Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Markov Chain”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9Linked to original sources
PubMed2003

Economic impact of extended time on peritoneal dialysis as a result of using polyglucose: the application of a Markov chain model to forecast changes in the development of the ESRD programme over time.

BACKGROUND: The use of polyglucose as a peritoneal dialysis (PD) fluid extends time on PD treatment. It is anticipated, therefore, that the share of patients treated with PD will be positively influenced. The relationship between extension of PD treatment time and an increase of the PD treatment share, however, is complex and needs further investigation. In this paper, a Markov chain model was applied to investigate the impact of extended time on PD treatment for the PD share in all dialysis patients in The Netherlands. Furthermore, the economic impact of the extended time on treatment (ETOT) was explored. METHODS: Scenarios were forecast over a 10 year period using aggregate data from the End-Stage Renal Registry in The Netherlands (Renine). Three scenarios were simulated in which the median PD technique survival was extended by 8, 10 and 12 months. Two other scenarios explored the impact of the combined effect of ETOT of 10 months together with a 10% and 20% increase of PD inflow shares. Reductions of costs to society due to ETOT were estimated using Dutch cost data on renal replacement therapies. RESULTS: PD share increases from 30.0% in the null scenario to 34.5% in the scenario with an ETOT of 10 months and an increased PD inflow share of 20%. The reduction in total costs to society of the renal replacement therapies is 0.96%. The average societal costs per discounted patient year for haemodialysis (HD) are 84 100 euros. For PD, these costs are 60 300 euros. A shift from HD to PD results in average cost savings of 28% per patient year. CONCLUSIONS: In view of high dialysis costs to society, a reduction of 0.96% can be considered to be relevant for healthcare policy makers.

Adolescent↗
PubMed2002

Multivariate Markov chain analysis of the probability of pregnancy in infertile couples undergoing assisted reproduction.

BACKGROUND: Estimating the probability of pregnancy leading to delivery and the influence of clinical factors on that probability is of fundamental importance in the treatment counselling of infertile couples. A variety of statistical techniques have been used to analyse fertility data, many borrowed from survival analysis. METHODS AND RESULTS: We propose an alternative method of analysis which is based on a discrete time Markov chain approach, with states 'pregnancy (leading to a delivery)', 'not pregnant', and 'censored' and in which the transition probabilities are dependent both on the clinical characteristics of the patient and the treatment given. CONCLUSIONS: We believe that the method of analysis presented here may be preferable to standard analyses in that it better reflects the clinical situation, it is a truly discrete time analysis applied to a discrete time situation, it explicitly models the censoring process (a process which in itself provides information of interest to the physician) and can be readily extended to a variety of clinical situations.

Age Factors↗
PubMed2003

Symbolic stochastic dynamical systems viewed as binary N-step Markov chains.

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the ith symbol in the chain equals zero (or unity) is a linear function of the number of unities among the preceding N symbols. The correlation and distribution functions as well as the variance of the number of symbols in the words of arbitrary length L are obtained analytically and numerically. A self-similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented. The diffusion Fokker-Planck equation governing the distribution function of the L words is explored. If the persistent correlations are not extremely strong, the distribution function is shown to be the Gaussian with the variance being nonlinearly dependent on L. The applicability of the developed theory to the coarse-grained written and DNA texts is discussed.

Journal Article↗
PubMed1993

Assessing the cost-effectiveness of medical treatments in acid-related diseases. The Markov chain approach applied to a comparison between intermittent and maintenance treatment of reflux esophagitis.

Escalating medical costs have made it increasingly important to carry out economic evaluations of drug therapy. In the area of acid-related diseases, much of the current interest is focused on comparisons between omeprazole and H2 receptor antagonists. After having discussed the basic methodology used in these analyses, viz. the decision-tree analysis, this paper presents an extension of this methodology, the Markov chain approach, which is more appropriate for analyses of longer time periods. Thereafter, this methodology is used to analyze the cost-effectiveness of omeprazole in intermittent versus maintenance treatment of reflux esophagitis. The cost data are from Sweden and the time period studied is one year. It is found that maintenance treatment provides 63 more healthy days per year at an extra direct cost of SEK 40 per day. From a sensitivity analysis it is concluded that the cost-effectiveness of intermittent versus maintenance treatment is mainly determined by the probability of relapse when off treatment, the severity of the symptoms in the case of a relapse and the value to the patient of a healthy day, i.e. a day free from reflux esophagitis.

Cost of Illness↗
PubMed2005

Determining joint carrier probabilities of cancer-causing genes using Markov chain Monte Carlo methods.

