Browsing by Subject "Markov Chains"
Now showing 1 - 14 of 14
Results Per Page
Sort Options
Item Open Access Ancestral population genomics: the coalescent hidden Markov model approach.(Genetics, 2009-09) Dutheil, Julien Y; Ganapathy, Ganesh; Hobolth, Asger; Mailund, Thomas; Uyenoyama, Marcy K; Schierup, Mikkel HWith incomplete lineage sorting (ILS), the genealogy of closely related species differs along their genomes. The amount of ILS depends on population parameters such as the ancestral effective population sizes and the recombination rate, but also on the number of generations between speciation events. We use a hidden Markov model parameterized according to coalescent theory to infer the genealogy along a four-species genome alignment of closely related species and estimate population parameters. We analyze a basic, panmictic demographic model and study its properties using an extensive set of coalescent simulations. We assess the effect of the model assumptions and demonstrate that the Markov property provides a good approximation to the ancestral recombination graph. Using a too restricted set of possible genealogies, necessary to reduce the computational load, can bias parameter estimates. We propose a simple correction for this bias and suggest directions for future extensions of the model. We show that the patterns of ILS along a sequence alignment can be recovered efficiently together with the ancestral recombination rate. Finally, we introduce an extension of the basic model that allows for mutation rate heterogeneity and reanalyze human-chimpanzee-gorilla-orangutan alignments, using the new models. We expect that this framework will prove useful for population genomics and provide exciting insights into genome evolution.Item Open Access Detecting structure of haplotypes and local ancestry.(Genetics, 2014-03) Guan, YongtaoWe present a two-layer hidden Markov model to detect the structure of haplotypes for unrelated individuals. This allows us to model two scales of linkage disequilibrium (one within a group of haplotypes and one between groups), thereby taking advantage of rich haplotype information to infer local ancestry of admixed individuals. Our method outperforms competing state-of-the-art methods, particularly for regions of small ancestral track lengths. Applying our method to Mexican samples in HapMap3, we found two regions on chromosomes 6 and 8 that show significant departure of local ancestry from the genome-wide average. A software package implementing the methods described in this article is freely available at http://bcm.edu/cnrc/mcmcmc.Item Open Access Economic evaluation of access to musculoskeletal care: the case of waiting for total knee arthroplasty.(BMC Musculoskelet Disord, 2014-01-18) Mather, Richard C; Hug, Kevin T; Orlando, Lori A; Watters, Tyler Steven; Koenig, Lane; Nunley, Ryan M; Bolognesi, Michael PBACKGROUND: The projected demand for total knee arthroplasty is staggering. At its root, the solution involves increasing supply or decreasing demand. Other developed nations have used rationing and wait times to distribute this service. However, economic impact and cost-effectiveness of waiting for TKA is unknown. METHODS: A Markov decision model was constructed for a cost-utility analysis of three treatment strategies for end-stage knee osteoarthritis: 1) TKA without delay, 2) a waiting period with no non-operative treatment and 3) a non-operative treatment bridge during that waiting period in a cohort of 60 year-old patients. Outcome probabilities and effectiveness were derived from the literature. Costs were estimated from the societal perspective with national average Medicare reimbursement. Effectiveness was expressed in quality-adjusted life years (QALYs) gained. Principal outcome measures were average incremental costs, effectiveness, and quality-adjusted life years; and net health benefits. RESULTS: In the base case, a 2-year wait-time both with and without a non-operative treatment bridge resulted in a lower number of average QALYs gained (11.57 (no bridge) and 11.95 (bridge) vs. 12.14 (no delay). The average cost was $1,660 higher for TKA without delay than wait-time with no bridge, but $1,810 less than wait-time with non-operative bridge. The incremental cost-effectiveness ratio comparing wait-time with no bridge to TKA without delay was $2,901/QALY. When comparing TKA without delay to waiting with non-operative bridge, TKA without delay produced greater utility at a lower cost to society. CONCLUSIONS: TKA without delay is the preferred cost-effective treatment strategy when compared to a waiting for TKA without non-operative bridge. TKA without delay is cost saving when a non-operative bridge is used during the waiting period. As it is unlikely that patients waiting for TKA would not receive non-operative treatment, TKA without delay may be an overall cost-saving health care delivery strategy. Policies aimed at increasing the supply of TKA should be considered as savings exist that could indirectly fund those strategies.Item Open Access Estimation and validation of a multiattribute model of Alzheimer disease progression.