scholarly journals PAA22 STATE TRANSITION MODELS FOR ESTIMATING TRANSITION PROBABILITIES IN MARKOV MODELS

2007 ◽  
Vol 10 (6) ◽  
pp. A404
Author(s):  
JD Campbell ◽  
DK Blough ◽  
SD Sullivan
2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ning Wang ◽  
Shu-dong Sun ◽  
Zhi-qiang Cai ◽  
Shuai Zhang ◽  
Can Saygin

Realistic prognostic tools are essential for effective condition-based maintenance systems. In this paper, a Duration-Dependent Hidden Semi-Markov Model (DD-HSMM) is proposed, which overcomes the shortcomings of traditional Hidden Markov Models (HMM), including the Hidden Semi-Markov Model (HSMM): (1) it allows explicit modeling of state transition probabilities between the states; (2) it relaxes observations’ independence assumption by accommodating a connection between consecutive observations; and (3) it does not follow the unrealistic Markov chain’s memoryless assumption and therefore it provides a more powerful modeling and analysis capability for real world problems. To facilitate the computation of the proposed DD-HSMM methodology, new forward-backward algorithm is developed. The demonstration and evaluation of the proposed methodology is carried out through a case study. The experimental results show that the DD-HSMM methodology is effective for equipment health monitoring and management.


2021 ◽  
Vol 41 (4) ◽  
pp. 453-464
Author(s):  
John Graves ◽  
Shawn Garbett ◽  
Zilu Zhou ◽  
Jonathan S. Schildcrout ◽  
Josh Peterson

We discuss tradeoffs and errors associated with approaches to modeling health economic decisions. Through an application in pharmacogenomic (PGx) testing to guide drug selection for individuals with a genetic variant, we assessed model accuracy, optimal decisions, and computation time for an identical decision scenario modeled 4 ways: using 1) coupled-time differential equations (DEQ), 2) a cohort-based discrete-time state transition model (MARKOV), 3) an individual discrete-time state transition microsimulation model (MICROSIM), and 4) discrete event simulation (DES). Relative to DEQ, the net monetary benefit for PGx testing (v. a reference strategy of no testing) based on MARKOV with rate-to-probability conversions using commonly used formulas resulted in different optimal decisions. MARKOV was nearly identical to DEQ when transition probabilities were embedded using a transition intensity matrix. Among stochastic models, DES model outputs converged to DEQ with substantially fewer simulated patients (1 million) v. MICROSIM (1 billion). Overall, properly embedded Markov models provided the most favorable mix of accuracy and runtime but introduced additional complexity for calculating cost and quality-adjusted life year outcomes due to the inclusion of “jumpover” states after proper embedding of transition probabilities. Among stochastic models, DES offered the most favorable mix of accuracy, reliability, and speed.


2020 ◽  
Author(s):  
Brett T. McClintock

AbstractHidden Markov models (HMMs) that include individual-level random effects have recently been promoted for inferring animal movement behaviour from biotelemetry data. These “mixed HMMs” come at significant cost in terms of implementation and computation, and discrete random effects have been advocated as a practical alternative to more computationally-intensive continuous random effects. However, the performance of mixed HMMs has not yet been sufficiently explored to justify their widespread adoption, and there is currently little guidance for practitioners weighing the costs and benefits of mixed HMMs for a particular research objective.I performed an extensive simulation study comparing the performance of a suite of fixed and random effect models for individual heterogeneity in the hidden state process of a 2-state HMM. I focused on sampling scenarios more typical of telemetry studies, which often consist of relatively long time series (30 – 250 observations per animal) for relatively few individuals (5 – 100 animals).I generally found mixed HMMs did not improve state assignment relative to standard HMMs. Reliable estimation of random effects required larger sample sizes than are often feasible in telemetry studies. Continuous random effect models performed reasonably well with data generated under discrete random effects, but not vice versa. Random effects accounting for unexplained individual variation can improve estimation of state transition probabilities and measurable covariate effects, but discrete random effects can be a relatively poor (and potentially misleading) approximation for continuous variation.When weighing the costs and benefits of mixed HMMs, three important considerations are study objectives, sample size, and model complexity. HMM applications often focus on state assignment with little emphasis on heterogeneity in state transition probabilities, in which case random effects in the hidden state process simply may not be worth the additional effort. However, if explaining variation in state transition probabilities is a primary objective and sufficient explanatory covariates are not available, then random effects are worth pursuing as a more parsimonious alternative to individual fixed effects.To help put my findings in context and illustrate some potential challenges that practitioners may encounter when applying mixed HMMs, I revisit a previous analysis of long-finned pilot whale biotelemetry data.