In genetic counseling for cancer risk, the probability of carrying a mutation of a cancer-causing gene plays an important role. Family history of various cancers is important in calculating this probability. BRCAPRO is a widely used software for calculating the probability of carrying mutations in BRCA1 and BRCA2 genes given the family history of breast and ovarian cancer in first- and second-degree relatives. BRCAPRO uses an analytical (exact) calculational procedure. Using Markov chain Monte Carlo (MCMC) methods, we extend BRCAPRO to handle, in principle, any type of cancer, family history, any number of genes and alleles that each gene may have. When the information used in this MCMC approach is the same as for BRCAPRO (two genes: BRCA1 and BRCA2; two cancers: breast and ovarian; first- and second-degree relatives only), the two approaches give essentially the same answer. Extending the model to include (1) prostate cancer, (2) two mutated alleles of BRCA2, namely, mutations in Ovarian Cancer Cluster Region (OCCR) and non-OCCR region, and (3) relatives of degree greater than second-degree, leads to different carrier probabilities. The MCMC approach is a useful tool in building a comprehensive model to give accurate estimates of carrier probabilities. Such an approach will be even more important as additional information about the genetics of various cancers becomes available.

Alleles↗
PubMed2005

A Markov chain model for animal estrous cycling data.

Estrous cycling data contain sequences of characters (e.g., DPEMD). Each sequence represents an animal's estrous cycle, with each character indicating the daily estrous cycle stage. Changes in the estrous cycle pattern, which is determined by estrous stage lengths, can provide information on adverse events. Stage lengths are not directly observable. However interval censored lengths for all but the first and the last stages in a sequence can be extracted from the data. We propose a Markov chain model to approximate the estrous cycling process. The transition probabilities from one stage to another can be derived by conditioning on stage lengths. Assuming Weibull distribution for stage lengths, with the second Weibull parameter depending upon treatment effects and animal-specific random effects, regression models on censored stage lengths are fitted. A Bayesian approach is used for inference on dose effects. The analysis is implemented with MCMC method in WinBUGS. An estrous cycling data set from a National Toxicology Program study is analyzed as an example.

Animals↗
PubMedDate not supplied

Bayesian analysis of ROC curves using Markov-chain Monte Carlo methods.

The authors introduce a Bayesian approach to generalized linear regression models for rating data observed in the evaluation of a diagnostic technology. Such models were previously studied using a non-Bayesian approach. In a Bayesian analysis, the difficulties inherent in an ordinal rating scale are circumvented by using data-augmentation techniques. Posterior distributions for the regression parameters- and thereby for receiver operating characteristic (ROC) curve parameters and values, for the area under a ROC curve, differences between areas, etc.-may then be computed by Markov-chain Monte Carlo methods. Inferences are made in standard Bayesian ways. The methods are exemplified by a study of ultrasonography rating data for the detection of hepatic metastases in patients with colon or breast cancer (previously analyzed) and the results compared.

Bayes Theorem↗
PubMed2004

Fed-batch optimization of alpha-amylase and protease-producing Bacillus subtilis using Markov chain methods.

A stoichiometry-based model for the fed-batch culture of the recombinant bacterium Bacillus subtilis ATCC 6051a, producing extracellular alpha-amylase as a desirable product and proteases as undesirable products, was developed and verified. The model was then used for optimizing the feeding schedule in fed-batch culture. To handle higher-order model equations (14 state variables), an optimization methodology for the dual-enzyme system is proposed by integrating Pontryagin's optimum principle with fermentation measurements. Markov chain Monte Carlo (MCMC) procedures were appropriate for model parameter and decision variable estimation by using a priori parameter distributions reflecting the experimental results. Using a simplified Metropolis-Hastings algorithm, the specific productivity of alpha-amylase was maximized and the optimum path was confirmed by experimentation. The optimization process predicted a further 14% improvement of alpha-amylase productivity that could not be realized because of the onset of sporulation. Among the decision variables, the switching time from batch to fed-batch operation (t(s)) was the most sensitive decision variable.

Algorithms↗
PubMed2004

Joint oligogenic segregation and linkage analysis using bayesian Markov chain Monte Carlo methods.

One of the most challenging areas in human genetics is the dissection of quantitative traits. In this context, the efficient use of available data is important, including, when possible, use of large pedigrees and many markers for gene mapping. In addition, methods that jointly perform linkage analysis and estimation of the trait model are appealing because they combine the advantages of a model-based analysis with the advantages of methods that do not require prespecification of model parameters for linkage analysis. Here we review a Markov chain Monte Carlo approach for such joint linkage and segregation analysis, which allows analysis of oligogenic traits in the context of multipoint linkage analysis of large pedigrees. We provide an outline for practitioners of the salient features of the method, interpretation of the results, effect of violation of assumptions, and an example analysis of a two-locus trait to illustrate the method.