(Med Decis Making, 2010-11) Stallard, Eric; Kinosian, Bruce; Zbrozek, Arthur S; Yashin, Anatoliy I; Glick, Henry A; Stern, YaakovOBJECTIVES: To estimate and validate a multiattribute model of the clinical course of Alzheimer disease (AD) from mild AD to death in a high-quality prospective cohort study, and to estimate the impact of hypothetical modifications to AD progression rates on costs associated with Medicare and Medicaid services. DATA AND METHODS: The authors estimated sex-specific longitudinal Grade of Membership (GoM) models for AD patients (103 men, 149 women) in the initial cohort of the Predictors Study (1989-2001) based on 80 individual measures obtained every 6 mo for 10 y. These models were replicated for AD patients (106 men, 148 women) in the 2nd Predictors Study cohort (1997-2007). Model validation required that the disease-specific transition parameters be identical for both Predictors Study cohorts. Medicare costs were estimated from the National Long Term Care Survey. RESULTS: Sex-specific models were validated using the 2nd Predictors Study cohort with the GoM transition parameters constrained to the values estimated for the 1st Predictors Study cohort; 57 to 61 of the 80 individual measures contributed significantly to the GoM models. Simulated, cost-free interventions in the rate of progression of AD indicated that large potential cost offsets could occur for patients at the earliest stages of AD. CONCLUSIONS: AD progression is characterized by a small number of parameters governing changes in large numbers of correlated indicators of AD severity. The analysis confirmed that the progression of AD represents a complex multidimensional physiological process that is similar across different study cohorts. The estimates suggested that there could be large cost offsets to Medicare and Medicaid from the slowing of AD progression among patients with mild AD. The methodology appears generally applicable in AD modeling.Item Open Access Identification and utilization of arbitrary correlations in models of recombination signal sequences.(Genome Biol, 2002) Cowell, Lindsay G; Davila, Marco; Kepler, Thomas B; Kelsoe, GarnettBACKGROUND: A significant challenge in bioinformatics is to develop methods for detecting and modeling patterns in variable DNA sequence sites, such as protein-binding sites in regulatory DNA. Current approaches sometimes perform poorly when positions in the site do not independently affect protein binding. We developed a statistical technique for modeling the correlation structure in variable DNA sequence sites. The method places no restrictions on the number of correlated positions or on their spatial relationship within the site. No prior empirical evidence for the correlation structure is necessary. RESULTS: We applied our method to the recombination signal sequences (RSS) that direct assembly of B-cell and T-cell antigen-receptor genes via V(D)J recombination. The technique is based on model selection by cross-validation and produces models that allow computation of an information score for any signal-length sequence. We also modeled RSS using order zero and order one Markov chains. The scores from all models are highly correlated with measured recombination efficiencies, but the models arising from our technique are better than the Markov models at discriminating RSS from non-RSS. CONCLUSIONS: Our model-development procedure produces models that estimate well the recombinogenic potential of RSS and are better at RSS recognition than the order zero and order one Markov models. Our models are, therefore, valuable for studying the regulation of both physiologic and aberrant V(D)J recombination. The approach could be equally powerful for the study of promoter and enhancer elements, splice sites, and other DNA regulatory sites that are highly variable at the level of individual nucleotide positions.Item Open Access Importance sampling for the infinite sites model.