State Transition Structure Research Articles

Evolutionarily conserved fMRI network dynamics in the mouse, macaque, and human brain

Evolutionarily relevant networks have been previously described in several mammalian species using time-averaged analyses of fMRI time-series. However, fMRI network activity is highly dynamic and continually evolves over timescales of seconds. Whether the dynamic organization of resting-state fMRI network activity is conserved across mammalian species remains unclear. Using frame-wise clustering of fMRI time-series, we find that intrinsic fMRI network dynamics in awake male macaques and humans is characterized by recurrent transitions between a set of 4 dominant, neuroanatomically homologous fMRI coactivation modes (C-modes), three of which are also plausibly represented in the male rodent brain. Importantly, in all species C-modes exhibit species-invariant dynamic features, including preferred occurrence at specific phases of fMRI global signal fluctuations, and a state transition structure compatible with infraslow coupled oscillator dynamics. Moreover, dominant C-mode occurrence reconstitutes the static organization of the fMRI connectome in all species, and is predictive of ranking of corresponding fMRI connectivity gradients. These results reveal a set of species-invariant principles underlying the dynamic organization of fMRI networks in mammalian species, and offer novel opportunities to relate fMRI network findings across the phylogenetic tree.

Dynamic responses of steady-state transition structures under impact loading

Advancements in materials science and mechanical system have spurred widespread investigation into non-traditional structures. In particular, engineers have shown interest in steady-state transition structures with phase transition properties. In this paper, a three-dimensional steady-state transition structure was established using the genetic algorithm and three-dimensional expansion, on which the low-velocity impact tests were carried out. Force response and energy absorption of the steady-state transition structures under impact were studied. From the force response and energy absorption curves, it can be seen that the steady-state transition structures absorb and store portion of impact energy temporarily, gradually releasing it after impact peak. This unique energy behavior results in a steady state transition structure with a long impact response time and a low peak impact force under impact. In addition, investigation into energy transfer within these structures reveals that energy oscillations occur among multilayered bistable surfaces during steady-state transitions, further improving the energy dissipation. Further, the dynamic response and damage modes of the honeycomb structure and the steady state transition structure were compared, showing that the damage mode of the steady state transition structure under the impact is an overall damage, in contrast to the penetration damage of the honeycomb structure. Notably, the steady-state transition structures showcase a higher proportion of elastic strain energy during impacts, effectively delaying structural damage onset, and dispersing impact energy, thus enhancing impact resistance. In light of these findings, the demonstrated behavior of steady-state transition structures in absorbing and dissipating impact energy showcases their potential as promising avenues for the development of more effective impact protection strategies.

Distinct processing of the state prediction error signals in frontal and parietal correlates in learning the environment model.

Goal-directed reinforcement learning constructs a model of how the states in the environment are connected and prospectively evaluates action values by simulating experience. State prediction error (SPE) is theorized as a crucial signal for learning the environment model. However, the underlying neural mechanisms remain unclear. Here, using electroencephalogram, we verified in a two-stage Markov task two neural correlates of SPEs: an early negative correlate transferring from frontal to central electrodes and a late positive correlate over parietal regions. Furthermore, by investigating the effects of explicit knowledge about the environment model and rewards in the environment, we found that, for the parietal correlate, rewards enhanced the representation efficiency (beta values of regression coefficient) of SPEs, whereas explicit knowledge elicited a larger SPE representation (event-related potential activity) for rare transitions. However, for the frontal and central correlates, rewards increased activities in a content-independent way and explicit knowledge enhanced activities only for common transitions. Our results suggest that the parietal correlate of SPEs is responsible for the explicit learning of state transition structure, whereas the frontal and central correlates may be involved in cognitive control. Our study provides novel evidence for distinct roles of the frontal and the parietal cortices in processing SPEs.

A Promising Approach to Optimizing Sequential Treatment Decisions for Depression: Markov Decision Process.

