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Markov Models (markov + models)

Distribution by Scientific Domains

Mathematics and Statistics	40%
Information Science and Computing	18%
Medical Sciences	14%
Life Sciences	11%
Engineering	7%
Chemistry	7%

Selected Abstracts

REVERSIBLE JUMP MARKOV CHAIN MONTE CARLO METHODS AND SEGMENTATION ALGORITHMS IN HIDDEN MARKOV MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2010
R. Paroli
Summary We consider hidden Markov models with an unknown number of regimes for the segmentation of the pixel intensities of digital images that consist of a small set of colours. New reversible jump Markov chain Monte Carlo algorithms to estimate both the dimension and the unknown parameters of the model are introduced. Parameters are updated by random walk Metropolis,Hastings moves, without updating the sequence of the hidden Markov chain. The segmentation (i.e. the estimation of the hidden regimes) is a further aim and is performed by means of a number of competing algorithms. We apply our Bayesian inference and segmentation tools to digital images, which are linearized through the Peano,Hilbert scan, and perform experiments and comparisons on both synthetic images and a real brain magnetic resonance image. [source]

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2009
C. A. McGrory
Summary The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach. [source]

ESTIMATING COMPONENTS IN FINITE MIXTURES AND HIDDEN MARKOV MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2005
D.S. Poskitt
Summary When the unobservable Markov chain in a hidden Markov model is stationary the marginal distribution of the observations is a finite mixture with the number of terms equal to the number of the states of the Markov chain. This suggests the number of states of the unobservable Markov chain can be estimated by determining the number of mixture components in the marginal distribution. This paper presents new methods for estimating the number of states in a hidden Markov model, and coincidentally the unknown number of components in a finite mixture, based on penalized quasi-likelihood and generalized quasi-likelihood ratio methods constructed from the marginal distribution. The procedures advocated are simple to calculate, and results obtained in empirical applications indicate that they are as effective as current available methods based on the full likelihood. Under fairly general regularity conditions, the methods proposed generate strongly consistent estimates of the unknown number of states or components. [source]

Natural head motion synthesis driven by acoustic prosodic features

COMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3-4 2005
Carlos Busso
Abstract Natural head motion is important to realistic facial animation and engaging human,computer interactions. In this paper, we present a novel data-driven approach to synthesize appropriate head motion by sampling from trained hidden markov models (HMMs). First, while an actress recited a corpus specifically designed to elicit various emotions, her 3D head motion was captured and further processed to construct a head motion database that included synchronized speech information. Then, an HMM for each discrete head motion representation (derived directly from data using vector quantization) was created by using acoustic prosodic features derived from speech. Finally, first-order Markov models and interpolation techniques were used to smooth the synthesized sequence. Our comparison experiments and novel synthesis results show that synthesized head motions follow the temporal dynamic behavior of real human subjects. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Context-aware environments: from specification to implementation

EXPERT SYSTEMS, Issue 5 2007
Patrick Reignier
Abstract: This paper deals with the problem of implementing a context model for a smart environment. The problem has already been addressed several times using many different data- or problem-driven methods. In order to separate the modelling phase from implementation, we first represent the context model by a network of situations. Then, different implementations can be automatically generated from this context model depending on user needs and underlying perceptual components. Two different implementations are proposed in this paper: a deterministic one based on Petri nets and a probabilistic one based on hidden Markov models. Both implementations are illustrated and applied to real-world problems. [source]

