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Results for “Monte Carlo Method”

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PubMed2004

Hierarchical models for tumor xenograft experiments in drug development.

In cancer drug development, demonstrated anticancer activity in animal models is an important step to bring a promising compound to clinic. Proper design and analysis of experiments using laboratory animals have received increasing attention recently. These experiments involve informatively censored longitudinal data with small samples. The problem is further complicated because of order constraints due to the intrinsic growth of control tumors without treatment. This article proposes a Bayesian hierarchical model to analyze informatively censored longitudinal data while accounting for the parameter constraints and providing valid small sample inference. We adopt a noniterative sampling approach, the inverse Bayes formulae (IBF) sampler, to generate independent posterior samples, which avoids convergence problems associated with Markov chain Monte-Carlo methods. To effectively deal with the restricted parameter problem, we use a linear transformation to simplify the constraints and exploit the IBF method to generate random samples from truncated multivariate normal distributions. Because diffuse priors are used, the posterior modes approximate the maximum likelihood estimates well, and the hierarchical model can be considered as an extended mixed-effects model. A real xenograft experiment on a new treatment is analyzed by using the proposed method.

Algorithms↗

PubMed2001

Absolute activity quantitation in simultaneous 123I/99mTc brain SPECT.

UNLABELLED: Dual-isotope imaging can allow simultaneous assessment of brain perfusion using a 99mTc-labeled tracer and neurotransmission using an 123I-labeled tracer. However, the images are affected by scatter, cross talk, attenuation, distance-dependent collimator response (DCR), and partial-volume effect. We determined the accuracy and precision of activity quantitation in simulated normal and pathologic studies of simultaneous 123I/99mTc brain SPECT when compensating for all degrading phenomena. METHODS: Monte Carlo simulations were performed using the Zubal brain phantom. Contamination caused by high-energy 123I decay photons was incorporated. Twenty-four 99mTc and 123I activity distributions were simulated on the basis of normal and pathologic patient activity distributions. Cross talk and scatter were corrected using a new method based on a multilayer perceptron artificial neural network (ANN), as well as by the asymmetric window (AW) approach; for comparison, unscattered (U) photons of 99mTc and 123I were recorded. Nonuniform attenuation and DCR were modeled in an iterative ordered-subset expectation maximization (OSEM) algorithm. Mean percentage biases and SDs over the 12 normal and 12 pathologic simulated studies were computed for each structure with respect to the known activity distributions. RESULTS: For 123I, AW + OSEM yielded a bias of 7% in the cerebellum, 21% in the frontal cortex, and 36% in the corpus callosum in the simulated normal population. The bias was increased significantly in the striata of simulated pathologic studies (P < 0.05). The bias associated with ANN was significantly lower (<9% in these brain structures, P < 0.05). For 99mTc with AW + OSEM, the bias was 60% in the corpus callosum, 36% in the striata, and 18%-22% in the cortical lobes in the simulated normal population. This bias was <11% in all brain structures with ANN. In the simulated pathologic population, the bias associated with AW increased significantly in the cortical lobes to 55% (P < 0.05), although it did not change significantly with ANN. CONCLUSION: The accuracy and variability over simulated normal and pathologic studies of both 99mTc and 123I activity estimates were very close with ANN to those obtained with U + OSEM. ANN + OSEM is a promising approach for absolute activity quantitation in simultaneous 99mTc/123I SPECT.

Alzheimer Disease↗

PubMed1993

Monte Carlo analysis on a large pedigree.

Monte Carlo methods for linkage and segregation analysis are applied to the HGAR1 pedigree. To address these data, the methods are extended in several ways. The results are compared with those provided by PAP.

Adolescent↗

PubMed2000

A Monte Carlo procedure for two-stage tests with correlated data.