The most appropriate next step in depression treatment after the initial treatment fails is unclear. This study explores the suitability of the Markov decision process for optimizing sequential treatment decisions for depression. We conducted a formal comparison of a Markov decision process approach and mainstream state-transition models as used in health economic decision analysis to clarify differences in the model structure. We performed two reviews: the first to identify existing applications of the Markov decision process in the field of healthcare and the second to identify existing health economic models for depression. We then illustrated the application of a Markov decision process by reformulating an existing health economic model. This provided input for discussing the suitability of a Markov decision process for solving sequential treatment decisions in depression. The Markov decision process and state-transition models differed in terms of flexibility in modeling actions and rewards. In all, 23 applications of a Markov decision process within the context of somatic disease were included, 16 of which concerned sequential treatment decisions. Most existing health economic models relating to depression have a state-transition structure. The example application replicated the health economic model and enabled additional capacity to make dynamic comparisons of more interventions over time than was possible with traditional state-transition models. Markov decision processes have been successfully applied to address sequential treatment-decision problems, although the results have been published mostly in economics journals that are not related to healthcare. One advantage of a Markov decision process compared with state-transition models is that it allows extended action space: the possibility of making dynamic comparisons of different treatments over time. Within the context of depression, although existing state-transition models are too basic to evaluate sequential treatment decisions, the assumptions of a Markov decision process could be satisfied. The Markov decision process could therefore serve as a powerful model for optimizing sequential treatment in depression. This would require a sufficiently elaborate state-transition model at the cohort or patient level.Supplementary InformationThe online version contains supplementary material available at 10.1007/s40273-022-01185-z.

Supervisory Control of Multiagent Discrete-Event Systems With Partial Observation

In this letter, we investigate multi-agent discrete-event systems with partial observation. The agents can be divided into several groups in each of which the agents have identical (isomorphic) state transition structures, and can thus be <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">relabeled</i> into the same template. Based on the template a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scalable supervisor</i> whose state size and computational cost are independent of the number of agents is designed for the case of partial observation. The scalable supervisor under partial observation does not need to be recomputed regardless of how many agents are added to or removed from the system. We generalize our earlier results from complete to partial observation by proposing sufficient conditions for safety and maximal permissiveness of the scalable least restrictive supervisor on the template level. An example is provided to illustrate the proposed scalable supervisory synthesis.

Canonical Automata via Distributive Law Homomorphisms

The classical powerset construction is a standard method converting a non-deterministic automaton into a deterministic one recognising the same language. Recently, the powerset construction has been lifted to a more general framework that converts an automaton with side-effects, given by a monad, into a deterministic automaton accepting the same language. The resulting automaton has additional algebraic properties, both in the state space and transition structure, inherited from the monad. In this paper, we study the reverse construction and present a framework in which a deterministic automaton with additional algebraic structure over a given monad can be converted into an equivalent succinct automaton with side-effects. Apart from recovering examples from the literature, such as the canonical residual finite-state automaton and the \'atomaton, we discover a new canonical automaton for a regular language by relating the free vector space monad over the two element field to the neighbourhood monad. Finally, we show that every regular language satisfying a suitable property parametric in two monads admits a size-minimal succinct acceptor.

A numerical study of Markov decision process algorithms for multi-component replacement problems

We present a unified modeling framework for Time-Based Maintenance (TBM) and Condition-Based Maintenance (CBM) for optimization of replacements in multi-component systems. The considered system has a K-out-of-N reliability structure, and components deteriorate according to a multivariate gamma process with Lévy copula dependence. The TBM and CBM models are formulated as Markov Decision Processes (MDPs), and optimal policies are found using dynamic programming. Solving the CBM model requires that the continuous deterioration process is discretized. We therefore investigate the discretization level required for obtaining a near-optimal policy. Our results indicate that a coarser discretization level than previously suggested in the literature is adequate, indicating that dynamic programming is a feasible approach for optimization in multi-component systems. We further demonstrate this through empirical results for the size limit of the MDP models when solved with an optimized implementation of modified policy iteration. The TBM model can generally be solved with more components than the CBM model, since the former has a sparser state transition structure. In the special case of independent component deterioration, transition probabilities can be calculated efficiently at runtime. This reduces the memory requirements substantially. For this case, we also achieved a tenfold speedup when using ten processors in a parallel implementation of algorithm. Altogether, our results show that the computational requirements for systems with independent component deterioration increase at a slower rate than for systems with stochastic dependence.