Prediction of coenzyme specificity in dehydrogenases/ reductases

FEBS JOURNAL, Issue 6 2006
A hidden Markov model-based method, its application on complete genomes
Dehydrogenases and reductases are enzymes of fundamental metabolic importance that often adopt a specific structure known as the Rossmann fold. This fold, consisting of a six-stranded ,-sheet surrounded by ,-helices, is responsible for coenzyme binding. We have developed a method to identify Rossmann folds and predict their coenzyme specificity (NAD, NADP or FAD) using only the amino acid sequence as input. The method is based upon hidden Markov models and sequence pattern analysis. The prediction sensitivity is 79% and the selectivity close to 100%. The method was applied on a set of 68 genomes, representing the three kingdoms archaea, bacteria and eukaryota. In prokaryotes, 3% of the genes were found to code for Rossmann-fold proteins, while the corresponding ratio in eukaryotes is only around 1%. In all genomes, NAD is the most preferred cofactor (41,49%), followed by NADP with 30,38%, while FAD is the least preferred cofactor (21%). However, the NAD preponderance over NADP is most pronounced in archaea, and least in eukaryotes. In all three kingdoms, only 3,8% of the Rossmann proteins are predicted to have more than one membrane-spanning segment, which is much lower than the frequency of membrane proteins in general. Analysis of the major protein types in eukaryotes reveals that the most common type (26%) of the Rossmann proteins are short-chain dehydrogenases/reductases. In addition, the identified Rossmann proteins were analyzed with respect to further protein types, enzyme classes and redundancy. The described method is available at http://www.ifm.liu.se/bioinfo, where the preferred coenzyme and its binding region are predicted given an amino acid sequence as input. [source]

Optimal drug pricing, limited use conditions and stratified net benefits for Markov models of disease progression

HEALTH ECONOMICS, Issue 11 2008
Gregory S. Zaric
Abstract Limited use conditions (LUCs) are a method of directing treatment with new drugs to those populations where they will be most cost effective. In this paper we investigate how a drug manufacturer could determine pricing and LUCs to maximize profits. We assume that the payer makes formulary decisions on the basis of net monetary benefits, that the disease can be modeled using a Markov model of disease progression, and that the drug reduces the probability of progression between states of the Markov model. LUCs are expressed as a range of probabilities of disease progression over which patients would have access to the new drug. We assume that the manufacturer determines the price and LUCs in order to maximize profits. We show that an explicit trade-off exists between the drug's price and the use conditions, that there is an upper bound on the drug price, that the proportion of the population targeted by the LUC does not depend on quality of life or costs in each health state or the payer's willingness to pay, and that high drug prices do not always correspond with high profits. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Performance of Markov models for frame-level errors in IEEE 802.11 wireless LANs

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 6 2009
Gennaro Boggia
Abstract Interference among different wireless hosts is becoming a serious issue due to the growing number of wireless LANs based on the popular IEEE 802.11 standard. Thus, an accurate modeling of error paths at the data link layer is indispensable for evaluating system performance and for tuning and optimizing protocols at higher layers. Error paths are usually described looking at sequences of consecutive correct or erroneous frames and at the distributions of their sizes. In recent years, a number of Markov-based stochastic models have been proposed in order to statistically characterize these distributions. Nevertheless, when applied to analyze the data traces we collected, they exhibit several flaws. In this paper, to overcome these model limitations, we propose a new algorithm based on a semi-Markov process, where each state characterizes a different error pattern. The model has been validated by using measures from a real environment. Moreover, we have compared our method with other promising models already available in the literature. Numerical results show that our proposal performs better than the other models in capturing the long-term temporal correlation of real measured traces. At the same time, it is able to estimate first-order statistics with the same accuracy of the other models, but with a minor computational complexity. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Dimensioning and optimization of push-to-talk over cellular server

INTERNATIONAL JOURNAL OF NETWORK MANAGEMENT, Issue 1 2008
M. T. Alam
The PoC (push-to-talk over cellular) application allows point-to-point or point-to-multipoint voice communication between mobile network users. The related work over PoC focuses on the performance analysis only and is ignorant about dimensioning a PoC controller to optimize revenue for service providers. In this paper, we dimension a PoC service with the assumption that the network grade of service is provided. The on-demand sessions should have access priority over pre-established sessions. A PoC controller should be able to terminate a PoC session based on an optimal timer. Moreover, the number of simultaneous session initiations by a PoC client is also a configurable parameter. We derived relations to provide access priority to special PoC sessions based on available transmit/receive units (TRU) and threshold level. Load sharing expressions are reported for a PoC controller using the Lagrange multiplier technique. A simple relation to control the PoC session timer is proposed. Finally, the derivation of maximum number of allowable simultaneous sessions is depicted using two-state Markov models. Numerical results have been computed with the corresponding derivation to provide a useful insight into the system behaviour. A PoC service can benefit from these optimal values of our work during the busy hour. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Not All hERG Pore Domain Mutations Have a Severe Phenotype: G584S Has an Inactivation Gating Defect with Mild Phenotype Compared to G572S, Which Has a Dominant Negative Trafficking Defect and a Severe Phenotype