One strategy for mapping disease loci using marker-disease associations is to test for association with case-control samples and follow up a positive result with a family-based test. Using a family-based test in the second stage can help provide protection against false-positive results that can result from use of inappropriate controls and provides assurance that association identified in the first stage is occurring between linked loci. It is crucial for this two-stage strategy that the first stage be as powerful as possible to detect association since only positive results are tested in the second stage. In certain situations, the power of the first-stage test can be increased by combining the case-control and family data. However, this introduces correlation between the first- and second-stage tests, and treating them as independent tests causes a bias. Here we propose a Monte Carlo method that accounts for the correlation and provides the correct significance level for the second-stage test. We also discuss the use of a two-stage procedure when doing a genome scan for the data presented in the Genetic Analysis Workshop 9 study.

Genetic Markers↗

PubMed2004

MCMC for hidden Markov models incorporating aggregation of states and filtering.

This paper is concerned with the statistical analysis of single ion channel records. Single channels are modelled by using hidden Markov models and a combination of Bayesian statistics and Markov chain Monte Carlo methods. The techniques presented here provide a straightforward generalization to those in Rosales et al. (2001, Biophys. J., 80, 1088-1103), allowing to consider constraints imposed by a gating mechanism such as the aggregation of states into classes. This paper also presents an extension that allows to consider correlated background noise and filtered data, extending the scope of the analysis toward real experimental conditions. The methods described here are based on a solid probabilistic basis and are less computationally intensive than alternative Bayesian treatments or frequentist approaches that consider correlated data.

Bayes Theorem↗

PubMed1996

Quasilikelihood estimation in measurement error models with correlated replicates.

We consider quasilikelihood models when some of the predictors are measured with error. In many cases, the true but fallible predictor is impossible to measure, and the best one can do is to obtain replicates of the fallible predictor. We consider the case that the replicates are not independent. If one assumes that replicates are independent and they are not, one typically underestimates the extent of the measurement error, leading to an inconsistent errors in variables correction. We devise techniques for estimating the measurement error covariance matrix. In addition, we discuss how one might perform a quasilikelihood analysis by computing the mean and variance functions of the observed data, both using approximations and also exactly through a Monte Carlo method. The methods are illustrated on a data set involving systolic blood pressure and urinary sodium chloride, where the measurement errors appear to be approximately normally distributed but highly correlated, and the distribution of the true predictor is reasonably modeled as a mixture of normals.

Analysis of Variance↗

PubMed2000

Russian roulette efficiency in Monte Carlo resonant absorption calculations

The resonant absorption calculation in media containing heavy resonant nuclei is one of the most difficult problems treated in reactor physics. Deterministic techniques need many approximations to solve this kind of problem. On the other hand, the Monte Carlo method is a reliable mathematical tool for evaluating the neutron resonance escape probability. But it suffers from large statistical deviations of results and long computation times. In order to overcome this problem, we have used the Splitting and Russian Roulette technique coupled separately to the survival biasing and to the importance sampling for the energy parameter. These techniques have been used to calculate the neutron resonance absorption in infinite homogenous media containing hydrogen and uranium characterized by the dilution (ratio of the concentrations of hydrogen to uranium). The punctual neutron source energy is taken at Es = 2 MeV and Es = 676.45 eV, whereas the energy cut-off is fixed at Ec = 2.768 eV. The results show a large reduction of computation time and statistical deviation, without altering the mean resonance escape probability compared to the usual analog simulation. The Splitting and Russian Roulette coupled to the survival biasing method is found to be the best methods for studying the neutron resonant absorption, particularly for high energies. A comparison is done between the Monte Carlo and deterministic methods based on the numerical solution of the neutron slowing down equations by the iterative method results for several dilutions.

Journal Article↗

PubMed2005

Bayesian inference for psychometric functions.

In psychophysical studies, the psychometric function is used to model the relation between physical stimulus intensity and the observer's ability to detect or discriminate between stimuli of different intensities. In this study, we propose the use of Bayesian inference to extract the information contained in experimental data to estimate the parameters of psychometric functions. Because Bayesian inference cannot be performed analytically, we describe how a Markov chain Monte Carlo method can be used to generate samples from the posterior distribution over parameters. These samples are used to estimate Bayesian confidence intervals and other characteristics of the posterior distribution. In addition, we discuss the parameterization of psychometric functions and the role of prior distributions in the analysis. The proposed approach is exemplified using artificially generated data and in a case study for real experimental data. Furthermore, we compare our approach with traditional methods based on maximum likelihood parameter estimation combined with bootstrap techniques for confidence interval estimation and find the Bayesian approach to be superior.