Characterization of the conditional stationary distribution in Markov chains via systems of linear inequalities

AbstractThis paper considers ergodic, continuous-time Markov chains $\{X(t)\}_{t \in (\!-\infty,\infty)}$ on $\mathbb{Z}^+=\{0,1,\ldots\}$ . For an arbitrarily fixed $N \in \mathbb{Z}^+$ , we study the conditional stationary distribution $\boldsymbol{\pi}(N)$ given the Markov chain being in $\{0,1,\ldots,N\}$ . We first characterize $\boldsymbol{\pi}(N)$ via systems of linear inequalities and identify simplices that contain $\boldsymbol{\pi}(N)$ , by examining the $(N+1) \times (N+1)$ northwest corner block of the infinitesimal generator $\textbf{\textit{Q}}$ and the subset of the first $N+1$ states whose members are directly reachable from at least one state in $\{N+1,N+2,\ldots\}$ . These results are closely related to the augmented truncation approximation (ATA), and we provide some practical implications for the ATA. Next we consider an extension of the above results, using the $(K+1) \times (K+1)$ ( $K &gt; N$ ) northwest corner block of $\textbf{\textit{Q}}$ and the subset of the first $K+1$ states whose members are directly reachable from at least one state in $\{K+1,K+2,\ldots\}$ . Furthermore, we introduce new state transition structures called (K, N)-skip-free sets, using which we obtain the minimum convex polytope that contains $\boldsymbol{\pi}(N)$ .

Control of asynchronous sequential machine with adversarial input based on the semi-tensor product of matrices

In this study, we investigate the control problem of asynchronous sequential machine with adversarial input by using the semi-tensor product (STP) of matrices. First, by applying the STP of matrices, a new algebraic expression of asynchronous sequential machines with an adversarial input is deduced. Next, by investigating the control process, the controller with the minimal state set is designed, and two algorithms for assigning the values to the state transition structure matrix and the output structure matrix of the controller are proposed. Then, in the framework of the algebraic expression of the asynchronous sequential machines with adversarial input and two proposed algorithms, an algebra expression of the closed-loop system dynamic is established; the theoretical results are verified by using this algebra expression. Finally, an example is presented to illustrate the validity and application of the proposed approach.

PSY35 A COMPARATIVE ANALYSIS OF HEALTH TECHNOLOGY ASSESSMENTS EVALUATING RECENTLY APPROVED BIOLOGICAL THERAPIES FOR ADULT PATIENTS WITH MODERATE-TO-SEVERE PSORIASIS IN THE US, CANADA AND UK

To compare recently approved biologics for the treatment of moderate-to-severe psoriasis by national HTA bodies in the US, Canada and UK. A comparative analysis on the evidence base, and resulting recommendations, by ICER, CADTH, NICE and SMC for the US, Canada and UK was conducted. Inclusion criteria included: appraisals published between 2016-2019, evaluating biological therapies for adult populations with moderate-to-severe psoriasis. Submitted clinical and economic evidence for included therapies were compared along patient population, comparators, endpoints, health-related quality of life, and approach with uncertainty in the data. Ixekizumab, brodalumab and guselkumab were included for review. While there was some variation in the submitted clinical evidence, study population, drug regimen, comparators and clinical endpoints were overall similar. PASI75, PASI90, PASI100, (s)PGA and IGA were included as primary clinical endpoints. DLQI and the SF-36 scores were the most commonly submitted patient reported outcomes. All HTA assessments included NMAs, with ITCs being the most common method used, to inform decision-making. Cost-effectiveness models with a Markov state transition structure were included in all CADTH and ICER appraisals, and the UK submissions for ixekizumab and brodalumab. Economic evidence submitted for guselkumab included cost minimization and comparison analyses for the UK. Submitted models evaluated treatment sequences, which varied to reflect local clinical practice. All HTA bodies recommended the three biologic therapies for use in patients with moderate to severe plaque psoriasis who have failed to respond to standard systemic therapies with discontinuation rules if no response was observed after 12-16 (16-20: ixekizumab (SMC)) weeks. The evidence base, and HTA agency decisions, for guselkumab, ixekizumab, and brodalumab submissions were principally aligned. As more biologics are being approved, understanding the requirements of HTA, and undertaking holistic evidence generation, will play a crucial role in enabling access to the novel biologics.