JOURNAL OF CARDIOVASCULAR ELECTROPHYSIOLOGY, Issue 8 2009
JING TING ZHAO Ph.D.
Introduction: Mutations in the pore domain of the human ether-a-go-go- related gene (hERG) potassium channel are associated with higher risk of sudden death. However, in many kindreds clinical presentation is variable, making it hard to predict risk. We hypothesized that in vitro phenotyping of the intrinsic severity of individual mutations can assist with risk stratification. Methods and Results: We analyzed 2 hERG pore domain mutations, G572S and G584S. Similar to 90% of hERG missense mutations, G572S-hERG subunits did not traffic to the plasma membrane but could coassemble with WT subunits and resulted in a dominant negative suppression of hERG current density. The G584S-hERG subunits traffic normally but have abnormal inactivation gating. Computer models of human ventricular myocyte action potentials (AP), incorporating Markov models of the hERG mutants, indicate that G572S-hERG channels would cause more severe AP prolongation than that seen with G584S-hERG channels. Conclusions: hERG-G572S and -G584S are 2 pore domain mutations that involve the same change in sidechain but have very different in vitro phenotypes; G572S causes a dominant negative trafficking defect, whereas G584S is the first hERG missense mutation where the cause of disease can be exclusively attributed to enhanced inactivation. The G572S mutation is intrinsically more severe than the G584S mutation, consistent with the overall clinical presentation in the 2 small kindreds studied here. Further investigation, involving a larger number of cohorts, to test the hypothesis that in vitro phenotyping of the intrinsic severity of a given mutation will assist with risk stratification is therefore warranted. [source]

Personalized recommendation with adaptive mixture of markov models

JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, Issue 12 2007
Yang Liu
With more and more information available on the Internet, the task of making personalized recommendations to assist the user's navigation has become increasingly important. Considering there might be millions of users with different backgrounds accessing a Web site everyday, it is infeasible to build a separate recommendation system for each user. To address this problem, clustering techniques can first be employed to discover user groups. Then, user navigation patterns for each group can be discovered, to allow the adaptation of a Web site to the interest of each individual group. In this paper, we propose to model user access sequences as stochastic processes, and a mixture of Markov models based approach is taken to cluster users and to capture the sequential relationships inherent in user access histories. Several important issues that arise in constructing the Markov models are also addressed. The first issue lies in the complexity of the mixture of Markov models. To improve the efficiency of building/maintaining the mixture of Markov models, we develop a lightweight adapt-ive algorithm to update the model parameters without recomputing model parameters from scratch. The second issue concerns the proper selection of training data for building the mixture of Markov models. We investigate two different training data selection strategies and perform extensive experiments to compare their effectiveness on a real dataset that is generated by a Web-based knowledge management system, Livelink. [source]

Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2006
Francesco Bartolucci
Summary., For a class of latent Markov models for discrete variables having a longitudinal structure, we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process. For the maximum likelihood estimation of a latent Markov model under hypotheses of this type, we outline an EM algorithm that is based on well-known recursions in the hidden Markov literature. We also show that, under certain assumptions, the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent Markov model, against a less stringent linear hypothesis on the transition probabilities of the same model, is of type. As a particular case, we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent Markov version, which may be used to test the hypothesis of absence of transition between latent states. The approach is illustrated through a series of simulations and two applications, the first of which is based on educational testing data that have been collected within the National Assessment of Educational Progress 1996, and the second on data, concerning the use of marijuana, which have been collected within the National Youth Survey 1976,1980. [source]

Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 1 2000
C. P. Robert
Hidden Markov models form an extension of mixture models which provides a flexible class of models exhibiting dependence and a possibly large degree of variability. We show how reversible jump Markov chain Monte Carlo techniques can be used to estimate the parameters as well as the number of components of a hidden Markov model in a Bayesian framework. We employ a mixture of zero-mean normal distributions as our main example and apply this model to three sets of data from finance, meteorology and geomagnetism. [source]

Health-economic analysis: cost-effectiveness of scheduled maintenance treatment with infliximab for Crohn's disease , modelling outcomes in active luminal and fistulizing disease in adults

ALIMENTARY PHARMACOLOGY & THERAPEUTICS, Issue 1 2008
J. LINDSAY
Summary Background, Infliximab has been shown to be efficacious in moderate-to-severe Crohn's disease (CD). Aim, To evaluate the cost-effectiveness of scheduled maintenance treatment with infliximab in luminal and fistulizing CD patients. Methods, Markov models were constructed to simulate the progression of adult CD patients with and without fistulae during treatment with infliximab (5 mg/kg). Transitions were estimated from published clinical trials of infliximab. Standard care, comprising immunomodulators and/or corticosteroids was used as a comparator. An average weight of 60 kg was used to estimate the dose of infliximab. The costs and outcomes were discounted at 3.5% over 5 years. The primary effectiveness measurement was quality-adjusted life years (QALYs) estimated using EQ-5D. One-way and probabilistic sensitivity analyses were performed by varying the infliximab efficacy estimates, costs and utilities. Results, The incremental cost per QALY gained was £26 128 in luminal CD and £29 752 in fistulizing CD at 5 years. Results were robust and remained in the range of £23 752,£38 848 for luminal CD and £27 047,£44 206 for fistulizing CD. Patient body weight was the most important factor affecting cost-effectiveness. Conclusion, Eight-week scheduled maintenance treatment with infliximab is a cost-effective treatment for adult patients suffering from active luminal or fistulizing CD. [source]

Evaluation of the cost-effectiveness of Helicobacter pylori eradication triple therapy vs. conventional therapy for ulcers in Japan

ALIMENTARY PHARMACOLOGY & THERAPEUTICS, Issue 11 2001
S. Ikeda
Background: Helicobacter pylori eradication triple therapy with a combination of lansoprazole, amoxicillin and clarithromycin was approved in Japan in September 2000. Aim: To compare the cost-effectiveness of this eradication therapy with conventional histamine-2 receptor antagonist therapy in Japan. Methods: We established two Markov models for gastric and duodenal ulcers. The model design was based on the Japanese H. pylori eradication guideline and a specialist's opinions, and the model inputs were obtained from a literature review. The models predict the direct medical costs, number of disease-free days and cost per disease-free day for 5 years. Results: In the gastric ulcer model, the expected total costs of eradication and conventional therapies per patient were ¥169 719 and ¥390 921, respectively; the expected numbers of disease-free days were 1454 days and 1313 days, respectively. In the duodenal ulcer model, the expected total costs were ¥134 786 and ¥324 689, respectively; the expected numbers of disease-free days were 1503 days and 1387 days, respectively. The sensitivity analyses showed that the results of the base case analysis were robust. Conclusions: This eradication therapy is less costly and more effective than conventional therapy for the treatment of gastric and duodenal ulcers in a Japanese medical setting. [source]