(Statistical applications in genetics and molecular biology, 2008-01) Hobolth, Asger; Uyenoyama, Marcy K; Wiuf, CarstenImportance sampling or Markov Chain Monte Carlo sampling is required for state-of-the-art statistical analysis of population genetics data. The applicability of these sampling-based inference techniques depends crucially on the proposal distribution. In this paper, we discuss importance sampling for the infinite sites model. The infinite sites assumption is attractive because it constraints the number of possible genealogies, thereby allowing for the analysis of larger data sets. We recall the Griffiths-Tavaré and Stephens-Donnelly proposals and emphasize the relation between the latter proposal and exact sampling from the infinite alleles model. We also introduce a new proposal that takes knowledge of the ancestral state into account. The new proposal is derived from a new result on exact sampling from a single site. The methods are illustrated on simulated data sets and the data considered in Griffiths and Tavaré (1994).Item Open Access Lifetime cost-effectiveness analysis of ticagrelor in patients with acute coronary syndromes based on the PLATO trial: a Singapore healthcare perspective.(Singapore medical journal, 2013-03) Chin, Chee Tang; Mellstrom, Carl; Chua, Terrance Siang Jin; Matchar, David BruceIntroduction
Ticagrelor is a novel antiplatelet drug developed to reduce atherothrombosis. The PLATO trial compared ticagrelor and aspirin to clopidogrel and aspirin in patients with acute coronary syndromes (ACS). Ticagrelor was found to be superior in the primary composite endpoint of cardiovascular death, myocardial infarction or stroke, without increasing major bleeding events. The current study estimates the lifetime cost-effectiveness of ticagrelor relative to generic clopidogrel from a Singapore public healthcare perspective.Methods
This study used a two-part cost-effectiveness model. The first part was a 12-month decision tree (using PLATO trial data) to estimate the rates of major cardiovascular events, healthcare costs and health-related quality of life. The second part was a Markov model estimating lifetime quality-adjusted survival and costs conditional on events during the initial 12 months. Daily drug costs applied were SGD 1.05 (generic clopidogrel) and SGD 6.00 (ticagrelor). Cost per quality-adjusted life years (QALY) was estimated from a Singapore public healthcare perspective using life tables and short-term costs from Singapore, and long-term costs from South Korea. Deterministic and probabilistic sensitivity analyses were performed.Results
Ticagrelor was associated with a lifetime QALY gain of 0.13, primarily driven by lower mortality. The resulting incremental cost per QALY gained was SGD 10,136.00. Probabilistic sensitivity analysis indicated that ticagrelor had a > 99% probability of being cost-effective, given the lower recommended WHO willingness-to-pay threshold of one GDP/capita per QALY.Conclusion
Based on PLATO trial data, one-year treatment with ticagrelor versus generic clopidogrel in patients with ACS, relative to WHO reference standards, is cost-effective from a Singapore public healthcare perspective.Item Open Access Likelihoods from summary statistics: recent divergence between species.(Genetics, 2005-11) Leman, Scotland C; Chen, Yuguo; Stajich, Jason E; Noor, Mohamed AF; Uyenoyama, Marcy KWe describe an importance-sampling method for approximating likelihoods of population parameters based on multiple summary statistics. In this first application, we address the demographic history of closely related members of the Drosophila pseudoobscura group. We base the maximum-likelihood estimation of the time since speciation and the effective population sizes of the extant and ancestral populations on the pattern of nucleotide variation at DPS2002, a noncoding region tightly linked to a paracentric inversion that strongly contributes to reproductive isolation. Consideration of summary statistics rather than entire nucleotide sequences permits a compact description of the genealogy of the sample. We use importance sampling first to propose a genealogical and mutational history consistent with the observed array of summary statistics and then to correct the likelihood with the exact probability of the history determined from a system of recursions. Analysis of a subset of the data, for which recursive computation of the exact likelihood was feasible, indicated close agreement between the approximate and exact likelihoods. Our results for the complete data set also compare well with those obtained through Metropolis-Hastings sampling of fully resolved genealogies of entire nucleotide sequences.Item Open Access Modeling the evolution of regulatory elements by simultaneous detection and alignment with phylogenetic pair HMMs.