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PubMed2000

Association models for a multivariate binary response.

Models for a multivariate binary response are parameterized by univariate marginal probabilities and dependence ratios of all orders. The w-order dependence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence. This parameterization supports likelihood-based inference for both regression parameters, relating marginal probabilities to explanatory variables, and association model parameters, relating dependence ratios to simple and meaningful mechanisms. Five types of association models are proposed, where responses are (1) independent given a necessary factor for the possibility of a success, (2) independent given a latent binary factor, (3) independent given a latent beta distributed variable, (4) follow a Markov chain, and (5) follow one of two first-order Markov chains depending on the realization of a binary latent factor. These models are illustrated by reanalyzing three data sets, foremost a set of binary time series on auranofin therapy against arthritis. Likelihood-based approaches are contrasted with approaches based on generalized estimating equations. Association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients.

Antirheumatic Agents↗

PubMed1982

Generalized first transit times with an illustration in human service system planning.

This paper is concerned with extending the notion of first transit time analysis in Markov chains to sets of states rather than individual states. The motivation for the research came as a result of the state structure of a Markov chain model being developed to aid government planners in operating service systems for the elderly. The mathematics of the analysis is presented, followed by numerical results showing the expected transit times from service to service for a country service system for the elderly in Pennsylvania.

Age Factors↗

PubMed1997

Large hierarchical Bayesian analysis of multivariate survival data.

Failure times that are grouped according to shared environments arise commonly in statistical practice. That is, multiple responses may be observed for each of many units. For instance, the units might be patients or centers in a clinical trial setting. Bayesian hierarchical models are appropriate for data analysis in this context. At the first stage of the model, survival times can be modelled via the Cox partial likelihood, using a justification due to Kalbfleisch (1978, Journal of the Royal Statistical Society, Series B 40, 214-221). Thus, questionable parametric assumptions are avoided. Conventional wisdom dictates that it is comparatively safe to make parametric assumptions at subsequent stages. Thus, unit-specific parameters are modelled parametrically. The posterior distribution of parameters given observed data is examined using Markov chain Monte Carlo methods. Specifically, the hybrid Monte Carlo method, as described by Neal (1993a, in Advances in Neural Information Processing 5, 475-482; 1993b, Probabilistic inference using Markov chain Monte Carlo methods), is utilized.

Antineoplastic Combined Chemotherapy Protocols↗

PubMed1980

On the distribution of the nucleotides in seven completely sequenced DNAs.

Several Markov chain models (up to fourth order) have been fitted to the sequences of the seven DNAs presented in Fuchs et al. (1980). Two methods for determining the order of Markov chain are applied to the data. The two methods lead to different conclusions and we discuss these discrepancies. When the distribution of the nucleotides in a DNA sequence is investigated, it is suggested that the study on the order of the Markov model should be supplemented with additional analysis.

Bacteriophage phi X 174↗

PubMed2001

An algorithm for statistical alignment of sequences related by a binary tree.

An algorithm is presented that allows the calculation of the probability of a set of sequences related by a binary tree that has evolved according to the Thorne-Kishino-Felsenstein model (1991) for a fixed set of parameters. There are two ideas underlying this algorithm. Firstly, a markov chain is defined that generates ancestral sequences and their alignment at two neighboring nodes in a tree. Secondly, a stochastic walk on the binary tree, that defines a markov chain generating ancestral sequences and their alignment at the internal nodes in the tree is described. The running time of this algorithm is O(l2 kappa), where l is the geometric average of the sequence lengths and kappa the number of sequences--leaves at the binary tree. This could be improved to O(l kappa).

Algorithms↗

PubMedDate not supplied

Biased polymers in the origin of life.

We delve into the study of a Markov chain formalism applied to the thermal prebiotic oligomerization of amino acids. We find for the case of only two types of electromagnetic interactions, that the steady state attainment by the Markov chain is a built in mechanism limiting the expected variability in sequences in a population of polymers. Such result may be of importance as it makes more accessible the replication of a minimal chemical machinery compatible with life.