Genome-wide analysis of the general stress response in Bacillus subtilis

MOLECULAR MICROBIOLOGY, Issue 4 2001
Chester W. Price
Bacteria respond to diverse growth-limiting stresses by producing a large set of general stress proteins. In Bacillus subtilis and related Gram-positive pathogens, this response is governed by the ,B transcription factor. To establish the range of cellular functions associated with the general stress response, we compared the transcriptional profiles of wild and mutant strains under conditions that induce ,B activity. Macroarrays representing more than 3900 annotated reading frames of the B. subtilis genome were hybridized to 33P-labelled cDNA populations derived from (i) wild-type and sigB mutant strains that had been subjected to ethanol stress; and (ii) a strain in which ,B expression was controlled by an inducible promoter. On the basis of their significant ,B -dependent expression in three independent experiments, we identified 127 genes as prime candidates for members of the ,B regulon. Of these genes, 30 were known previously or inferred to be ,B dependent by other means. To assist in the analysis of the 97 new genes, we constructed hidden Markov models (HMM) that identified possible ,B recognition sequences preceding 21 of them. To test the HMM and to provide an independent validation of the hybridization experiments, we mapped the ,B -dependent messages for seven representative genes. For all seven, the 5, end of the message lay near typical ,B recognition sequences, and these had been predicted correctly by the HMM for five of the seven examples. Lastly, all 127 gene products were assigned to functional groups by considering their similarity to known proteins. Notably, products with a direct protective function were in the minority. Instead, the general stress response increased relative message levels for known or predicted regulatory proteins, for transporters controlling solute influx and efflux, including potential drug efflux pumps, and for products implicated in carbon metabolism, envelope function and macromolecular turnover. [source]

A re-examination of the expected effects of disturbance on diversity

OIKOS, Issue 3 2000
Robin L. Mackey
Disturbance is often cited as one of the main factors determining patterns of species diversity. Several models have predicted qualitatively that species richness should be highest at intermediate intensities and/or frequencies of disturbances, but none indicate whether this effect should be strong (statistically accounting for much variability in diversity) or only subtle. Empirical evidence on the point is very mixed. This study examines Markov models of the dynamics of six real communities. We derive the predicted changes in species richness and evenness when these communities are subjected to quantified disturbance frequency and intensity gradients. We also use several different sampling intensities (i.e. numbers of individuals counted) to determine how this affects richness-disturbance relationships. Our models predict that peaked responses of diversity to disturbance should be less common than monotonic ones. Species richness should vary, on average, by only 3% over gradients of no disturbance to complete disturbance. In the most extreme case, richness varied two-fold over this gradient. Moreover, richness may increase monotonically, decrease monotonically, or be a peaked function of disturbance, interacting in a non-intuitive fashion with both the sampling intensity and the community in question. These results are broadly consistent with a review of published richness-disturbance relationships. Evenness varies somewhat more strongly along disturbance gradients, but the effect is still small. We conclude that extant models provide little reason to believe that disturbance should play more than a subtle role in determining patterns of diversity in nature, contrary to most contemporary literature. [source]

Reliable prediction of T-cell epitopes using neural networks with novel sequence representations

PROTEIN SCIENCE, Issue 5 2003
Morten Nielsen
Abstract In this paper we describe an improved neural network method to predict T-cell class I epitopes. A novel input representation has been developed consisting of a combination of sparse encoding, Blosum encoding, and input derived from hidden Markov models. We demonstrate that the combination of several neural networks derived using different sequence-encoding schemes has a performance superior to neural networks derived using a single sequence-encoding scheme. The new method is shown to have a performance that is substantially higher than that of other methods. By use of mutual information calculations we show that peptides that bind to the HLA A*0204 complex display signal of higher order sequence correlations. Neural networks are ideally suited to integrate such higher order correlations when predicting the binding affinity. It is this feature combined with the use of several neural networks derived from different and novel sequence-encoding schemes and the ability of the neural network to be trained on data consisting of continuous binding affinities that gives the new method an improved performance. The difference in predictive performance between the neural network methods and that of the matrix-driven methods is found to be most significant for peptides that bind strongly to the HLA molecule, confirming that the signal of higher order sequence correlation is most strongly present in high-binding peptides. Finally, we use the method to predict T-cell epitopes for the genome of hepatitis C virus and discuss possible applications of the prediction method to guide the process of rational vaccine design. [source]