Bayes Theorem↗

PubMed2005

Estimation of amino acid residue substitution rates at local spatial regions and application in protein function inference: a Bayesian Monte Carlo approach.

The amino acid sequences of proteins provide rich information for inferring distant phylogenetic relationships and for predicting protein functions. Estimating the rate matrix of residue substitutions from amino acid sequences is also important because the rate matrix can be used to develop scoring matrices for sequence alignment. Here we use a continuous time Markov process to model the substitution rates of residues and develop a Bayesian Markov chain Monte Carlo method for rate estimation. We validate our method using simulated artificial protein sequences. Because different local regions such as binding surfaces and the protein interior core experience different selection pressures due to functional or stability constraints, we use our method to estimate the substitution rates of local regions. Our results show that the substitution rates are very different for residues in the buried core and residues on the solvent-exposed surfaces. In addition, the rest of the proteins on the binding surfaces also have very different substitution rates from residues. Based on these findings, we further develop a method for protein function prediction by surface matching using scoring matrices derived from estimated substitution rates for residues located on the binding surfaces. We show with examples that our method is effective in identifying functionally related proteins that have overall low sequence identity, a task known to be very challenging.

Amino Acid Substitution↗

PubMed1979

Statistical mechanics of supercoils and the torsional stiffness of the DNA double helix.

The distribution of closed unknotted polymer chains over the writhing number is calculated by the Monte-Carlo method. For circular duplex DNA the variance of the distribution equals approximately half the observed variance of equilibrium distribution over the linking number. The balance which arises from fluctuations in DNA twisting makes it possible to estimate the torsional stiffness of the double helix.

DNA, Superhelical↗

PubMed2004

Multiple "time step" Monte Carlo simulations: application to charged systems with Ewald summation.

Recently, we have proposed an efficient scheme for Monte Carlo simulations, the multiple "time step" Monte Carlo (MTS-MC) [J. Chem. Phys. 117, 8203 (2002)] based on the separation of the potential interactions into two additive parts. In this paper, the structural and thermodynamic properties of the simple point charge water model combined with the Ewald sum are compared for the MTS-MC real-/reciprocal-space split of the Ewald summation and the common Metropolis Monte Carlo method. We report a number of observables as a function of CPU time calculated using MC and MTS-MC. The correlation functions indicate that speedups on the order of 4.5-7.5 can be obtained for systems of 108-500 waters for n=10 splitting parameter.

Algorithms↗

PubMed1986

Monte Carlo calculations of order parameter profiles in models of lipid-protein interactions in bilayers.

The Monte Carlo method has been utilized to calculate lipid chain order parameters in model monomolecular layers (half-bilayers) containing several different model polypeptides. The systems all consist of a periodic array of identical cells, each containing 35 hydrocarbon chains and 1 "perturbant" (a small model polypeptide or protein). The lipid chains are each 10 CH2 subunits long, have one end constrained to lie in the bilayer plane, and interact via van der Waals forces between all subunits. The chains also interact with the perturbant via van der Waals forces. With standard Monte Carlo procedures order parameter profiles are calculated for chains that are close to the perturbant and for the nonneighboring chains. In order to examine a wide range of possibilities, several different model polypeptides are considered: (i) a rigid smooth cylinder, (ii) a cylinder with identical side chains at alpha-helical positions, (iii) a cylinder with nonidentical side chains at alpha-helical positions, and (iv) a cylinder identical with (ii) but which only extends about halfway through the monolayer. Although results differ for the different systems studied, in all cases only slight conformational differences between the bulk chains and the chains that are nearest the perturbants are found, and it is not possible to characterize the boundary chains as "more ordered" or "less ordered" than the nonboundary chains.