Biopolymers↗

PubMed1990

Graphs, random sums, and sojourn time distributions, with application to ion-channel modeling.

This paper considers the distribution of a sojourn time in a class of states of a stochastic process having finite discrete state space where sojourn times in any individual state are independent and identically distributed, and transitions between states follow a Markov chain. The state space and possible transitions of the process are represented by a graph. Class sojourn time distributions are derived by modifying this graph using 'composition' of states, defining a new Markov chain on the modified graph, and expressing the sojourn time in a composition state as a random sum. Appropriate compositions are chosen according to the possible "cores" of sojourns in the particular class, where a core describes the structure of a sojourn in terms of a single state or a chain in the original graph. Graph methods provide an algorithmic basis for the derivation, which can be simplified by using symmetry results. Models of ion-channel kinetics are used throughout for illustration; class sojourn time distributions are important in such models because individual states are often indistinguishable experimentally. Markov processes are the special case where sojourn times in individual states are exponentially distributed. In this case kinetic parameter estimation based on the observed class sojourn time distribution is briefly discussed; explicit estimating equations applicable to sequential models of nicotinic receptor kinetics are given.

Ion Channels↗

PubMedDate not supplied

Systemic lupus erythematosus in Indian patients: prognosis, survival and life expectancy.

BACKGROUND: There have been several studies on survival patterns in Indian patients with systemic lupus erythematosus but it is still not clear as to which factors at diagnosis predict survival outcome. The impact of specific organ involvement, and of disease activity itself, needs to be studied further. METHODS: We conducted a non-concurrent prospective study of 98 lupus patients between 1981 and 1993. The clinical symptoms, signs and investigation results at onset, and at subsequent visits, were abstracted from the case notes. A systemic lupus erythematosus disease activity index (SLEDAI) was constructed at the initial presentation and for each subsequent visit. Patients not attending for at least 6 months were traced by post. The quantitative data from the SLEDAI was used to construct a Markov chain mathematical expression designed to predict life expectancy. RESULTS: The cumulative percentage survival at 1, 5 and 10 years was found to be 89%, 77% and 60%, respectively. The Markov chain predicted a life expectancy of 13.9 years. Central nervous system and renal involvement were poor prognostic factors. Proteinuria (> 0.5 g/day) caused a 50% reduction in life expectancy but increased disease activity at onset did not predispose to a poor outcome. CONCLUSION: The survival of patients with systemic lupus erythematosus continues to be poor. Central nervous system and renal disease indicate a poor outcome. Hence, new treatment strategies must be evolved to improve the survival of such patients.

Female↗

PubMed2004

External control in Markovian genetic regulatory networks: the imperfect information case.

Probabilistic Boolean Networks, which form a subclass of Markovian Genetic Regulatory Networks, have been recently introduced as a rule-based paradigm for modeling gene regulatory networks. In an earlier paper, we introduced external control into Markovian Genetic Regulatory networks. More precisely, given a Markovian genetic regulatory network whose state transition probabilities depend on an external (control) variable, a Dynamic Programming-based procedure was developed by which one could choose the sequence of control actions that minimized a given performance index over a finite number of steps. The control algorithm of that paper, however, could be implemented only when one had perfect knowledge of the states of the Markov Chain. This paper presents a control strategy that can be implemented in the imperfect information case, and makes use of the available measurements which are assumed to be probabilistically related to the states of the underlying Markov Chain.

Algorithms↗

PubMed2004

Markov entropy backbone electrostatic descriptors for predicting proteins biological activity.