(PLoS Comput Biol, 2010-12-16) Majoros, William H; Ohler, UweThe computational detection of regulatory elements in DNA is a difficult but important problem impacting our progress in understanding the complex nature of eukaryotic gene regulation. Attempts to utilize cross-species conservation for this task have been hampered both by evolutionary changes of functional sites and poor performance of general-purpose alignment programs when applied to non-coding sequence. We describe a new and flexible framework for modeling binding site evolution in multiple related genomes, based on phylogenetic pair hidden Markov models which explicitly model the gain and loss of binding sites along a phylogeny. We demonstrate the value of this framework for both the alignment of regulatory regions and the inference of precise binding-site locations within those regions. As the underlying formalism is a stochastic, generative model, it can also be used to simulate the evolution of regulatory elements. Our implementation is scalable in terms of numbers of species and sequence lengths and can produce alignments and binding-site predictions with accuracy rivaling or exceeding current systems that specialize in only alignment or only binding-site prediction. We demonstrate the validity and power of various model components on extensive simulations of realistic sequence data and apply a specific model to study Drosophila enhancers in as many as ten related genomes and in the presence of gain and loss of binding sites. Different models and modeling assumptions can be easily specified, thus providing an invaluable tool for the exploration of biological hypotheses that can drive improvements in our understanding of the mechanisms and evolution of gene regulation.Item Open Access Optimal management of Riata leads with no known electrical abnormalities or externalization: a decision analysis.(Journal of cardiovascular electrophysiology, 2015-02) Pokorney, Sean D; Zhou, Ke; Matchar, David B; Love, Sean; Zeitler, Emily P; Lewis, Robert; Piccini, Jonathan PIntroduction
Riata and Riata ST implantable cardioverter-defibrillator (ICD) leads (St. Jude Medical, Sylmar, CA, USA) can develop conductor cable externalization and/or electrical failure. Optimal management of these leads remains unknown.Methods and results
A Markov model compared 4 lead management strategies: (1) routine device interrogation for electrical failure, (2) systematic yearly fluoroscopic screening and routine device interrogation, (3) implantation of new ICD lead with capping of the in situ lead, and (4) implantation of new ICD lead with extraction of the in situ lead. The base case was a 64-year-old primary prevention ICD patient. Modeling demonstrated average life expectancies as follows: capping with new lead implanted at 134.5 months, extraction with new lead implanted at 134.0 months, fluoroscopy with routine interrogation at 133.9 months, and routine interrogation at 133.5 months. One-way sensitivity analyses identified capping as the preferred strategy with only one parameter having a threshold value: when risk of nonarrhythmic death associated with lead abandonment is greater than 0.05% per year, lead extraction is preferred over capping. A second-order Monte Carlo simulation (n = 10,000), as a probabilistic sensitivity analysis, found that lead revision was favored with 100% certainty (extraction 76% and capping 24%).Conclusions
Overall there were minimal differences in survival with monitoring versus active lead management approaches. There is no evidence to support fluoroscopic screening for externalization of Riata or Riata ST leads.Item Open Access Phylodynamic inference for structured epidemiological models.(PLoS Comput Biol, 2014-04) Rasmussen, David A; Volz, Erik M; Koelle, KatiaCoalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.Item Open Access Strategies for treating latent multiple-drug resistant tuberculosis: a decision analysis.(PLoS One, 2012) Holland, David P; Sanders, Gillian D; Hamilton, Carol D; Stout, Jason EBACKGROUND: The optimal treatment for latent multiple-drug resistant tuberculosis infection remains unclear. In anticipation of future clinical trials, we modeled the expected performance of six potential regimens for treatment of latent multiple-drug resistant tuberculosis. METHODS: A computerized Markov model to analyze the total cost of treatment for six different regimens: Pyrazinamide/ethambutol, moxifloxacin monotherapy, moxifloxacin/pyrazinamide, moxifloxacin/ethambutol, moxifloxacin/ethionamide, and moxifloxacin/PA-824. Efficacy estimates were extrapolated from mouse models and examined over a wide range of assumptions. RESULTS: