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.     

A quantitative approach for polymerase chain reactions based on a hidden Markov model

Polymerase chain reaction (PCR) is a major DNA amplification technology from molecular biology. The quantitative analysis of PCR aims at determining the initial amount of the DNA molecules from the observation of typically several PCR amplifications curves. The mainstream observation scheme of the DNA amplification during PCR involves fluorescence intensity measurements. Under the classical assumption that the measured fluorescence intensity is proportional to the amount of present DNA molecules, and under the assumption that these measurements are corrupted by an additive Gaussian noise, we analyze a single amplification curve using a hidden Markov model(HMM). The unknown parameters of the HMM may be separated into two parts. On the one hand, the parameters from the amplification process are the initial number of the DNA molecules and the replication efficiency, which is the probability of one molecule to be duplicated. On the other hand, the parameters from the observational scheme are the scale parameter allowing to convert the fluorescence intensity into the number of DNA molecules and the mean and variance characterizing the Gaussian noise. We use the maximum likelihood estimation procedure to infer the unknown parameters of the model from the exponential phase of a single amplification curve, the main parameter of interest for quantitative PCR being the initial amount of the DNA molecules. An illustrative example is provided. This research was financed by the Swedish foundation for Strategic Research through the Gothenburg Mathematical Modelling Centre.     

A conditional Markov model for clustered progressive multistate processes under incomplete observation

Clustered progressive chronic disease processes arise when interest lies in modeling damage in paired organ systems (e.g., kidneys, eyes), in diseases manifest in different organ systems, or in systemic conditions for which damage may occur in several locations of the body. Multistate Markov models have considerable appeal for modeling damage in such settings, particularly when patients are only under intermittent observation. Generalizations are necessary, however, to deal with the fact that processes within subjects may not be independent. We describe a conditional Markov model in which the clustering in processes within subjects is addressed by the use of multiplicative random effects for each transition intensity. The random effects for the different transition intensities may be correlated within subjects, but are assumed to be independent for different subjects. We apply the mixed Markov model to a motivating data set of patients with psoriatic arthritis, and characterize the progressive course of damage in joints of the hand. A generalization to accommodate a subpopulation of "stayers" and extensions which facilitate regression are indicated and illustrated.     

Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo

A common problem in molecular phylogenetics is choosing a model of DNA substitution that does a good job of explaining the DNA sequence alignment without introducing superfluous parameters. A number of methods have been used to choose among a small set of candidate substitution models, such as the likelihood ratio test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Bayes factors. Current implementations of any of these criteria suffer from the limitation that only a small set of models are examined, or that the test does not allow easy comparison of non-nested models. In this article, we expand the pool of candidate substitution models to include all possible time-reversible models. This set includes seven models that have already been described. We show how Bayes factors can be calculated for these models using reversible jump Markov chain Monte Carlo, and apply the method to 16 DNA sequence alignments. For each data set, we compare the model with the best Bayes factor to the best models chosen using AIC and BIC. We find that the best model under any of these criteria is not necessarily the most complicated one; models with an intermediate number of substitution types typically do best. Moreover, almost all of the models that are chosen as best do not constrain a transition rate to be the same as a transversion rate, suggesting that it is the transition/transversion rate bias that plays the largest role in determining which models are selected. Importantly, the reversible jump Markov chain Monte Carlo algorithm described here allows estimation of phylogeny (and other phylogenetic model parameters) to be performed while accounting for uncertainty in the model of DNA substitution.     

应用马尔科夫链模型对草地螟发生程度的预测

草地螟Loxostege stictialis L.是我国北方农牧业生产上一种重要迁飞性、暴发性害虫,一旦暴发会给当地农牧生产造成严重危害.根据康保县1977-2008年1代草地螟幼虫发生程度的时间序列资料,应用马尔科夫链的转移概率预测法,构建了1～3阶转移概率矩阵,组建模型对该县2009-2011年1代草地螟发生程度进行了预测,结果与大田实际发生情况完全一致,准确率100％.对1980-2011年的历史资料进行回检,历史符合率89.9％,该方法可对草地螟进行长期预报,为草地螟长期预报提供了一种准确有效的方法,对草地螟发生程度的长期预报具有重要指导意义.     

Bayesian analysis of discrete survival data with a hidden Markov chain

This paper considers the discrete survival data from a Bayesian point of view. A sequence of the baseline hazard functions, which plays an important role in the discrete hazard function, is modeled with a hidden Markov chain. It is explained how the resultant model is implemented via Markov chain Monte Carlo methods. The model is illustrated by an application of real data.     

