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PubMed1999

Mapping quantitative trait loci by genotyping haploid tissues.

Mapping strategies based on a half- or full-sib family design have been developed to map quantitative trait loci (QTL) for outcrossing species. However, these strategies are dependent on controlled crosses where marker-allelic frequency and linkage disequilibrium between the marker and QTL may limit their application. In this article, a maximum-likelihood method is developed to map QTL segregating in an open-pollinated progeny population using dominant markers derived from haploid tissues from single meiotic events. Results from the haploid-based mapping strategy are not influenced by the allelic frequencies of markers and their linkage disequilibria with QTL, because the probabilities of QTL genotypes conditional on marker genotypes of haploid tissues are independent of these population parameters. Parameter estimation and hypothesis testing are implemented via expectation/conditional maximization algorithm. Parameters estimated include the additive effect, the dominant effect, the population mean, the chromosomal location of the QTL in the interval, and the residual variance within the QTL genotypes, plus two population parameters, outcrossing rate and QTL-allelic frequency. Simulation experiments show that the accuracy and power of parameter estimates are affected by the magnitude of QTL effects, heritability levels of a trait, and sample sizes used. The application and limitation of the method are discussed.

Alleles↗

PubMed1997

Comparison of ED, EID, and API criteria for the robust optimization of sampling times in pharmacokinetics.

Optimization of the sampling schedule can be used in pharmacokinetic (PK) experiments to increase the accuracy and the precision of parameter estimation or to reduce the number of samples required. Several optimization criteria that formally incorporate prior parameter uncertainty have been proposed earlier. These criteria consist in finding the sampling schedule that maximizes the expectation (over a given parameter distribution) of det F (ED-optimality) or Log(det F) (API-optimality), or minimizes the expectation of 1/det F (EID-optimality), where F is the Fisher information matrix. The precision and the accuracy of parameter estimation after having fitted a PK model to a small number of optimal data points (determined according to D, ED, EID, and API criteria) or to a naive sampling schedule were compared in a Monte Carlo simulation study. A one-compartment model with first-order absorption rate (3 parameters) and a two-compartment model with zero-order infusion rate (4 parameters) were considered. Data were simulated for 300 subjects with both structural models, combined with several residual error models (homoscedastic, heteroscedastic with constant or variable coefficient of variation). Interindividual variabilities in PK parameters ranged from 25-66%. ED-, EID-, and API-optimal sampling times were calculated using the software OSP-Fit. Three or five samples were allowed for parameter estimation by extended least-squares. Performances of each design criterion were evaluated in terms of mean prediction error, root mean squared error, and number of acceptable estimates (i.e., with a SE less than 30%). Compared to the D-optimal design, the EID and API designs reduced the bias and the imprecision of the estimation of the parameters having a large interindividual variability. Moreover, the API design resulted in some cases in a higher number of acceptable estimates.

Models, Biological↗

PubMed1992

Potential of population pharmacokinetics to reduce the frequency of blood sampling required for estimating kinetic parameters in neonates.

Data obtained from neonates receiving zidovudine as part of a phase I study were used to estimate the population pharmacokinetic parameters of this drug and to determine the minimum number of data points necessary to provide accurate estimates of the kinetic parameters and their variability. Analysis was performed with 541 concentrations of zidovudine, obtained from 32 infants and with a variety of reduced data sets using NONMEM (nonlinear mixed effect model). The reduced data sets were derived by randomly reducing the number of sampling time points per dosing interval and/or by randomly reducing the number of available subjects. We determined that accurate estimates of pharmacokinetic parameters and their variability were obtained with the inclusion of all 32 patients using only two concentration-time points per dose interval, provided that one of the points was obtained during the first 2 h after administration of the drug. The parameters themselves were adequately estimated with only 24 subjects and two concentration-time points per dose interval. We suggest that NONMEM should be used in addition to the traditional pharmacokinetic analysis to obtain more precise information directly in the population of interest with a minimum of blood sampling from each patient. This is especially critical in infants whose blood volumes are limited.

Biological Availability↗

PubMed2005

Frequency-domain characteristics and filtering of blood flow following the onset of exercise: implications for kinetics analysis.