The spherical truncation of electrostatic interactions between aminoacids makes it possible to break down long-range spatial electrostatic interactions, resulting in short-range interactions. As a result, a Markov Chain model may be used to calculate the probabilities with which the effect of a given interaction reaches aminoacids at different distances within the backbone. The entropies of a Markov Chain model of this type may then be used to codify information about the spatial distribution of charges in the protein used in this study exploring the structure-activity relationship. In this paper, a linear discriminant analysis is reported, which correctly classified 92.3% of 26 under investigation in training and leave-one-out cross validation, purely for illustrative purposes. Classification was carried out for three possible activities: lysozymes, dihydrofolate reductases, and alcohol dehydrogenases. The discriminant analysis equations were contracted into two canonical roots. These simple canonical roots have high regression coefficients (R(c1)=0.903 and R(c2)=0.70). Root1 explains the biological activity of alcohol dehydrogenases while Root2 discriminates between lysozymes and dihydrofolate reductases. It was possible to profile the effect of core, middle, and surface aminoacids on biological activity. In contrast, a model considering classic physicochemical parameters such as: polarizability, refractivity, and partition coefficient classify correctly only the 80.8% of the proteins.

Alcohol Dehydrogenase↗

PubMed2005

Scaling and data collapse for the mean exit time of asset prices.

We study theoretical and empirical aspects of the mean exit time (MET) of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a prefactor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both two-state and three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

Journal Article↗

PubMed2003

Estimation of infection and recovery rates for highly polymorphic parasites when detectability is imperfect, using hidden Markov models.

A Bayesian hierarchical model is proposed for estimating parasitic infection dynamics for highly polymorphic parasites when detectability of the parasite using standard tests is imperfect. The parasite dynamics are modelled as a non-homogeneous hidden two-state Markov process, where the observed process is the detection or failure to detect a parasitic genotype. This is assumed to be conditionally independent given the hidden process, that is, the underlying true presence of the parasite, which evolves according to a first-order Markov chain. The model allows the transition probabilities of the hidden states as well as the detectability parameter of the test to depend on a number of covariates. Full Bayesian inference is implemented using Markov chain Monte Carlo simulation. The model is applied to a panel data set of malaria genotype data from a randomized controlled trial of bed nets in Tanzanian children aged 6-30 months, with the age of the host and bed net use as covariates. This analysis confirmed that the duration of infections with parasites belonging to the MSP-2 FC27 allelic family increased with age.

Algorithms↗

PubMed1995

Computational methods for Markov series with large state spaces, with application to AIDS modeling.

AIDS models, and epidemiological models generally, are almost exclusively either differential equations or Markov processes. Of course, the phenomena are fundamentally random, so at best differential equations track the expectation of the process and variability is masked. There are few techniques in the literature for numerical analysis of Markov chains of any size, and so those wishing to analyze stochastic epidemics presently have little alternative to simulation. The contribution of the present paper is to propose numerical techniques capable of finding marginal probabilities of Markov chains having thousands and even millions of states. The ideas are illustrated by application to AIDS models in the literature which formerly had been investigated only through Monte Carlo. This introductory foray has not plumbed the depths of the computational methodology, which yet needs refinement and streamlining that comes through experience. Yet in its primitive form, it is shown herein to be adequate for a computation on the scale of a two-population partition of the San Francisco homosexual epidemic. The closing discussion compares the strengths and weaknesses of the present numerical techniques with the simulation approach to investigation of Markov epidemics.

Acquired Immunodeficiency Syndrome↗

PubMed2006

PredSL: a tool for the N-terminal sequence-based prediction of protein subcellular localization.

The ability to predict the subcellular localization of a protein from its sequence is of great importance, as it provides information about the protein's function. We present a computational tool, PredSL, which utilizes neural networks, Markov chains, profile hidden Markov models, and scoring matrices for the prediction of the subcellular localization of proteins in eukaryotic cells from the N-terminal amino acid sequence. It aims to classify proteins into five groups: chloroplast, thylakoid, mitochondrion, secretory pathway, and "other". When tested in a five-fold cross-validation procedure, PredSL demonstrates 86.7% and 87.1% overall accuracy for the plant and non-plant datasets, respectively. Compared with TargetP, which is the most widely used method to date, and LumenP, the results of PredSL are comparable in most cases. When tested on the experimentally verified proteins of the Saccharomyces cerevisiae genome, PredSL performs comparably if not better than any available algorithm for the same task. Furthermore, PredSL is the only method capable for the prediction of these subcellular localizations that is available as a stand-alone application through the URL:http://bioinformatics.biol.uoa.gr/PredSL/.