PCN106 A REVIEW OF DECISION ANALYTIC MODELS TO EVALUATE THE COST-EFFECTIVENESS OF CANCER TREATMENTS: 5-YEARS OF PUBLICATIONS AND SINGLE-TECHNOLOGY APPRAISALS

As demand for treatment grows and healthcare budgets remain finite, decision makers require the results of cost-effectiveness analysis to make informed decisions in relation to the reimbursement of new cancer treatments. This study summarises the key modelling approaches used to show cost-effectiveness in oncology, as well as their advantages and limitations. A literature review identified published economic evaluations of cancer treatments using a model, and single technology appraisals (STAs) submitted to the National Institute for Health and Care Excellence (NICE). Searches were performed in November 2018, capturing relevant publications and STAs published since 2013 up to the date of searching. Published literature was identified using Medline and EMBASE via Ovid. The review was supplemented with methods literature known to the authors discussing cancer modelling. The review identified 100 NICE STAs and 124 published studies relevant to the topic. Published studies appeared to report a greater use of discrete-time state transition-models (n=102, 82%) when compared to NICE submissions. Partitioned-survival analysis (n=54, 54%) and discrete-time state-transition structures (n=41, 41%) were the main structures submitted to NICE. Justification of model structures and consideration of structural uncertainty were very limited across both the publications and the NICE submissions. There appears to be a stronger dominance of the partitioned-survival analysis approach in submissions to NICE, however, we believe many of the published state transition models have been incorrectly labelled and are partitioned-survival analysis. Other structures, such as a decision tree or discrete-event simulation, have also been utilised in submissions and within the published literature but only in minority of cases. Justification for the model structure was very limited, despite a recognition in the literature that model structure can greatly influence cost-effectiveness results and the validity of the economic evaluation and studies would be improved with a thorough rationale for this choice.

Can the symmetrical Dewar pyridine be observed experimentally? A theoretical study

ABSTRACTIn this work we study the possibility of the photochemical formation of the symmetrical Dewar pyridine (1-azabicyclo-[2,2,0]-hexa-2,5-diene), by applying the complete active space self-consistent field method and the multiconfigurational second-order perturbation theory to explore the corresponding ground and excited state potential energy surfaces. According to our theoretical calculations there are three possible paths that can be followed, one is a biphotonic process which involves irradiating pyridine in its ground state with a 358 nm laser guiding the system to an intersystem crossing S1/T1/S0 of triple character whereby deactivation to the ground state, S0, Dewar minimum occurs, the second one, which is a ground state thermal reaction involves the use of a far-Infra-Red laser where planar pyridine is vibrationally excited to a very high vibrational level whose energy is comparable to that of the ground state transition structure, S0(TS), connecting the symmetrical S0 Dewar pyridine and the ground state of planar pyridine. The third process is also a biphotonic one involving excitation of planar pyridine with an energy which is in the limits of its ionisation potential. In this case there is a theoretically accessible S1/S0 Conical Intersection which leads directly to the ground state of the symmetrical Dewar pyridine.

A Review of Recent Decision-Analytic Models Used to Evaluate the Economic Value of Cancer Treatments.

