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Use of Bayesian Markov Chain Monte Carlo methods to model cost-of-illness data.

It is well known that the modeling of cost data is often problematic due to the distribution of such data. Commonly observed problems include 1) a strongly right-skewed data distribution and 2) a significant percentage of zero-cost observations. This article demonstrates how a hurdle model can be implemented from a Bayesian perspective by means of Markov Chain Monte Carlo simulation methods using the freely available software WinBUGS. Assessment of model fit is addressed through the implementation of two cross-validation methods. The relative merits of this Bayesian approach compared to the classical equivalent are discussed in detail. To illustrate the methods described, patient-specific non-health-care resource-use data from a prospective longitudinal study and the Norfolk Arthritis Register (NOAR) are utilized for 218 individuals with early inflammatory polyarthritis (IP). The NOAR database also includes information on various patient-level covariates.

Arthritis↗
PubMed1986

Forecasting the German population with Monte Carlo methods.

"This paper presents an approach of constructing confidence intervals by means of Monte Carlo simulation. This technique attempts to incorporate the uncertainty involved in projecting the [West] German population by letting the fertility, mortality and net immigration rates vary as a random variable with a specific distribution. Since fertility and migration are by far the most volatile, and therefore, the most critical components to population forecasting, this technique has the potential of accounting for this uncertainty, if the subjective distributions are specified with enough care."

Developed Countries↗
PubMed1988

Confidence intervals for population projections based on Monte Carlo methods.

"This paper presents an approach of constructing confidence intervals by means of Monte Carlo simulation. This technique attempts to incorporate the uncertainty involved in projecting human populations by letting the fertility and net immigration rates vary as a random variable with a specific distribution. Since fertility and migration are by far the most volatile, and therefore, the most critical components to population forecasting, this technique has the potential of accounting for this uncertainty, if the subjective distributions are specified with enough care. Considering the results of the model for the U.S. in 2082, for example, it is shown that the population will number between 255 million and 355 million with a probability of 90 percent."

Americas↗
PubMed2002

A DNA sequence evolution analysis generalized by simulation and the markov chain monte carlo method implicates strand slippage in a majority of insertions and deletions.

To study the mechanisms for local evolutionary changes in DNA sequences involving slippage-type insertions and deletions, an alignment approach is explored that can consider the posterior probabilities of alignment models. Various patterns of insertion and deletion that can link the ancestor and descendant sequences are proposed and evaluated by simulation and compared by the Markov chain Monte Carlo (MCMC) method. Analyses of pseudogenes reveal that the introduction of the parameters that control the probability of slippage-type events markedly augments the probability of the observed sequence evolution, arguing that a cryptic involvement of slippage occurrences is manifested as insertions and deletions of short nucleotide segments. Strikingly, approximately 80% of insertions in human pseudogenes and approximately 50% of insertions in murids pseudogenes are likely to be caused by the slippage-mediated process, as represented by BC in ABCD --> ABCBCD. We suggest that, in both human and murids, even very short repetitive motifs, such as CAGCAG, CACACA, and CCCC, have approximately 10- to 15-fold susceptibility to insertions and deletions, compared to nonrepetitive sequences. Our protocol, namely, indel-MCMC, thus seems to be a reasonable approach for statistical analyses of the early phase of microsatellite evolution.

Base Sequence↗
PubMed2005

Diffusion Monte Carlo method with lattice regularization.

We introduce an efficient lattice regularization scheme for quantum Monte Carlo calculations of realistic electronic systems. The kinetic term is discretized by a finite difference Laplacian with two mesh sizes, a and a', chosen so that the electrons can diffuse in a configuration space which is in practice indistinguishable from the continuum, and the different length scales in the system can be efficiently taken in account. The regularized Hamiltonian goes to the continuous limit for a --> 0 and allows the inclusion of nonlocal potentials in a consistent variational scheme, substantially improving the accuracy upon previous nonvariational approaches.

Journal Article↗
PubMed2005

Comparison of deterministic and Monte Carlo methods in shielding design.

