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At least 793 records · Page 44Linked to original sources
PubMed2003

The linear-quadratic model and fractionated stereotactic radiotherapy.

PURPOSE: To determine the dose per fraction that could be used when gamma knife or linear accelerator-based stereotactic treatments are delivered in 2 or more fractions. METHODS AND MATERIALS: The linear-quadratic (LQ) model was used to calculate the dose per fraction for a multiple-fraction regimen which is biologically equivalent to a given single-fraction treatment. The results are summarized in lookup tables. RESULTS AND CONCLUSION: The tables can be used by practicing clinicians as a guide in planning fractionated treatment. For the large doses used in typical stereotactic treatments and for small fraction numbers, the model is not very sensitive to the value of the alpha/beta ratio in the LQ model. A simple rule of thumb is found that for two-fraction and three-fraction treatments the dose per fraction is roughly two-thirds and one-half of the single-fraction treatment dose, respectively.

Linear Models↗
PubMed2006

A general bilinear model to describe growth or decline time profiles.

Linear models are widely used because of their unrivaled simplicity, but they cannot be applied for data that have a turning-or rate-change-point, even if the data show good linearity sufficiently far from this point. To describe such bilinear-type data, a completely generalized version of a linearized biexponential model (LinBiExp) is proposed here to make possible smooth and fully parametrizable transitions between two linear segments while still maintaining a clear connection with the linear models. Applications and brief conclusions are presented for various time profiles of biological and medical interest including growth profiles, such as those of human stature, agricultural crops and fruits, multicellular tumor spheroids, single fission yeast cells, or even labor productivity, and decline profiles, such as age-effects on cognition in patients who develop dementia and lactation yields in dairy cattle. In all these cases, quantitative model selection criteria such as the Akaike and the Schwartz Bayesian information criteria indicated the superiority of the bilinear model compared to adequate less parametrized alternatives such as linear, parabolic, exponential, or classical growth (e.g., logistic, Gompertz, Weibull, and Richards) models. LinBiExp provides a versatile and useful five-parameter bilinear functional form that is convenient to implement, is suitable for full optimization, and uses intuitive and easily interpretable parameters.

Adolescent↗
PubMed2006

Tutorial in biostatistics: Analyzing associations between total plasma homocysteine and B vitamins using optimal categorization and segmented regression.

Data analysts consider standard regression models (e.g., generalized linear model) or nonparametric smoothing techniques (e.g., loess or splines) when examining the association between two variables. Before this step, a quantile-based summarization is typically used for exploring the exposure-response relationship. Unfortunately, these exploratory approaches may not be optimal or efficient for guiding the formal analysis in many biological and nutritional data settings. We suggest a recently developed method for selection of cutpoints as a tool of data summary and segmented regression as a modeling approach in the analysis of plasma total homocysteine and related vitamins. These methods are often complementary in discovering the underlying complex pattern of association.

Algorithms↗
PubMed2003

The hemodynamic impulse response to a single neural event.

This article investigates the relation between stimulus-evoked neural activity and cerebral hemodynamics. Specifically, the hypothesis is tested that hemodynamic responses can be modeled as a linear convolution of experimentally obtained measures of neural activity with a suitable hemodynamic impulse response function. To obtain a range of neural and hemodynamic responses, rat whisker pad was stimulated using brief (</=2 seconds) electrical stimuli consisting of single pulses (0.3 millisecond, 1.2 mA) combined both at different frequencies and in a paired-pulse design. Hemodynamic responses were measured using concurrent optical imaging spectroscopy and laser Doppler flowmetry, whereas neural responses were assessed through current source density analysis of multielectrode recordings from a single barrel. General linear modeling was used to deconvolve the hemodynamic impulse response to a single "neural event" from the hemodynamic and neural responses to stimulation. The model provided an excellent fit to the empirical data. The implications of these results for modeling schemes and for physiologic systems coupling neural and hemodynamic activity are discussed.

Animals↗
PubMed1999

Genetic variance components analysis for binary phenotypes using generalized linear mixed models (GLMMs) and Gibbs sampling.