基于马尔可夫链的基因芯片特异性探针选择方法

对于基因表达芯片,特异性探针的选择是探针设计的重要环节,由于基因组序列数据量极大,不可能对每个候选探针都在全序列中进行特异性评价并进行取舍。对此问题,提出了一种采用马尔可夫链概率准则的探针特异性选择方法,即把基因组序列看作马尔可夫链,任何探针序列的互补序列作为它的一个子序列,都具有一定的出现概率,概率越小,越可能具有特异性。据此,选择其中概率最小的N个候选探针,能够大大减少进行特异性评价的探针数量,缩短探针设计的计算时间。对实际数据的测试结果表明,该方法选择的探针具有很高的特异性。     

A Markov chain occurring in enzyme kinetics

A certain Markov chain which was encountered by T. L. Hill in the study of the kinetics of a linear array of enzymes is studied. An explicit formula for the steady state probabilities is given and some conjectures raised by T. L. Hill are proved.     

A comparison of strategies for Markov chain Monte Carlo computation in quantitative genetics

In quantitative genetics, Markov chain Monte Carlo (MCMC) methods are indispensable for statistical inference in non-standard models like generalized linear models with genetic random effects or models with genetically structured variance heterogeneity. A particular challenge for MCMC applications in quantitative genetics is to obtain efficient updates of the high-dimensional vectors of genetic random effects and the associated covariance parameters. We discuss various strategies to approach this problem including reparameterization, Langevin-Hastings updates, and updates based on normal approximations. The methods are compared in applications to Bayesian inference for three data sets using a model with genetically structured variance heterogeneity.     

DIM SUM: demography and individual migration simulated using a Markov chain

An increasing number of studies seek to infer demographic history, often jointly with genetic relationships. Despite numerous analytical methods for such data, few simulations have investigated the methods' power and robustness, especially when underlying assumptions have been violated. DIM SUM (Demography and Individual Migration Simulated Using a Markov chain) is a stand-alone Java program for the simulation of population demography and individual migration while recording ancestor-descendant relationships. It does not employ coalescent assumptions or discrete population boundaries. It is extremely flexible, allowing the user to specify border positions, reactions of organisms to borders, local and global carrying capacities, individual dispersal kernels, rates of reproduction and strategies for sampling individuals. Spatial variables may be specified using image files (e.g., as exported from gis software) and may vary through time. In combination with software for genetic marker simulation, DIM SUM will be useful for testing phylogeographic (e.g., nested clade phylogeographic analysis, coalescent-based tests and continuous-landscape frameworks) and landscape-genetic methods, specifically regarding violations of coalescent assumptions. It can also be used to explore the qualitative features of proposed demographic scenarios (e.g. regarding biological invasions) and as a pedagogical tool. DIM SUM (with user's manual) can be downloaded from http://code.google.com/p/bio-dimsum.     

Predictive glycoengineering of biosimilars using a Markov chain glycosylation model

Biosimilar drugs must closely resemble the pharmacological attributes of innovator products to ensure safety and efficacy to obtain regulatory approval. Glycosylation is one critical quality attribute that must be matched, but it is inherently difficult to control due to the complexity of its biogenesis. This usually implies that costly and time‐consuming experimentation is required for clone identification and optimization of biosimilar glycosylation. Here, a computational method that utilizes a Markov model of glycosylation to predict optimal glycoengineering strategies to obtain a specific glycosylation profile with desired properties is described. The approach uses a genetic algorithm to find the required quantities to perturb glycosylation reaction rates that lead to the best possible match with a given glycosylation profile. Furthermore, the approach can be used to identify cell lines and clones that will require minimal intervention while achieving a glycoprofile that is most similar to the desired profile. Thus, this approach can facilitate biosimilar design by providing computational glycoengineering guidelines that can be generated with a minimal time and cost.     

A multistate model for bivariate interval-censored failure time data

SUMMARY: Interval-censored life-history data arise when the events of interest are only detectable at periodic assessments. When interest lies in the occurrence of two such events, bivariate-interval censored event time data are obtained. We describe how to fit a four-state Markov model useful for characterizing the association between two interval-censored event times when the assessment times for the two events may be generated by different inspection processes. The approach treats the two events symmetrically and enables one to fit multiplicative intensity models that give estimates of covariate effects as well as relative risks characterizing the association between the two events. An expectation-maximization (EM) algorithm is described for estimation in which the maximization step can be carried out with standard software. The method is illustrated by application to data from a trial of HIV patients where the events are the onset of viral shedding in the blood and urine among individuals infected with cytomegalovirus.