In shielding calculation, deterministic methods have some advantages and also some disadvantages relative to other kind of codes, such as Monte Carlo. The main advantage is the short computer time needed to find solutions while the disadvantages are related to the often-used build-up factor that is extrapolated from high to low energies or with unknown geometrical conditions, which can lead to significant errors in shielding results. The aim of this work is to investigate how good are some deterministic methods to calculating low-energy shielding, using attenuation coefficients and build-up factor corrections. Commercial software MicroShield 5.05 has been used as the deterministic code while MCNP has been used as the Monte Carlo code. Point and cylindrical sources with slab shield have been defined allowing comparison between the capability of both Monte Carlo and deterministic methods in a day-by-day shielding calculation using sensitivity analysis of significant parameters, such as energy and geometrical conditions.

Algorithms↗
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↗
PubMed1980

Verification by Monte Carlo methods of a power law tissue-air ratio algorithm for inhomogeneity corrections in photon beam dose calculations.

A Monte Carlo computer program has been used to calculate axial and off-axis depth dose distributions arising from the interaction of an external beam of 60Co radiation with a medium containing inhomogeneities. An approximation for applying the Monte Carlo data to the configuration where the lateral extent of the inhomogeneity is less than the beam area, is also presented. These new Monte Carlo techniques rely on integration over the dose distributions from constituent sub-beams of small area and the accuracy of the method is thus independent of beam size. The power law correction equation (Batho equation) describing the dose distribution in the presence of tissue inhomogeneities is derived in its most general form. By comparison with Monte Carlo reference data, the equation is validated for routine patient dosimetry. It is explained why the Monte Carlo data may be regarded as a fundamental reference point in performing these tests of the extension to the Batho equation. Other analytic correction techniques, e.g. the equivalent radiological path method, are shown to be less accurate. The application of the generalised power law equation in conjunction with CT scanner data is discussed. For ease of presentation, the details of the Monte Carlo techniques and the analytic formula have been separated into appendices.

Cobalt Radioisotopes↗
PubMed2001

Backscatter factors for mammography calculated with Monte Carlo methods.

The objective of this study is to establish a comprehensive set of backscatter factors for mammography based on the exposure model proposed by the European Protocol on Dosimetry in Mammography. The Monte Carlo calculated backscatter factors (BSFs) presented in this study are for various exposure conditions encountered in mammographic practice as well as in calibration procedures. The data demonstrate the variation of the BSF as a function of the exposure parameters, hence enabling a better match with calibration conditions and, at the same time, reviewing the BSF data already recommended by the European Protocol. Furthermore, earlier data for BSF for general diagnostic radiology are validated.

Calibration↗
PubMed1997

Markov chain Monte Carlo methods for radiation hybrid mapping.

The ordering of genetic loci is central to genetic mapping at all levels. Markov chain Monte Carlo (MCMC) techniques can provide estimates of the posterior density of orders while accounting naturally for missing data, data errors, and unknown parameters. MCMC sampling schemes have been proposed for mapping problems such as linkage mapping and radiation hybrid mapping. The sampling schemes tend, however, to suffer from poor mixing caused by strong correlations between the model parameters. The method described here investigates the effect of using a modified sampling scheme, simulated tempering, on the mixing characteristics of the Markov chain. The method is illustrated by the analysis of haploid radiation hybrid mapping data; the principles are, however, applicable to a range of mapping problems. The results demonstrate that simulated tempering greatly improves the performance of the MCMC sampling scheme. For the radiation hybrid problem, the approach is probably not suitable for simultaneously ordering very large number of loci (> 100); it could, however, be useful for fine scale mapping of subsections of chromosomes.

Algorithms↗
PubMed1999

Significance testing of clinical data using virus dynamics models with a Markov chain Monte Carlo method: application to emergence of lamivudine-resistant hepatitis B virus.

Bayesian analysis using a virus dynamics model is demonstrated to facilitate hypothesis testing of patterns in clinical time-series. Our Markov chain Monte Carlo implementation demonstrates that the viraemia time-series observed in two sets of hepatitis B patients on antiviral (lamivudine) therapy, chronic carriers and liver transplant patients, are significantly different, overcoming clinical trial design differences that question the validity of non-parametric tests. We show that lamivudine-resistant mutants grow faster in transplant patients than in chronic carriers, which probably explains the differences in emergence times and failure rates between these two sets of patients. Incorporation of dynamic models into Bayesian parameter analysis is of general applicability in medical statistics.

Antiviral Agents↗