage in QALYs compared with gastric banding. The youngest cohort showed the greatest discrepancy between the two surgical methods, with 7.8, 6.4, and 4.7 QALYs gained with L-RYGB over LAGB for the age groups 35, 45, and 55, respectively. Those with the highest presurgical body mass index (BMI) acquired the most advantage with L-RYGB, with 2.8, 6.4, and 9.6 QALYs gained with L-RYGB over LAGB for the BMI groups 40, 50, and 60. Males had a slightly higher advantage with L-RYGB, with 6.5 QALYs gained with L-RYGB over LAGB compared with 6.0 QALYs for females.

Conclusions: For the cohorts studied, L-RYGB is the preferred surgical treatment for obesity if the sole metric is QALYs. The young and extremely obese are core groups who will gain the most QALYs following L-RYGB.

Objectives: The objective of this study was to estimate the cost-effectiveness of infliximab use in patients with rheumatoid arthritis (RA) in Swedish clinical practice, based on patient-level data from the Stockholm TNF-alpha follow-up registry (STURE).

Methods: Real-world patient-level data on infliximab use from the STURE registry were implemented in a Markov cohort model, in which health states of functional status were classified according to the Health Assessment Questionnaire Disability Index (HAQ—five categories) and twenty-eight joint count Disease Activity Score (DAS28). The transition probabilities between HAQ and DAS28 states during treatment, as well as discontinuation rates were modeled based on data from the registry for patients using infliximab as their first-line biological treatment. The transition probabilities in the comparator arm, that is, disease progression without biologic treatment, as well as mortality rates, costs, and utilities were based on published literature. The analysis had a societal cost perspective.

Results: Infliximab was associated with an incremental gain in quality-adjusted life-years of 1.02 and an incremental cost of €23,264 per patient compared with progression without biologic treatment, producing an incremental cost-effectiveness ratio (ICER) of €22,830 (SEK211,136 or US$31,230). Sensitivity analyses of input parameters and model assumptions produced ICERs in the range from €18,000 to €47,000.

Conclusions: Results from base-case and sensitivity analyses fell well below established benchmarks for cost-effectiveness in Sweden. The results, therefore, indicated that infliximab treatment for RA has provided good societal value for money in Swedish clinical practice, compared with a scenario of no biological treatment.

Background: The classic cut and sew surgical Maze procedure has been shown to reduce atrial fibrillation (AF), and recently newer surgical ablation techniques with reduced technical complexity have been introduced. This study sought to systematically review the efficacy and safety of these newer techniques and to evaluate their long-term cost-effectiveness at the time of scheduled mitral valve (MV) surgery.

Methods: A systematic literature search and meta-analysis was performed to generate the most reliable efficacy and safety parameter estimates for a Markov decision analysis model comparing MV surgery alone to MV surgery plus an ablation Maze procedure. Both basic and probabilistic sensitivity analyses were conducted.

Results: Based on the six randomized controlled trials (RCTs) identified, the pooled 1-year estimate of AF after surgery alone was 71 percent (95 percent confidence interval [CI], 64 percent to 78 percent). The pooled risk ratio of AF after surgical ablation treatment at the time of mitral valve surgery relative to valve surgery alone was 0.33 (95 percent CI, 0.19 to 0.55). The pooled analyses showed that no statistical significant increases in operative mortality, permanent pacemaker implantation, and postoperative bleeding with the ablative Maze procedures. An ablation-based Maze procedure at the time of mitral valve surgery had an incremental cost-effectiveness ratio (ICER) of $4,446CAD ($3,850US) per quality-adjusted life-year (QALY) compared with valve surgery alone. Specifically costs were an extra $900CAD but with improved clinical outcomes (0.20 QALYs), including a prolonged life expectancy of 0.10 life-years. In one-way sensitivity analyses, survival time after MV surgery had the largest impact on ICER. Other variables influencing the ICER included the risk ratio of AF, utility, and cost estimates. Probabilistic sensitivity analysis suggests that 58.1 percent, 73.9 percent, and 89.3 percent of the simulations of the Maze strategy are cost-effective at willingness to pay thresholds of $20,000, $50,000, and $100,000CAD per QALY gained, respectively.

Conclusions: Our meta-analysis suggests that a Maze surgical ablation procedure at the time of MV surgery is associated with a reduced postoperative AF risk. Our economic model further suggests that the surgical ablation strategy at the time of mitral valve surgery is likely a cost-effective intervention, provided patients have a good long-term postsurgical prognosis.

Objectives: The aim of this study is to evaluate the cost-effectiveness of Magnetic Resonance Guided Focused Ultrasound (MRgFUS) compared with alternative treatments for uterine fibroids in the United States.

Methods: We used techniques of decision analysis and data from secondary sources to develop and estimate an economic model of the management of uterine fibroids among premenopausal women. Patients in the model receive treatment with MRgFUS, uterine artery embolization (UAE), abdominal myomectomy, hysterectomy, or pharmacotherapy. The model predicts total costs (including subsequent procedures) and quality-adjusted life-years (QALYs) for each treatment strategy over a lifetime horizon, discounted at 3 percent, from a societal perspective. Data on treatment efficacy and safety were obtained from published and unpublished studies. Costs (2005 US$) were obtained from an analysis of a large administrative database and other secondary sources. Lost productivity costs were included in the base-case analysis, but excluded in a sensitivity analysis.

Results: UAE was associated with the most QALYs (17.39), followed by MRgFUS (17.36), myomectomy (17.31), hysterectomy (17.18), and pharmacotherapy (16.70). Pharmacotherapy was the least costly strategy ($9,200 per patient), followed by hysterectomy ($19,800), MRgFUS ($27,300), UAE ($28,900), and myomectomy ($35,100). Incremental cost-effectiveness ratios (cost per QALY gained) were $21,800 for hysterectomy, $41,400 for MRgFUS, and $54,200 for UAE; myomectomy was more costly and less effective than both MRgFUS and UAE. Results were sensitive to MRgFUS recurrence rates, MRgFUS procedure costs, and assumptions about quality of life following hysterectomy.

Conclusions: Our findings suggest that MRgFUS is in the range of currently accepted criteria for cost-effectiveness, along with hysterectomy and UAE.