Cost-effectiveness analysis provides information on the potential value of new cancer treatments, which is particularly pertinent for decision makers as demand for treatment grows while healthcare budgets remain fixed. A range of decision-analytic modelling approaches can be used to estimate cost effectiveness. This study summarises the key modelling approaches considered in oncology, alongside their advantages and limitations. A review was conducted to identify single technology appraisals (STAs) submitted to the National Institute for Health and Care Excellence (NICE) and published papers reporting full economic evaluations of cancer treatments published within the last 5 years. The review was supplemented with the existing methods literature discussing cancer modelling. In total, 100 NICE STAs and 124 published studies were included. Partitioned-survival analysis (n = 54) and discrete-time state transition structures (n = 41) were the main structures submitted to NICE. Conversely, the published studies reported greater use of discrete-time state transition models (n = 102). Limited justification of model structure was provided by authors, despite an awareness in the existing literature that the model structure should be considered thoroughly and can greatly influence cost-effectiveness results. Justification for the choice of model structure was limited and studies would be improved with a thorough rationale for this choice. The strengths and weaknesses of each approach should be considered by future researchers. Alternative methods (such as multi-state modelling) are likely to be utilised more frequently in the future, and so justification of these more advanced methods is paramount to their acceptability to inform healthcare decision making.Electronic supplementary materialThe online version of this article (10.1007/s40258-019-00513-3) contains supplementary material, which is available to authorized users.

On scalable supervisory control of multi-agent discrete-event systems

In this paper we study multi-agent discrete-event systems where the agents can be divided into several groups, and within each group the agents have similar or identical state transition structures. We employ a relabeling map to generate a “template structure” for each group, and synthesize a scalable supervisor whose state size and computational process are independent of the number of agents. This scalability allows the supervisor to remain invariant (no recomputation or reconfiguration needed) if and when there are agents removed due to failure or added for increasing productivity. The constant computational effort for synthesizing the scalable supervisor also makes our method promising for handling large-scale multi-agent systems. Moreover, based on the scalable supervisor we design scalable local controllers, one for each component agent, to establish a purely distributed control architecture.

PRM127 - ECONOMIC MODELLING CONSIDERATIONS IN RARE DISEASES: A TARGETED REVIEW OF HIGHLY SPECIALISED TECHNOLOGY APPRAISALS

Economic evaluation of rare diseases is associated with methodological challenges. This study will assess models submitted under the National Institute for Health and Care Excellence (NICE) highly specialised technologies (HST) programme to identify challenges associated with rare disease model development. A targeted review of the NICE website was conducted on 7th June 2018. All published HST appraisals were included. Data were extracted from identified studies regarding modelling approach, patient population, interventions, results, NICE recommendation, and modelling challenges cited by the evidence review group (ERG). A total of 7 published HST appraisals were identified. All 7 HST appraisals received a positive recommendation. A further 10 HST guidelines are in development. Of 7 published HST appraisals identified, 6 presented cost-consequence analyses while only 1 presented a fully incremental cost-utility analysis. All models employed a Markov state-transition structure. The primary challenge noted by the ERG was a lack of high-quality randomised clinical trial data, cited in 6 of 7 published HST appraisals. Further common challenges included use of surrogate outcomes in clinical trials, a lack of robust utility data, and uncertainty surrounding the natural history of the disease. Moreover, it is often unclear how best to reflect societal benefits associated with new treatments for rare diseases. The review identified barriers to achieving traditional cost-effectiveness thresholds, including high drug acquisition costs and the use of specialist administration centres. Non-randomised clinical trial data obtained from small samples will lead to substantial model input uncertainty. The use of surrogate outcomes in trials leads to the requirement for extrapolation to endpoints pertinent to the model time horizon. Such challenges should be explicitly recognised as it is often impossible to follow best practice when conducting economic evaluations in rare diseases. Patient and clinician involvement throughout model development is key to bridge such data gaps.