Lipid Bilayers↗

PubMed1997

Monte Carlo calculated stopping-power ratios, water/air, for clinical proton dosimetry (50-250 MeV).

Calculations of stopping power ratios, water to air, for the determination of absorbed dose to water in clinical proton beams using ionization chamber measurements have been undertaken using the Monte Carlo method. A computer code to simulate the transport of protons in water (PETRA) has been used to calculate sw.air-data under different degrees of complexity, ranging from values based on primary protons only to data including secondary electrons and high-energy secondary protons produced in nonelastic nuclear collisions. All numerical data are based on ICRU 49 proton stopping powers. Calculations using primary protons have been compared to the simple continuous slowing-down approximation (c.s.d.a.) analytical technique used in proton dosimetry protocols, not finding significant differences that justify elaborate Monte Carlo simulations except beyond the mean range of the protons (the far side of the Bragg peak). The influence of nuclear nonelastic processes, through the detailed generation and transport of secondary protons, on the calculated stopping-power ratios has been found to be negligible. The effect of alpha particles has also been analysed, finding differences smaller than 0.1% from the results excluding them. Discrepancies of up to 0.6% in the plateau region have been found, however, when the production and transport of secondary electrons are taken into account. The large influence of nonelastic nuclear interactions on proton depth-dose distributions shows that the removal of primary protons from the incident beam decreases the peak-to-plateau ratio by a large factor, up to 40% at 250 MeV. It is therefore emphasized that nonelastic nuclear reactions should be included in Monte Carlo simulations of proton beam depth-dose distributions.

Air↗

PubMed2003

Absorbed fraction of alpha-particles emitted in bifurcation regions of the human tracheo-bronchial tree.

A model for bifurcation regions of the human tracheo-bronchial tree was developed. Equations for the surfaces are given to enable calculations of doses from alpha-particles emitted in these regions. It has been found that a bifurcation region is well approximated by a quasi-ellipsoid. The absorbed fractions of alpha-particles emitted in bifurcation regions were calculated by the Monte Carlo method. The average absorbed fraction under the bifurcation geometry is close to that found under the cylindrical geometry in the bronchial region. In the bronchiolar region, the absorbed fractions under the bifurcation geometry are up to 20% larger than those under the cylindrical geometry.

Air Pollutants, Radioactive↗

PubMed1996

Proximity effects for chromosome aberrations measured by FISH.

A Monte Carlo simulation computer program for radiation-produced chromosome aberrations, based on the breakage-and-reunion model, was extended to include proximity effects due to localization of chromosomes and limited range for break-break interactions. Two adjustable parameters were used. One corresponds to total dose: the other determines proximity effects by specifying the number of 'interaction regions' in a cell nucleus. The use of additional adjustable parameters was avoided by assuming randomness of break induction and aberration production. FISH chromosome painting data were obtained from 1.9 Gy 60Co gamma-rays-irradiated human lymphocytes. The data were compared with the computer simulation results, taking individual chromosome lengths into account. With about 13 interaction regions, agreement between the experiment and the simulation was good, even when detailed categories of damage were scored. An estimated average dsb-dsb interaction distance, based on 13 interaction regions, is about 1.3 micron. Monte Carlo methods give useful quantitative estimates of relative aberration yields, with a minimum of adjustable parameters and the theoretical assumptions, and indicated proximity effects. Computer simulation of FISH experiments can be adapted to any number of colours, any scoring criteria and any method of grouping aberrations into categories. Simulation allows systematic extrapolation of aberration data on painted chromosomes to whole-genome aberration frequencies.

Chromosome Aberrations↗

PubMed2002

Grid and slot scan scatter reduction in mammography: comparison by using Monte Carlo techniques.