2020 ◽  
Author(s):  
John Graves ◽  
Shawn Garbett ◽  
Zilu Zhou ◽  
Jonathan S. Schildcrout ◽  
Josh Peterson

ABSTRACTWe discuss tradeoffs and errors associated with approaches to modeling health economic decisions. Through an application in pharmacogenomic (PGx) testing to guide drug selection for individuals with a genetic variant, we assessed model accuracy, optimal decisions and computation time for an identical decision scenario modeled four ways: using (1) coupled-time differential equations [DEQ]; (2) a cohort-based discrete-time state transition model [MARKOV]; (3) an individual discrete-time state transition microsimulation model [MICROSIM]; and (4) discrete event simulation [DES]. Relative to DEQ, the Net Monetary Benefit for PGx testing (vs. a reference strategy of no testing) based on MARKOV with rate-to-probability conversions using commonly used formulas resulted in different optimal decisions. MARKOV was nearly identical to DEQ when transition probabilities were embedded using a transition intensity matrix. Among stochastic models, DES model outputs converged to DEQ with substantially fewer simulated patients (1 million) vs. MICROSIM (1 billion). Overall, properly embedded Markov models provided the most favorable mix of accuracy and run-time, but introduced additional complexity for calculating cost and quality-adjusted life year outcomes due to the inclusion of “jumpover” states after proper embedding of transition probabilities. Among stochastic models, DES offered the most favorable mix of accuracy, reliability, and speed.


2019 ◽  
Vol 39 (5) ◽  
pp. 509-522 ◽  
Author(s):  
Beate Jahn ◽  
Christina Kurzthaler ◽  
Jagpreet Chhatwal ◽  
Elamin H. Elbasha ◽  
Annette Conrads-Frank ◽  
...  

Background. In state-transition models (STMs), decision problems are conceptualized using health states and transitions among those health states after predefined time cycles. The naive, commonly applied method (C) for cycle length conversion transforms all transition probabilities separately. In STMs with more than 2 health states, this method is not accurate. Therefore, we aim to describe and compare the performance of method C with that of alternative matrix transformation methods. Design. We compare 2 alternative matrix transformation methods (Eigenvalue method [E], Schure-Padé method [SP]) to method C applied in an STM of 3 different treatment strategies for women with breast cancer. We convert the given annual transition matrix into a monthly-cycle matrix and evaluate induced transformation errors for the transition matrices and the long-term outcomes: life years, quality-adjusted life-years, costs and incremental cost-effectiveness ratios, and the performance related to the decisions. In addition, we applied these transformation methods to randomly generated annual transition matrices with 4, 7, 10, and 20 health states. Results. In theory, there is no generally applicable correct transformation method. Based on our simulations, SP resulted in the smallest transformation-induced discrepancies for generated annual transition matrices for 2 treatment strategies. E showed slightly smaller discrepancies than SP in the strategy, where one of the direct transitions between health states was excluded. For long-term outcomes, the largest discrepancy occurred for estimated costs applying method C. For higher dimensional models, E performs best. Conclusions. In our modeling examples, matrix transformations (E, SP) perform better than transforming all transition probabilities separately (C). Transition probabilities based on alternative conversion methods should therefore be applied in sensitivity analyses.


Author(s):  
Daniel Figueiredo ◽  
Eugénio Rocha ◽  
Manuel António Martins ◽  
Madalena Chaves

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