Algorithms↗

PubMed2004

Use of runs statistics for pattern recognition in genomic DNA sequences.

In this article, the use of the finite Markov chain imbedding (FMCI) technique to study patterns in DNA under a hidden Markov model (HMM) is introduced. With a vision of studying multiple runs-related statistics simultaneously under an HMM through the FMCI technique, this work establishes an investigation of a bivariate runs statistic under a binary HMM for DNA pattern recognition. An FMCI-based recursive algorithm is derived and implemented for the determination of the exact distribution of this bivariate runs statistic under an independent identically distributed (IID) framework, a Markov chain (MC) framework, and a binary HMM framework. With this algorithm, we have studied the distributions of the bivariate runs statistic under different binary HMM parameter sets; probabilistic profiles of runs are created and shown to be useful for trapping HMM maximum likelihood estimates (MLEs). This MLE-trapping scheme offers good initial estimates to jump-start the expectation-maximization (EM) algorithm in HMM parameter estimation and helps prevent the EM estimates from landing on a local maximum or a saddle point. Applications of the bivariate runs statistic and the probabilistic profiles in conjunction with binary HMMs for pattern recognition in genomic DNA sequences are illustrated via case studies on DNA bendability signals using human DNA data.

Algorithms↗

PubMed1979

A Markov model description of changeover probabilities on concurrent variable-interval schedules.

The primary data were peck-by-peck sequential records of four pigeons responding on several different concurrent variable-interval schedules. According to the hypothesis that the subject chooses the alternative with the highest probability of reinforcement at the moment, response-by-response performance in concurrent schedules should show sequential dependencies. However, such dependencies were not found, and it was possible to describe molecular-level performance with simple Markov chain models. The Markov model description implies that the momentary changeover probabilities were proportional to the overall relative reinforcement frequencies, and that changeover probabilities did not change as a function of previous responding. A second finding was that although a changeover-delay procedure was omitted, relative response frequencies closely approximated relative reinforcement frequencies.

Journal Article↗

PubMed2001

A new prognosis factor analysis based on nonhomogeneous Markov description.

To evaluate prognosis factors, Cox's proportional hazard model has been used. But it was found that the analytical ability was not sufficient. So we propose a new evaluation method combining Markov chain model and multiple logistic regression analysis to estimate the prognosis factors. Stage II breast cancer was chosen as the subject. The data was retrospective data gathered in National Cancer Center Central Hospital. As first step, a simple Markov chain model was constructed to describe the state transition of a breast cancer. Then the multiple property of each state transition was investigated in detail. And the patients who had gotten a recurrence for the first two and a half years were discriminated as the poor prognosis group by a nonparametric test (p < 0.05). And the result proved to corresponding with the clinical experience. As second step, three factors (n classification of pathological diagnosis, ductal spread, and estrogen receptor) were selected as the prognosis factors for the early death in Stage II breast cancer by a multiple logistic regression analysis. This new prognosis factor analysis could find out some scientific evidences. Especially, it was found to be remarkable efficient in proving clinically experienced observation.

Breast Neoplasms↗

PubMed2002

Statistical characteristics of radionuclide concentration field around a nuclear power plant.

A Markov chain model with two states is used for investigating the space and time structure of the concentration field around an elevated continuous source. The concentration field is computed with a time-dependent Gaussian puff dispersion model run with observed meteorological data as input. Spatial distributions of transition probability, Besson persistence coefficient and order of Markov chain are presented for tritium routinely released from a nuclear power plant located about 100 miles east of Bucharest, Romania.

Markov Chains↗