The common complex diseases such as asthma are an important focus of genetic research, and studies based on large numbers of simple pedigrees ascertained from population-based sampling frames are becoming commonplace. Many of the genetic and environmental factors causing these diseases are unknown and there is often a strong residual covariance between relatives even after all known determinants are taken into account. This must be modelled correctly whether scientific interest is focused on fixed effects, as in an association analysis, or on the covariances themselves. Analysis is straightforward for multivariate Normal phenotypes, but difficulties arise with other types of trait. Generalized linear mixed models (GLMMs) offer a potentially unifying approach to analysis for many classes of phenotype including multivariate Normal traits, binary traits, and censored survival times. Markov Chain Monte Carlo methods, including Gibbs sampling, provide a convenient framework within which such models may be fitted. In this paper, Bayesian inference Using Gibbs Sampling (a generic Gibbs sampler; BUGS) is used to fit GLMMs for multivariate Normal and binary phenotypes in nuclear families. BUGS is easy to use and readily available. We motivate a suitable model structure for Normal phenotypes and show how the model extends to binary traits. We discuss parameter interpretation and statistical inference and show how to circumvent a number of important theoretical and practical problems that we encountered. Using simulated data we show that model parameters seem consistent and appear unbiased in smaller data sets. We illustrate our methods using data from an ongoing cohort study.

Binomial Distribution↗
PubMed2003

Theory of the lattice Boltzmann method: three-dimensional model for linear viscoelastic fluids.

A three-dimensional lattice Boltzmann model with thirty two discrete velocity distribution functions for viscoelastic fluid is presented in this work. The model is based upon the generalized lattice Boltzmann equation constructed in moment space. The nonlinear equilibria of the model have a number of coupling constants that are free parameters. The dispersion equation of the model is analyzed under various conditions to obtain the constraints on the free parameters such that the model satisfies isotropy and Galilean invariance. The macroscopic equations are also derived from the lattice Boltzmann model through the dispersion equation analysis and the Chapman-Enskog analysis. We demonstrate that the dispersion equation analysis can be used as a general and effective means to derive hydrodynamic equations, excluding some nonlinear source terms, from the lattice Boltzmann model, to obtain conditions for its isotropy and Galilean invariance, and to optimize its stability. We show that the hydrodynamic behavior of the lattice Boltzmann model has memory effects, and that in the linear regime, it behaves as a viscoelastic fluid described by the Jeffreys model. Some numerical results to verify the theoretical analysis of the model are also presented.

Journal Article↗
PubMed1991

A linear-quadratic model of cell survival considering both sublethal and potentially lethal radiation damage.

We assessed the dose-dependence of repair of potentially lethal damage in Chinese hamster ovary cells x-irradiated in vitro. The recovery ratio (RR) by which survival (SF) of the irradiated cells was enhanced increased exponentially with a linear and a quadratic component, namely xi and psi: RR = e xi D + psi D2. Survival of irradiated cells can thus be expressed by a combined linear-quadratic model considering four variable, namely alpha and beta for the capacity of the cells to accumulate sublethal damage, and xi and psi for their capacity to repair potentially lethal damage: SF = e(xi - alpha)D + (psi - beta)D2.

Animals↗
PubMed1995

Estimation of risk of developing bladder cancer among workers exposed to coal tar pitch volatiles in the primary aluminum industry.

To confirm the relationship between exposure to coal tar pitch volatiles and bladder cancer among primary aluminum production workers, we carried out a case-control study among blue-collar workers who had worked more than 1 year between 1950-1979 in a major plant using mostly the Soderberg process in the Province of Québec. Cases of bladder cancer (ICD code 188) diagnosed between 1970-1979 (n = 69) were mostly included in a previously reported study. To these were added cases diagnosed between 1980-1988 (n = 69). Each case was matched to three controls on date of birth, date of hiring, and length of service at the company. Smoking habits were assessed from the medical records at the company. Benzene-soluble matter (BSM) and benzo(a)pyrene (BaP) were used as indicators of environmental exposure to coal tar pitch volatiles in the workplace. The estimated risk for current smokers was 2.63 (95% C.I. 1.29-5.37). Estimates of risk by occupational exposure were adjusted for smoking. Men who had worked in the Soderberg potrooms were at higher risk of developing the disease, the risk increasing with the time spent in these departments. Similarly, a strong association between risk and cumulative exposure to BSM or to BaP was observed. The risks associated with cumulative exposure to BSM (mg/m3-years) and to BaP (microgram/m3-years) were described with mathematical models. Using a linear model (1 + bx) and lagging 10 years before the diagnosis, BaP cumulative exposure was a better indicator of risk than BSM cumulative exposure. The risk for each year of exposure to BaP at a concentration of 1 microgram/m3 increased by 1.7% (0.8%-3.2%). Using the same model for BSM, a worker exposed to the current threshold limit value of 0.2 mg/m3 for 40 years will sustain a risk of 2.22 (1.56-3.48). Comparison of risks according to different periods of diagnosis (1970-1979 vs. 1980-1988) did not reveal any significant temporal changes on risk estimates.