On Scalable Supervisory Control of Multi-Agent Discrete-Event Systems

In this paper we study multi-agent discrete-event systems where the agents can be divided into several groups, and within each group the agents have similar or identical state transition structures. We employ a relabeling map to generate a "template structure" for each group, and synthesize a scalable supervisor whose state size and computational process are independent of the number of agents. This scalability allows the supervisor to remain invariant (no recomputation or reconfiguration needed) if and when there are agents removed due to failure or added for increasing productivity. The constant computational effort for synthesizing the scalable supervisor also makes our method promising for handling large-scale multi-agent systems. Moreover, based on the scalable supervisor we design scalable local controllers, one for each component agent, to establish a purely distributed control architecture.

Widom Lines in Binary Mixtures of Supercritical Fluids

Recent experiments on pure fluids have identified distinct liquid-like and gas-like regimes even under supercritical conditions. The supercritical liquid-gas transition is marked by maxima in response functions that define a line emanating from the critical point, referred to as Widom line. However, the structure of analogous state transitions in mixtures of supercritical fluids has not been determined, and it is not clear whether a Widom line can be identified for binary mixtures. Here, we present first evidence for the existence of multiple Widom lines in binary mixtures from molecular dynamics simulations. By considering mixtures of noble gases, we show that, depending on the phase behavior, mixtures transition from a liquid-like to a gas-like regime via distinctly different pathways, leading to phase relationships of surprising complexity and variety. Specifically, we show that miscible binary mixtures have behavior analogous to a pure fluid and the supercritical state space is characterized by a single liquid-gas transition. In contrast, immiscible binary mixture undergo a phase separation in which the clusters transition separately at different temperatures, resulting in multiple distinct Widom lines. The presence of this unique transition behavior emphasizes the complexity of the supercritical state to be expected in high-order mixtures of practical relevance.

State-Dependent Resource Harvesting with Lagged Information about System States.

Markov decision processes (MDPs), which involve a temporal sequence of actions conditioned on the state of the managed system, are increasingly being applied in natural resource management. This study focuses on the modification of a traditional MDP to account for those cases in which an action must be chosen after a significant time lag in observing system state, but just prior to a new observation. In order to calculate an optimal decision policy under these conditions, possible actions must be conditioned on the previous observed system state and action taken. We show how to solve these problems when the state transition structure is known and when it is uncertain. Our focus is on the latter case, and we show how actions must be conditioned not only on the previous system state and action, but on the probabilities associated with alternative models of system dynamics. To demonstrate this framework, we calculated and simulated optimal, adaptive policies for MDPs with lagged states for the problem of deciding annual harvest regulations for mallards (Anas platyrhynchos) in the United States. In this particular example, changes in harvest policy induced by the use of lagged information about system state were sufficient to maintain expected management performance (e.g. population size, harvest) even in the face of an uncertain system state at the time of a decision.

Cost-Effectiveness of Ivermectin 1% Cream in Adults with Papulopustular Rosacea in the United States.