Bayes Theorem↗
PubMed2006

Seriation in paleontological data using markov chain Monte Carlo methods.

Given a collection of fossil sites with data about the taxa that occur in each site, the task in biochronology is to find good estimates for the ages or ordering of sites. We describe a full probabilistic model for fossil data. The parameters of the model are natural: the ordering of the sites, the origination and extinction times for each taxon, and the probabilities of different types of errors. We show that the posterior distributions of these parameters can be estimated reliably by using Markov chain Monte Carlo techniques. The posterior distributions of the model parameters can be used to answer many different questions about the data, including seriation (finding the best ordering of the sites) and outlier detection. We demonstrate the usefulness of the model and estimation method on synthetic data and on real data on large late Cenozoic mammals. As an example, for the sites with large number of occurrences of common genera, our methods give orderings, whose correlation with geochronologic ages is 0.95.

Animals↗
PubMed2005

Inference of demographic history from genealogical trees using reversible jump Markov chain Monte Carlo.

BACKGROUND: Coalescent theory is a general framework to model genetic variation in a population. Specifically, it allows inference about population parameters from sampled DNA sequences. However, most currently employed variants of coalescent theory only consider very simple demographic scenarios of population size changes, such as exponential growth. RESULTS: Here we develop a coalescent approach that allows Bayesian non-parametric estimation of the demographic history using genealogies reconstructed from sampled DNA sequences. In this framework inference and model selection is done using reversible jump Markov chain Monte Carlo (MCMC). This method is computationally efficient and overcomes the limitations of related non-parametric approaches such as the skyline plot. We validate the approach using simulated data. Subsequently, we reanalyze HIV-1 sequence data from Central Africa and Hepatitis C virus (HCV) data from Egypt. CONCLUSIONS: The new method provides a Bayesian procedure for non-parametric estimation of the demographic history. By construction it additionally provides confidence limits and may be used jointly with other MCMC-based coalescent approaches.

Algorithms↗
PubMedDate not supplied

Markov chain Monte Carlo estimation of a multiparameter decision model: consistency of evidence and the accurate assessment of uncertainty.

Decision models are usually populated 1 parameter at a time, with 1 item of information informing each parameter. Often, however, data may not be available on the parameters themselves but on several functions of parameters, and there may be more items of information than there are parameters to be estimated. The authors show how in these circumstances all the model parameters can be estimated simultaneously using Bayesian Markov chain Monte Carlo methods. Consistency of the information and/or the adequacy of the model can also be assessed within this framework. Statistical evidence synthesis using all available data should result in more precise estimates of parameters and functions of parameters, and is compatible with the emphasis currently placed on systematic use of evidence. To illustrate this, WinBUGS software is used to estimate a simple 9-parameter model of the epidemiology of HIV in women attending prenatal clinics, using information on 12 functions of parameters, and to thereby compute the expected net benefit of 2 alternative prenatal testing strategies, universal testing and targeted testing of high-risk groups. The authors demonstrate improved precision of estimates, and lower estimates of the expected value of perfect information, resulting from the use of all available data.

AIDS Serodiagnosis↗
PubMed2005

The monoculture vs. rotation strategies in forestry: formalization and prediction by means of Markov-chain modelling.

The monoculture strategy of forest management, where the same tree species (e.g., Picea abies) is cultivated in a number of successive planting-growing-felling cycles, is generally considered to be economically efficient, yet not sustainable as it reduces biodiversity in the forest. The sound alternative suggests a long-term strategy of forest management in which different forest types rotate either with planting after clear cutting, or by natural forest succession, yet the commercial output remains dubious. We suggest an approach to formalization and modelling forest dynamics in the long-term by means of Markov chains, the monoculture strategy resulting in an absorbing chain and the rotation one in a regular chain. The approach is illustrated with a case study of Russkii Les, a managed forest located in the Moscow Region, Russia, and the nearby forest reserve having been used as a data source for undisturbed forest dynamics. Starting with conceptual schemes of transitions among certain forest types (states of the chain) in the monoculture and rotation cases, we estimated the transition probabilities by an original method based on average duration of the corresponding states and on the likelihood of alternative transitions from a state into the next one. Formal analysis of the regular chain reveals an opportunity to achieve particular management objectives within the rotation strategy, in particular, to get the distribution of forest types in accordance with an adopted hierarchy of their commercial values, i.e. more valuable types have greater shares.

Biodiversity↗
PubMed2003

Markov Chain Monte Carlo approaches to analysis of genetic and environmental components of human developmental change and G x E interaction.