Air Pollutants, Occupational↗
PubMed2005

[Methodology of mapping quantitative trait loci for discrete traits using maximum likelihood].

The maximum likelihood method was used to compare the efficiency of interval mapping with either the threshold model or the linear model. The irfluencing factors of quantitative trait loci (QTL) detection efficiency (e.g. QTL effect, heritability and incidence of categories) were simulated in our study. Daughter design with multiple families was applied, and the number of segregating population was 500. The results showed that the threshold model was superior in terms of parameter estimation. It was a more efficient and accurate model of QTL mapping for discrete traits. In addition, the accuracy of QTL mapping depended on the effect of the putative QTL, the value of heritability and incidence directly. With an increase of QTL effect, heritability and incidence of categories, the accuracy of QTL mapping improved correspondingly.

Algorithms↗
PubMed1998

[Models of arterial pressure using a Windkessel type model: role of the functional arterial properties].

UNLABELLED: The Windkessel model is a linear model which does not take into account the structural and functional variations of the arteries related to the pulsatility of the blood pressure (BP) and its variations between systole and diastole. OBJECTIVE: To analyse the performance of a BP modelisation where the parameters of AC are adjusted in a dynamic fashion according to a curvilinear relationship of the arterial properties (compliance) in relationship to the BP between systole and diastole. DESIGN AND METHODS: 9 control subjects (age 25 +/- 3). The non invasive measures of the radial BP waveform (Millar tonometry) was compared to that constructed by an electric simulator reproducing the model in a sysmetrical network subdivised into 121 segments where we introduced for each subject: at cardiac level, the aortic stroke volume (Doppler echocardiography), and at the radial level, the dynamic values of compliance and diameter according to an arc-tangent model (measured by arterial echography NiUS02). RESULTS: The BP obtained by the adjusted model, where the AC parameter follows the curvilinear, relationship dV/dP measured experimentally, was not significantly different from the experimental, while in the constant model (AC at mean BP level) the systolic BP was different. CONCLUSION: This work shows in an experimental way the limits inherent in simplification in the Windkessel modelisation of the vascular system with constant parameters. It shows in a conduction artery the influence of the functional properties of the arterial wall on the level of systolic and diastolic BP.

Adult↗
PubMed2000

Variance components analysis for pedigree-based censored survival data using generalized linear mixed models (GLMMs) and Gibbs sampling in BUGS.

Complex human diseases are an increasingly important focus of genetic research. Many of the determinants of these diseases are unknown and there is often a strong residual covariance between relatives even when all known genetic and environmental factors have been taken into account. This must be modeled correctly whether scientific interest is focused on fixed effects, as in an association analysis, or on the covariance structure itself. Analysis is straightforward for multivariate normally distributed traits, but difficulties arise with other types of trait. Generalized linear mixed models (GLMMs) offer a potentially unifying approach to analysis for many classes of phenotype including right censored survival times. This includes age-at-onset and age-at-death data and a variety of other censored traits. Markov chain Monte Carlo (MCMC) methods, including Gibbs sampling, provide a convenient framework within which such GLMMs may be fitted. In this paper, we use BUGS ("Bayesian inference using Gibbs sampling": a readily available, generic Gibbs sampler) to fit GLMMs for right-censored survival times in nuclear and extended families. We discuss parameter interpretation and statistical inference, and show how to circumvent a number of important theoretical and practical problems. Using simulated data, we show that model parameters are consistent. We further illustrate our methods using data from an ongoing cohort study. Finally, we propose that the random effects associated with a genetic component of variance (e.g., sigma(2)(A)) in a GLMM may be regarded as an adjusted "phenotype" and used as input to a conventional model-based or model-free linkage analysis. This provides a simple way to conduct a linkage analysis for a trait reflected in a right-censored survival time while comprehensively adjusting for observed confounders at the level of the individual and latent environmental effects shared across families.