Subunit-specific desensitization of heteromeric kainate receptors

THE JOURNAL OF PHYSIOLOGY, Issue 4 2010
David D. Mott
Kainate receptor subunits can form functional channels as homomers of GluK1, GluK2 or GluK3, or as heteromeric combinations with each other or incorporating GluK4 or GluK5 subunits. However, GluK4 and GluK5 cannot form functional channels by themselves. Incorporation of GluK4 or GluK5 into a heteromeric complex increases glutamate apparent affinity and also enables receptor activation by the agonist AMPA. Utilizing two-electrode voltage clamp of Xenopus oocytes injected with cRNA encoding kainate receptor subunits, we have observed that heteromeric channels composed of GluK2/GluK4 and GluK2/GluK5 have steady state concentration,response curves that were bell-shaped in response to either glutamate or AMPA. By contrast, homomeric GluK2 channels exhibited a monophasic steady state concentration,response curve that simply plateaued at high glutamate concentrations. By fitting several specific Markov models to GluK2/GluK4 heteromeric and GluK2 homomeric concentration,response data, we have determined that: (a) two strikingly different agonist binding affinities exist; (b) the high-affinity binding site leads to channel opening; and (c) the low-affinity agonist binding site leads to strong desensitization after agonist binding. Model parameters also approximate the onset and recovery kinetics of desensitization observed for macroscopic currents measured from HEK-293 cells expressing GluK2 and GluK4 subunits. The GluK2(E738D) mutation lowers the steady state apparent affinity for glutamate by 9000-fold in comparison to GluK2 homomeric wildtype receptors. When this mutant subunit was expressed with GluK4, the rising phase of the glutamate steady state concentration,response curve overlapped with the wildtype curve, whereas the declining phase was right-shifted toward lower affinity. Taken together, these data are consistent with a scheme whereby high-affinity agonist binding to a non-desensitizing GluK4 subunit opens the heteromeric channel, whereas low-affinity agonist binding to GluK2 desensitizes the whole channel complex. [source]

Optimal corrective maintenance contract planning for aging multi-state system

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2009
Yi Ding
Abstract This paper considers an aging multi-state system, where the system failure rate varies with time. After any failure, maintenance is performed by an external repair team. Repair rate and cost of each repair are determined by a corresponding corrective maintenance contract with a repair team. The service market can provide different kinds of maintenance contracts to the system owner, which also can be changed after each specified time period. The owner of the system would like to determine a series of repair contracts during the system life cycle in order to minimize the total expected cost while satisfying the system availability. Operating cost, repair cost and penalty cost for system failures should be taken into account. The paper proposes a method for determining such optimal series of maintenance contracts. The method is based on the piecewise constant approximation for an increasing failure rate function in order to assess lower and upper bounds of the total expected cost and system availability by using Markov models. The genetic algorithm is used as the optimization technique. Numerical example is presented to illustrate the approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

REVERSIBLE JUMP MARKOV CHAIN MONTE CARLO METHODS AND SEGMENTATION ALGORITHMS IN HIDDEN MARKOV MODELS

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

Nested Markov Compliance Class Model in the Presence of Time-Varying Noncompliance

BIOMETRICS, Issue 2 2009
Julia Y. Lin
Summary We consider a Markov structure for partially unobserved time-varying compliance classes in the Imbens,Rubin (1997, The Annals of Statistics25, 305,327) compliance model framework. The context is a longitudinal randomized intervention study where subjects are randomized once at baseline, outcomes and patient adherence are measured at multiple follow-ups, and patient adherence to their randomized treatment could vary over time. We propose a nested latent compliance class model where we use time-invariant subject-specific compliance principal strata to summarize longitudinal trends of subject-specific time-varying compliance patterns. The principal strata are formed using Markov models that relate current compliance behavior to compliance history. Treatment effects are estimated as intent-to-treat effects within the compliance principal strata. [source]