We examined the validity and usefulness of a low-pass filter (LPFILTER) to reduce point-to-point variability and enhance parameter estimation of the kinetics of blood flow (BF). Computer simulations were used to determine the power spectrum of simulated responses. Moreover, we studied the leg BF response to a single transition in four subjects during supine knee-extension exercise using three methods of data processing [beat-by-beat, average of 3 cardiac cycles (AVG3 BEATS), and LPFILTER]. The power spectrum of BF containing the kinetics information ( 0.05; n=4). However, LPFILTER (cutoff=0.2 Hz) resulted in a significantly lower standard error of the estimate for all parameters (P<0.05). The means+/-SD for the standard error of the estimate for Beat-by-Beat, AVG3 BEATS, and LPFILTER were, respectively, time constant-phase 1=5.0+/-1.1 s, 4.5+/-2.1 s, and 0.3+/-0.2 s; time delay-phase 2=17.8+/-7.9 s, 12.8+/-7.5 s, and 1.4+/-1.4 s; time constant-phase 2=15.8+/-4.6 s, 9.9+/-2.9 s, and 1.1+/-0.5 s. In conclusion, LPFILTER appeared to be a valid procedure providing a high signal-to-noise ratio and data density and thus LPFILTER resulted in the smallest confidence interval for parameter estimates of BF kinetics.

Adult↗

PubMed2003

Estimated genetic parameters for palatability traits of steaks from Brahman cattle.

Heritabilities and genetic and phenotypic correlations were estimated from carcass and beef palatability data collected from Brahman calves (n = 504) born in central Florida from 1996 to 2000. Traits evaluated included Warner-Bratzler shear force (after 7, 14, and 21 d of aging), panel tenderness score, connective tissue amount, juiciness, flavor intensity, and off flavor (after 14 d of aging), percentages of raw and cooked lipids, and milligrams per gram of muscle calpastatin activity. Parameters were estimated using an animal model and derivative-free restricted maximum likelihood procedures. Estimated heritabilities for d 7, 14, and 21 shear force were 0.14,0.14, and 0.06, respectively, indicating that improvement in these traits by selection would be slow. Estimated heritabilities of sensory panel attributes were 0.11, 0.12, 0.05, 0.04, and 0.01 for tenderness, connective tissue amount, juiciness, flavor intensity, and off flavor, respectively. The estimated heritabilities for percentages of raw and cooked lipids, and calpastatin activity were 0.34, 0.17, and 0.07, respectively. Most of the estimated genetic correlations among palatability traits and for palatability traits with fat thickness, marbling score, and loin muscle area were consistent with other estimates from the literature. Results indicated that improvement in tenderness based on selection for favorable shear force, sensory panel tenderness, or calpastatin activity would be slow; therefore, postslaughter intervention programs should also be considered.

Animals↗

PubMed2004

[Using VCE4.0 package to estimate genetic parameters on growth traits in Landrace].

It is an accurate and quick methods to apply VCE4.0 to estimating genetic parameter. It makes full use of all information, analyzing selection and culling effects. The Genetic parameters for the age to 30kg(AGE30), age to 100kg (AGE100), and average daily gain from 30kg to 100kg (ADG) and backfat thickness at 100kg(probed,FAT) are estimated using VCE4.0 applied to REML with a multivariate individual animal model in Landrace pigs. Estimates of heritabilities for AGE30, AGE100,ADG and FAT are 0.207,0.396,0.304 and 0.493, respectively. Genetic correlations for FAT/ADG, FAT/AGE100, ADG/AGE100, ADG /AGE30 and AGE30/AGE100 are -0.343,0.180,-0.941,-0.48,and 0.745, respectively, its phenotypic correlations are -0.139,0.138,-0.82,-0.026, and 0.565, respectively. The common litter environment effects for AGE30,AGE100, ADG and FAT are 0.194,0.156,0.157 and 0.043, respectively.

Animals↗

PubMed1993

Lipid data from NHLBI veteran twins: interpreting genetic analyses when model assumptions fail.

Analyses were performed on lipid data from the NHLBI Veteran Twin Study. The analyses focused on longitudinal multivariate models, describing how the genetic effects on lipids vary over time. Our pedigree-based model selection approach allows simultaneous estimation of both covariance structure parameters and regression parameters. The analyses reveal strong correlations between additive genetic effects over time, implying that genetic effects on lipids are somewhat constant throughout the life span represented within this sample. Both univariate preliminary analyses and robust fitting applied to the longitudinal models indicate that several assumptions underlying the twin analyses are violated. Although variance component and correlation parameter estimates are not much changed by robust fitting analyses, questions remain about the behavior of parameter estimates in multivariate genetic models under departures from model assumptions.

Humans↗

PubMed1991

Estimating standardized parameters from generalized linear models.

Although the traditional unrestricted ('non-parametric') estimators of directly standardized rates and rate differences remain unbiased in sparse data, they tend to suffer from instability (low precision). As a result, many authors have proposed more precise estimators based on parametric models for the rates. This paper provides a general approach for constructing estimators of standardized parameters using generalized linear models, and shows that, in some common special cases, these model-based ('smoothed') estimators can have an exceptionally simple form.

Adult↗

PubMed1997

A simple method for estimating the parameter of substitution rate variation among sites.