Bayes Theorem↗
PubMed1993

Serum insulin distributions and reproducibility of the relationship between 2-hour insulin and plasma glucose levels in Asian Indian, Creole, and Chinese Mauritians. Mauritius NCD Study Group.

The relationship of 2-hour (post-75 g oral glucose) serum insulin levels with plasma glucose levels was studied in a population-based random sample comprising 2,627 Hindu Indians, 685 Muslim Indians, 1,351 Creoles (African, European, and Indian admixture), and 415 Chinese from the Indian Ocean island of Mauritius. Known diabetic subjects taking oral hypoglycemic drugs or insulin were excluded from these analyses; 64% of all diabetic subjects had usable glucose and insulin data. Both fasting and 2-hour postload insulin levels were significantly higher in women than in men, and levels in both sexes were significantly greater in Hindu and Muslim Indian subjects than in Creoles or Chinese even after controlling for differences in age, body mass index (BMI), waist to hip ratio (WHR), and plasma glucose level. Levels in Muslims were higher than those in Hindus; it was unclear whether these ethnic differences represented hereditary or unmeasured environmental factors closely associated with ethnicity. All four ethnic groups demonstrated similar inverted U- or V-shaped curves when 2-hour insulin was plotted against either basal or 2-hour glucose. Both quadratic (U) and two-piece (V) regression models improved over linear models for 2-hour insulin versus either fasting or 2-hour glucose in all ethnic groups, although in statistical terms they were good models only for the 2-hour glucose comparison. The two-piece models were associated with modest increases in R2 compared with the quadratic models, but it was not possible to precisely determine optimal turning points with either model. However, in all ethnic groups, 2-hour insulin levels decreased above glucose levels of 7.1 to 7.8 (fasting) and 11.3 to 13.5 mmol/L (2-hour) in quadratic models, and 7.5 to 9.5 (fasting) and 8.5 to 10.5 mmol/L (2-hour) in two-piece models. The shape and point of inflection of the quadratic and two-piece curves were influenced little by gender, obesity, fat distribution, and physical activity. These results are in accord with those observed in cross-sectional and longitudinal studies in other ethnic groups, and support the generality of the plasma glucose levels currently used to define diabetes mellitus, which physiologically correspond with a decrease in beta-cell responsiveness to glucose. Asian Indians appear to have an ethnic propensity to hyperinsulinemia that is not explained by obesity or adverse fat distribution.

Adult↗
PubMed2006

Using nonlinear models in fMRI data analysis: model selection and activation detection.

There is an increasing interest in using physiologically plausible models in fMRI analysis. These models do raise new mathematical problems in terms of parameter estimation and interpretation of the measured data. In this paper, we show how to use physiological models to map and analyze brain activity from fMRI data. We describe a maximum likelihood parameter estimation algorithm and a statistical test that allow the following two actions: selecting the most statistically significant hemodynamic model for the measured data and deriving activation maps based on such model. Furthermore, as parameter estimation may leave much incertitude on the exact values of parameters, model identifiability characterization is a particular focus of our work. We applied these methods to different variations of the Balloon Model (Buxton, R.B., Wang, E.C., and Frank, L.R. 1998. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39: 855-864; Buxton, R.B., Uludağ, K., Dubowitz, D.J., and Liu, T.T. 2004. Modelling the hemodynamic response to brain activation. NeuroImage 23: 220-233; Friston, K. J., Mechelli, A., Turner, R., and Price, C. J. 2000. Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12: 466-477) in a visual perception checkerboard experiment. Our model selection proved that hemodynamic models better explain the BOLD response than linear convolution, in particular because they are able to capture some features like poststimulus undershoot or nonlinear effects. On the other hand, nonlinear and linear models are comparable when signals get noisier, which explains that activation maps obtained in both frameworks are comparable. The tools we have developed prove that statistical inference methods used in the framework of the General Linear Model might be generalized to nonlinear models.

Adult↗
PubMed2001

Fitting linear compartmental models by a matrix diagonalization method.

A general method is presented for fitting experimental data to arbitrary linear compartmental models, based on readily available public domain software. The model is defined by input data so that the same program can be used for different compartmental models. Its use is exemplified by application to the four-compartment problem recently treated by Charkes and Siegel.

Computer Simulation↗
PubMed2005

Imputation and variable selection in linear regression models with missing covariates.