In the base-case, moxifloxacin monotherapy was the lowest cost strategy, but moxifloxacin/ethambutol was cost-effective at an incremental cost-effectiveness ratio of $21,252 per quality-adjusted life-year. Both pyrazinamide-containing regimens were dominated due to their toxicity. A hypothetical regimen of low toxicity and even modest efficacy was cost-effective compared to "no treatment." CONCLUSION: In our model, moxifloxacin/ethambutol was the preferred treatment strategy under a wide range of assumptions; pyrazinamide-containing regimens fared poorly because of high rates of toxicity. Although more data are needed on efficacy of treatments for latent MDR-TB infection, data on toxicity and treatment discontinuation, which are easier to obtain, could have a substantial impact on public health practice.Item Open Access Three periods of regulatory innovation during vertebrate evolution.(Science (New York, N.Y.), 2011-08) Lowe, Craig B; Kellis, Manolis; Siepel, Adam; Raney, Brian J; Clamp, Michele; Salama, Sofie R; Kingsley, David M; Lindblad-Toh, Kerstin; Haussler, DavidThe gain, loss, and modification of gene regulatory elements may underlie a substantial proportion of phenotypic changes on animal lineages. To investigate the gain of regulatory elements throughout vertebrate evolution, we identified genome-wide sets of putative regulatory regions for five vertebrates, including humans. These putative regulatory regions are conserved nonexonic elements (CNEEs), which are evolutionarily conserved yet do not overlap any coding or noncoding mature transcript. We then inferred the branch on which each CNEE came under selective constraint. Our analysis identified three extended periods in the evolution of gene regulatory elements. Early vertebrate evolution was characterized by regulatory gains near transcription factors and developmental genes, but this trend was replaced by innovations near extracellular signaling genes, and then innovations near posttranslational protein modifiers.Item Open Access Tricuspid regurgitation and right ventricular function after mitral valve surgery with or without concomitant tricuspid valve procedure.(J Thorac Cardiovasc Surg, 2013-11) Desai, Ravi R; Vargas Abello, Lina Maria; Klein, Allan L; Marwick, Thomas H; Krasuski, Richard A; Ye, Ying; Nowicki, Edward R; Rajeswaran, Jeevanantham; Blackstone, Eugene H; Pettersson, Gösta BOBJECTIVES: To study the effect of mitral valve repair with or without concomitant tricuspid valve repair on functional tricuspid regurgitation and right ventricular function. METHODS: From 2001 to 2007, 1833 patients with degenerative mitral valve disease, a structurally normal tricuspid valve, and no coronary artery disease underwent mitral valve repair, and 67 underwent concomitant tricuspid valve repair. Right ventricular function (myocardial performance index and tricuspid annular plane systolic excursion) was measured before and after surgery using transthoracic echocardiography for randomly selected patients with tricuspid regurgitation grade 0, 1+, and 2+ (100 patients for each grade) and 93 with grade 3+/4+, 393 patients in total. RESULTS: In patients with mild (<3+) preoperative tricuspid regurgitation, mitral valve repair alone was associated with reduced tricuspid regurgitation and mild worsening of right ventricular function. Tricuspid regurgitation of 2+ or greater developed in fewer than 20%, and right ventricular function had improved, but not to preoperative levels, at 3 years. In patients with severe (3+/4+) preoperative tricuspid regurgitation, mitral valve repair alone reduced tricuspid regurgitation and improved right ventricular function; however, tricuspid regurgitation of 2+ or greater returned and right ventricular function worsened toward preoperative levels within 3 years. Concomitant tricuspid valve repair effectively eliminated severe tricuspid regurgitation and improved right ventricular function. Also, over time, tricuspid regurgitation did not return and right ventricular function continued to improve to levels comparable to that of patients with lower grades of preoperative tricuspid regurgitation. CONCLUSIONS: In patients with mitral valve disease and severe tricuspid regurgitation, mitral valve repair alone was associated with improved tricuspid regurgitation and right ventricular function. However, the improvements were incomplete and temporary. In contrast, concomitant tricuspid valve repair effectively and durably eliminated severe tricuspid regurgitation and improved right ventricular function toward normal, supporting an aggressive approach to important functional tricuspid regurgitation.