When the rate variation among sites is described by a gamma distribution, an important problem is how to estimate the shape parameter alpha, which is an index of the degree of among-site rate variation. The parsimony-based methods for estimating alpha are simple but biased, i.e., alpha tends to be overestimated. On the other hand, the likelihood-based methods are asymptotically unbiased but take a huge amount of computational time. In this paper, we have developed a new method to solve this problem: we first estimate the expected number of substitutions at each site, which is corrected for multiple hits, and then estimate the parameter alpha. Our method is computationally as fast as the parsimony method, and the estimation accuracy is much higher than that of parsimony and similar to that of the likelihood method.

Amino Acid Sequence↗

PubMed1999

GLLS for optimally sampled continuous dynamic system modeling: theory and algorithm.

The original generalized linear least squares (GLLS) algorithm was developed for non-uniformly sampled biomedical system parameter estimation using finely sampled instantaneous measurements (D. Feng, S.C. Huang, Z. Wang, D. Ho, An unbiased parametric imaging algorithm for non-uniformly sampled biomedical system parameter estimation, IEEE Trans. Med. Imag. 15 (1996) 512-518). This algorithm is particularly useful for image-wide generation of parametric images with positron emission tomography (PET), as it is computationally efficient and statistically reliable (D. Feng, D. Ho, Chen, K., L.C. Wu, J.K. Wang, R.S. Liu, S.H. Yeh, An evaluation of the algorithms for determining local cerebral metabolic rates of glucose using positron emission tomography dynamic data, IEEE Trans. Med. Imag. 14 (1995) 697-710). However, when dynamic PET image data are sampled according to the optimal image sampling schedule (OISS) to reduce memory and storage space (X. Li, D. Feng, K. Chen, Optimal image sampling schedule: A new effective way to reduce dynamic image storage space and functional image processing time, IEEE Trans. Med. Imag. 15 (1996) 710-718), only a few temporal image frames are recorded (e.g. only four images are recorded for the four parameter fluoro-deoxy-glucose (FDG) model). These image frames are recorded in terms of accumulated radio-activity counts and as a result, the direct application of GLLS is not reliable as instantaneous measurement samples can no longer be approximated by averaging of accumulated measurements over the sampling intervals. In this paper, we extend GLLS to OISS-GLLS which deals with the fewer accumulated measurement samples obtained from OISS dynamic systems. The theory and algorithm of this new technique are formulated and studied extensively. To investigate statistical reliability and computational efficiency of OISS-GLLS, a simulation study using dynamic PET data was performed. OISS-GLLS using 4-measurement samples was compared to the non-linear least squares (NLS) method using 22-measurement samples, GLLS using 22-measurement samples and OISS-NLS using 4-measurement samples. Results demonstrated that OISS-GLLS was able to achieve parameter estimates of equivalent accuracy and reliability in comparison to NLS or GLLS using finely sampled measurements (22-measurement samples), or OISS-NLS using optimally sampled measurements (4-measurement samples). Further more, as fewer measurement samples are used in OISS-GLLS, this algorithm is computationally faster than NLS or GLLS. Therefore, OISS-GLLS is well-suited for image-wide parameter estimation when PET image data are recorded according to the optimal image sampling schedule.

Algorithms↗

PubMed1990

Variability of estimated binding parameters.

The standard deviation is often used as a measure of the accuracy or reliability of estimated binding parameters and this implies that the parameter values are normally distributed. This may not be the case and we show that the unknown distribution of acceptable parameter values associated with a specific model and a particular set of experimental data can be calculated easily. This can be done for any binding model, linear or non-linear, and the method is very robust and accurate. The effect of the magnitude of the experimental error and the distribution of data points on the variability of the parameters is readily investigated. This makes the method useful for the practical design of experiments in terms of the number and range of concentrations (or doses) which need to be studied in order to obtain the desired accuracy.

Journal Article↗

PubMed1995

Effect of non-random sampling on the estimation of parameters in population genetics.

The amount and pattern of genetic variation in a population can be estimated from genes or DNA sequences sampled from the population. Although random sampling is assumed in almost all cases, we often do not know whether sampling is random or not. Using a simple non-random sampling model, the effects of non-random sampling on the estimation of parameters in population genetics were investigated. This non-random sampling model assumes that n genes are randomly sampled with replacement from m genes which were randomly sampled from a large random mating population, and various degrees of non-randomness can be generated by changing the value of m. The results obtained show that the effect of non-random sampling on the number of alleles and the number of segregating sites is substantially large whereas the effect of non-random sampling on heterozygosity and the average number of nucleotide differences is negligibly small unless non-randomness is extremely large. The effects of non-random sampling on the tests of neutrality were also investigated, and the results obtained indicate that the effect of non-random sampling is stronger on Fu and Li's tests than on Tajima's test.