The linear structural model has provided the statistical backbone of the analysis of twin and family data for 25 years. A new generation of questions cannot easily be forced into the framework of current approaches to modeling and data analysis because they involve nonlinear processes. Maximizing the likelihood with respect to parameters of such nonlinear models is often cumbersome and does not yield easily to current numerical methods. The application of Markov Chain Monte Carlo (MCMC) methods to modeling the nonlinear effects of genes and environment in MZ and DZ twins is outlined. Nonlinear developmental change and genotype x environment interaction in the presence of genotype-environment correlation are explored in simulated twin data. The MCMC method recovers the simulated parameters and provides estimates of error and latent (missing) trait values. Possible limitations of MCMC methods are discussed. Further studies are necessary explore the value of an approach that could extend the horizons of research in developmental genetic epidemiology.

Child↗
PubMed2005

A multistate Markov chain model for longitudinal, categorical quality-of-life data subject to non-ignorable missingness.

Quality-of-life (QOL) is an important outcome in clinical research, particularly in cancer clinical trials. Typically, data are collected longitudinally from patients during treatment and subsequent follow-up. Missing data are a common problem, and missingness may arise in a non-ignorable fashion. In particular, the probability that a patient misses an assessment may depend on the patient's QOL at the time of the scheduled assessment. We propose a Markov chain model for the analysis of categorical outcomes derived from QOL measures. Our model assumes that transitions between QOL states depend on covariates through generalized logit models or proportional odds models. To account for non-ignorable missingness, we incorporate logistic regression models for the conditional probabilities of observing measurements, given their actual values. The model can accommodate time-dependent covariates. Estimation is by maximum likelihood, summing over all possible values of the missing measurements. We describe options for selecting parsimonious models, and we study the finite-sample properties of the estimators by simulation. We apply the techniques to data from a breast cancer clinical trial in which QOL assessments were made longitudinally, and in which missing data frequently arose.

Antineoplastic Agents↗
PubMed2001

Markov chain Monte Carlo computation of confidence intervals for substitution-rate variation in proteins.

We suggest a method implemented in a computer program, immodestly dubbed TSUNAMI, that allows us to compare two homologous protein subfamilies with respect to the distribution of substitution rates along sequences. This study furthers our earlier work on a wavelet model of rate variation (1). The current approach allows sensitive detection of subtle discordances in the selection patterns between two protein subfamilies. In addition to performing fast computation of the maximum posterior probability estimates of the relative substitution rates, the method can select the most appropriate number of wavelet parameters for a particular dataset. TSUNAMI is based on a Markov chain Monte Carlo technique, and appears to be more applicable to larger datasets than is the full likelihood-based approach.

Amino Acid Substitution↗
PubMed2001

A system of complementary genes in hybrids between Drosophila koepferae and D. buzzatii: a Markov chain model allows to make inferences about their number and relationships.

In backcrosses between D. koepferae and D. buzzatii, the disruption of a system of species-specific complementary factors brings about hybrid male inviability. This system consists of a lethal factor, hmi-1, linked to the X chromosome of D. koepferae, and several conspecific autosomal suppressors. However, hmi-1 hybrid males can also be rescued by factors present in some strains of D. buzzatii. The present work aims to estimate the number of hmi-1 suppressors in one of these strains by means of Markov chains. The obtained results allow discarding models with one or more chromosomes having independent suppressor effect. On the other hand, models having n chromosomes that interact in groups of r, being 1 < r < or = n, to produce rescue effect, provide good approximations to the observed results. The best fit to the data is obtained with four or five chromosomes with suppressor effect, interacting epistatically in groups of three to rescue the viability of hmi-1 males.

Animals↗
PubMed2006

Markov Chain Monte Carlo Algorithm based metabolic flux distribution analysis on Corynebacterium glutamicum.

MOTIVATION: Metabolic flux analysis via a (13)C tracer experiment has been achieved using a Monte Carlo method with the assumption of system noise as Gaussian noise. However, an unbiased flux analysis requires the estimation of fluxes and metabolites jointly without the restriction on the assumption of Gaussian noise. The flux distributions under such a framework can be freely obtained with various system noise and uncertainty models. RESULTS: In this paper, a stochastic generative model of the metabolic system is developed. Following this, the Markov Chain Monte Carlo (MCMC) approach is applied to flux distribution analysis. The disturbances and uncertainties in the system are simplified as truncated Gaussian multiplicative models. The performance in a real metabolic system is illustrated by the application to the central metabolism of Corynebacterium glutamicum. The flux distributions are illustrated and analyzed in order to understand the underlying flux activities in the system. AVAILABILITY: Algorithms are available upon request.

Algorithms↗