PURPOSE: To evaluate a comprehensive array of scatter cleanup techniques in mammography by using a consistent methodology. MATERIALS AND METHODS: Monte Carlo techniques were used to evaluate the Bucky factor (BF) and the contrast improvement factor (CIF) for linear and cellular grids and for slot scan and scanning multiple-slot assembly (SMSA) systems. RESULTS: For a 28-kVp molybdenum anode-molybdenum filter spectrum with a standard detector and a 6-cm-thick 50% adipose-50% glandular breast phantom, slot scan techniques delivered an ideal BF. For slot widths greater than 4 mm, however, the CIF was lower than that achieved by the high-transmission cellular grid with a grid ratio of 3.8:1. A tungsten-septa air-interspaced cellular grid with a 4:1 grid ratio outperformed the high-transmission cellular grid in both BF and CIF. The SMSA was shown to be efficacious when 4-mm-wide slots were separated by at least 20 mm. In comparison with the literature, 3.6% agreement was achieved with other Monte Carlo studies, 3.3% with an experimental study that used a digital detector, and 13%-29% agreement was demonstrated in comparison to film-based experimental studies. CONCLUSION: With use of consistent methods for comparison, cellular grids were shown to substantially outperform linear grids but have slightly higher BFs compared with that of slot scan geometries at the same CIF.

Mammography↗

PubMed2004

Dosimetric study of the 15 mm ROPES eye plaque.

The main aim of this paper is to make a study of dose-rate distributions obtained around the 15 mm, radiation oncology physics and engineering services, Australia (ROPES) eye plaque loaded with 125I model 6711 radioactive seeds. In this study, we have carried out a comparison of the dose-rate distributions obtained by the algorithm used by the Plaque Simulator (PS) (BEBIG GmbH, Berlin, Germany) treatment planning system with those obtained by means of the Monte Carlo method for the ROPES eye plaque. A simple method to obtain the dose-rate distributions in a treatment planning system via the superposition of the dose-rate distributions of a seed placed in the eye plaque has been developed. The method uses eye plaque located in a simplified geometry of the head anatomy and distributions obtained by means of the Monte Carlo code GEANT4. The favorable results obtained in the development of this method suggest that it could be implemented on a treatment planning system to improve dose-rate calculations. We have also found that the dose-rate falls sharply along the eye and that outside the eye the dose-rate is very low. Furthermore, the lack of backscatter photons from the air located outside the eye-head phantom produces a dose reduction negligible for distances from the eye-plaque r<1 cm but reaches up to 20% near the air-eye interface. Results showed that the treatment planning system lacks accuracy around the border of the eye (in the sclera and the surrounding area) due to the simplicity of the algorithm used. The BEBIG treatment planning system uses a global attenuation factor that takes into account the effect of the eye plaque seed carrier and the lack of backscatter photons caused by the metallic cover, which in the case of a ROPES eye plaque has a default value of T= 1 (no correction). In the present study, a global attenuation factor T=0.96 and an air-interface correction factor which improve on treatment planning system calculations were obtained.

Brachytherapy↗

PubMed1996

Maximizing accuracy and precision using individual and grouped exposure assessments.

OBJECTIVES: Random errors in exposure data were explored to determine their effect on exposure-response relationships using individual, grouped, or combined (grouped and individual) exposure assessment methods. METHODS: Monte Carlo simulations were conducted by generating small "studies" of one hundred subjects divided into four exposure groups. Observed exposure data were generated for each individual using assumed inter- and intraindividual variances and a lognormal distribution. The data were used to calculate the following three estimates of exposure: an individual mean, a group mean, and a hybrid estimate using the James-Stein shrinkage estimator. The exposure estimates were regressed on generated (continuous) "health outcomes," and the regression results were stored and analyzed. RESULTS: Random errors in exposure data resulted in attenuation of the exposure-response relationship when the individual estimates were used, especially when the within-subject variability was high. The attenuation was substantially controlled by the group mean estimate, however, at a cost of decreased precision. The hybrid estimator simultaneously controlled both bias and imprecision in the observed exposure-response function. CONCLUSIONS: While estimates of exposure based on individual means may result in attenuation of the exposure-response relationship, grouped estimates may control bias while decreasing precision. Combining individual and group estimates can simultaneously control both types of error. However, further research is required to determine how robust these findings are to different error structures, grouping strategies, exposure-response models, and exposure assessment methods.

Bias↗