Papulopustular rosacea is a chronic skin disease involving central facial erythema in combination with papules and pustules. Papulopustular rosacea is treated with topical, systemic, or a combination of topical and systemic therapies. Currently approved topical therapies include azelaic acid gel/cream/foam twice daily (BID) and metronidazole cream/gel/lotion BID. Ivermectin 1% cream once daily (QD) is a new topical agent for the treatment of papulopustular rosacea that has been approved for the management of inflammatory lesions of rosacea and offers an alternative to current treatments. To evaluate the cost-effectiveness of ivermectin 1% cream QD compared with current topical treatments in order to understand the cost of adding ivermectin as a treatment option that would bring additional clinical benefit for adults with papulopustular rosacea in the United States. The cost-effectiveness of ivermectin 1% cream QD was compared with metronidazole 0.75% cream BID and azelaic acid 15% gel BID for adults in the United States with moderate-to-severe papulopustular rosacea using a Markov cohort state transition structure with 2 mutually exclusive health states (rosacea and no rosacea) and 5 phases. Patients could succeed or fail to respond to treatment and experience a relapse after treatment success. The model took a health care payer perspective (direct medical costs of topical and/or systemic therapy plus health care costs for physician and specialist visits) and used a 3-year time horizon. The model was run for a cohort of 1,000 patients. Costs (2014 U.S. dollars) and benefits (disease-free days and quality-adjusted life-years [QALYs]) were discounted at a rate of 3% per annum. Cost-effectiveness was determined by the incremental cost-effectiveness ratio (ICER) and measured in terms of incremental cost per QALY gained (estimated from health state utilities for patients with and without rosacea). Univariate and probabilistic sensitivity analyses (PSA) were conducted to assess the robustness of model outcomes. Compared with metronidazole 0.75% cream BID, ivermectin 1% cream QD was associated with higher costs but provided greater clinical benefit, with an ICER of $13,211 per QALY gained. For a cohort of 1,000 patients, ivermectin 1% cream QD provided an additional 72,922 disease-free days (200 years) over a 3-year period compared with metronidazole 0.75% cream BID, leading to a lower cost per disease-free day for ivermectin 1% cream QD ($4.54) compared with metronidazole 0.75% cream BID ($4.85). Ivermectin 1% cream QD was associated with lower total costs and greater clinical benefit compared with azelaic acid 15% gel BID at year 3 and dominated this treatment. After 3 years, ivermectin 1% cream QD was associated with the lowest health care costs ($62,767 compared with $73,284 for metronidazole 0.75% cream BID and $77,208 for azelaic acid 15% gel BID), reflecting a 15% reduction in physician visit costs, when compared with metronidazole 0.75% cream BID, and almost a 20% reduction, when compared with azelaic acid 15% gel BID. The univariate sensitivity analyses indicated that the results are sensitive to the time horizon selected: the longer the time horizon, the more beneficial the results for ivermectin 1% cream QD relative to the comparators, although even at 1 year, ivermectin 1% cream QD dominated azelaic acid 15% gel BID. The PSA suggested that ivermectin 1% cream QD was the most likely treatment to be cost-effective at a willingness-to-pay threshold of $15,000 and above. Ivermectin 1% cream QD had favorable incremental cost-effectiveness when compared with metronidazole 0.75% cream BID and dominated azelaic acid 15% gel BID in the treatment of papulopustular rosacea in the United States. Therefore, ivermectin 1% cream QD may be a good first-line treatment for papulopustular rosacea, providing additional clinical benefit at no or low additional cost. This study was sponsored by Galderma Laboratories. The sponsor was involved in the design of the model structure but not in the collection of the data used to populate the model. Manuscript preparation was also funded by Galderma. Taieb is an investigator and advisor for Galderma. Gold is an investigator for Galderma. Feldman is a consultant and speaker for Galderma and has received grants from Galderma. Dansk and Bertranou received a research grant from Galderma to conduct this study. Dansk and Bertranou contributed to the design of the model structure, the sourcing and inputting of the data, and the interpretation of the results. Taieb, Feldman, and Gold contributed to the interpretation of the results. All authors reviewed draft versions of the manuscript and gave permission for the submission of the final version.

Multistate Bayesian Control Chart Over a Finite Horizon

We study a multistate partially observable process control model with a general state transition structure. The process is initially in control and subject to Markovian deterioration that can bring it to out-of-control states. The process may continue making transitions among the out-of-control states, or even back to the in-control state until it reaches an absorbing state. We assume that at least one out-of-control state is absorbing. The objective is to minimize the expected total cost over a finite horizon. By transforming the standard Cartesian belief space into the spherical coordinate system, we show that the optimal policy has a simple control-limit structure. We also examine two specialized models. The first is the phase-type transition time model, in which we develop an algorithm whose complexity is not affected by the number of phases. The second is a model with multiple absorbing out-of-control states, by which we show that certain out-of-control states may incur less total cost than the in-control state, a phenomenon never occurs in the two-state models. We conclude that there are fundamental differences between multistate models and two-state models, and that the spherical coordinate transformation offers significant analytical and computational benefits.