Across multiply imputed data sets, variable selection methods such as stepwise regression and other criterion-based strategies that include or exclude particular variables typically result in models with different selected predictors, thus presenting a problem for combining the results from separate complete-data analyses. Here, drawing on a Bayesian framework, we propose two alternative strategies to address the problem of choosing among linear regression models when there are missing covariates. One approach, which we call "impute, then select" (ITS) involves initially performing multiple imputation and then applying Bayesian variable selection to the multiply imputed data sets. A second strategy is to conduct Bayesian variable selection and missing data imputation simultaneously within one Gibbs sampling process, which we call "simultaneously impute and select" (SIAS). The methods are implemented and evaluated using the Bayesian procedure known as stochastic search variable selection for multivariate normal data sets, but both strategies offer general frameworks within which different Bayesian variable selection algorithms could be used for other types of data sets. A study of mental health services utilization among children in foster care programs is used to illustrate the techniques. Simulation studies show that both ITS and SIAS outperform complete-case analysis with stepwise variable selection and that SIAS slightly outperforms ITS.

Algorithms↗
PubMed2006

Pooled analysis of data from multiple quantitative trait locus mapping populations.

Quantitative trait locus (QTL) analysis on pooled data from multiple populations (pooled analysis) provides a means for evaluating, as a whole, evidence for existence of a QTL from different studies and examining differences in gene effect of a QTL among different populations. Objectives of this study were to: (1) develop a method for pooled analysis and (2) conduct pooled analysis on data from two soybean mapping populations. Least square interval mapping was extended for pooled analysis by inclusion of populations and cofactor markers as indicator variables and covariate variables separately in the multiple linear models. The general linear test approach was applied for detecting a QTL. Single population-based and pooled analyses were conducted on data from two F(2:3) mapping populations, Hamilton (susceptible) x PI 90763 (resistant) and Magellan (susceptible) x PI 404198A (resistant), for resistance to soybean cyst nematode (SCN) in soybean. It was demonstrated that where a QTL was shared among populations, pooled analysis showed increased LOD values on the QTL candidate region over single population analyses. Where a QTL was not shared among populations, however, the pooled analysis showed decreased LOD values on the QTL candidate region over single population analyses. Pooled analysis on data from genetically similar populations may have higher power of QTL detection than single population-based analyses. QTLs were identified by pooled analysis on linkage groups (LGs) G, B1 and J for resistance to SCN race 2 whereas QTLs on LGs G, B1 and E for resistance to SCN race 5 in soybean PI 90763 and PI 404198A. QTLs on LG G and B1 were identified in both PI 90763 and PI 404198A whereas QTLs on LG E and J were identified in PI 90763 only. QTLs on LGs G and B1 for resistance to race 2 may be the same or closely linked with QTLs on LG G and B1 for resistance to race 5, respectively. It was further demonstrated that QTLs on G and B1 carried by PI 90763 were not significantly different in gene effect from QTLs on LGs G and B1 in PI 404198A, respectively.

Chromosome Mapping↗
PubMedDate not supplied

Prediction of peptide retention at different HPLC conditions from multiple linear regression models.

To quantitatively characterize the structure of a peptide and to predict its gradient retention time at given HPLC conditions three structural descriptors are used: (i) logarithm of the sum of retention times of the amino acids composing the peptide, log SumAA, (ii) logarithm of the van der Waals volume of the peptide, log VDW(Vol), (iii) and the logarithm of the peptide's calculated n-octanol-water partition coefficient, clog P. The log SumAA descriptor is obtained from empirical data for 20 natural amino acids, determined in a given HPLC system. The two other descriptors are calculated from the peptides' structural formulas using molecular modeling methods. The quantitative structure-retention relationships (QSRR), build by multiple linear regression, describe HPLC retention of peptide on a given chromatographic system on which the retention of the 20 amino acids was predetermined. A structurally diversified series of 98 peptides was employed. The predicted gradient retention times on several chromatographic systems were in good agreement with the experimental data. The QSRR equations, derived for a given system operated at variable gradient times and temperatures allowed for the prediction of peptide retention in that system. Matching the experimental HPLC retention to the theoretically predicted for a presumed peptide could facilitate original protein identification in proteomics. In conjunction with MS data, prediction of the retention time for a given peptide might be used to improve the confidence of peptide identifications and to increase the number of correctly identified peptides.

Amino Acid Sequence↗