Alleles↗

PubMed2004

Dynamics of cellular level function and regulation derived from murine expression array data.

A major open question of systems biology is how genetic and molecular components interact to create phenotypes at the cellular level. Although much recent effort has been dedicated to inferring effective regulatory influences within small networks of genes, the power of microarray bioinformatics has yet to be used to determine functional influences at the cellular level. In all cases of data-driven parameter estimation, the number of model parameters estimable from a set of data is strictly limited by the size of that set. Rather than infer parameters describing the detailed interactions of just a few genes, we chose a larger-scale investigation so that the cumulative effects of all gene interactions could be analyzed to identify the dynamics of cellular-level function. By aggregating genes into large groups with related behaviors (megamodules), we were able to determine the effective aggregate regulatory influences among 12 major gene groups in murine B lymphocytes over a variety of time steps. Intriguing observations about the behavior of cells at this high level of abstraction include: (i) a medium-term critical global transcriptional dependence on ATP-generating genes in the mitochondria, (ii) a longer-term dependence on glycolytic genes, (iii) the dual role of chromatin-reorganizing genes in transcriptional activation and repression, (iv) homeostasis-favoring influences, (v) the indication that, as a group, G protein-mediated signals are not concentration-dependent in their influence on target gene expression, and (vi) short-term-activating/long-term-repressing behavior of the cell-cycle system that reflects its oscillatory behavior.

Animals↗

PubMedDate not supplied

Population kinetics and conditional assessment of the optimal dosage regimen using the P-PHARM software package.

The adjustment of individual dosage regimen is an adaptive control process based upon an individual response to a pharmacokinetic model. To attain this objective, it is very helpful to know the characteristics of the population to which the subject belongs, in terms of mean parameters and interindividual variability. Usually the available information consists of incomplete and sparse data. For this reason it is essential to employ a computational methodology based on non-linear mixed-effect procedures in order to obtain a population parameter estimate. A Bayesian methodology can then be applied from the population parameters to the specific data for the individual requiring a dosage adjustment (such data includes drug concentration(s) of the active drug, demographic data, etc). The result of the Bayesian calculation supplies the required individual pharmacokinetic parameters. An optimal dosage regimen can be defined on the basis of therapeutical criteria (concentration ranges) as well as practical constraints such as: the size of available unitary drug dosages, feasible drug intake times, penalties associated with expected concentrations falling outside the therapeutic concentration ranges. In this paper we present the methodology and results obtained using the P-Pharm software tool. P-Pharm implements a non-linear mixed-effect population parameter estimation algorithm based on the EM algorithm. This method allows the inclusion of explicit variables into the calculations, it implements an individual Bayesian parameter estimation procedure and also an algorithm for the conditional assessment of the optimal dosage regimen given a list of practical constraints.

Algorithms↗

PubMed2002

Asymptotic standard errors of estimated standard errors in structural equation modelling.

Asymptotic standard errors of the estimated asymptotic standard errors for parameter estimates in structural equation modelling are derived using the delta method with the assumption of multivariate normality for observed variables. The derivation covers the cases with and without restrictions on parameters. The result can be used to derive the asymptotic standard error of the z score (a parameter estimate divided by its estimated standard error), which is frequently substantially different from one. The case of standardized observed variables is dealt with as a typical example with restrictions on parameters. For actual covariance (correlation) structure models, the exploratory factor analysis model with factor rotation and the confirmatory factor analysis model are presented with numerical examples. Simulations are performed to assess the accuracy of our method for normally and non-normally distributed variables.

Behavior↗

PubMed2006

Frequentist model-averaged estimators and tests for univariate twin models.

Parameter estimates from analyses of univariate twin data usually do not reflect the uncertainty due to the model selection phase of the data analysis. To address the effect of model selection uncertainty on parameter estimates, we introduce frequentist model-averaged estimators for univariate twin data analysis that use information-theoretic criteria to assign model weights. We conduct simulation studies to examine the performance of model-averaged estimators of additive genetic variance, and for tests for additive genetic variance based on model-averaged estimators. In simulation studies with small or moderate sample sizes, model-averaged estimators of additive genetic variance typically have lower mean-squared error than either (i) estimators from individual twin models, or (ii) estimators obtained from a decision procedure where the best-fitting model from likelihood-ratio testing is used to estimate additive genetic variance. For each sample size simulated, bootstrap tests based on model-averaged estimators have higher power to detect additive genetic variance than currently-used tests in most cases.

Analysis of Variance↗

PubMed2002

A framework for ML estimation of parameters of (mixtures of) common reaction time distributions given optional truncation or censoring.

We present a framework for distributional reaction time (RT) analysis, based on maximum likelihood (ML) estimation. Given certain information relating to chosen distribution functions, one can estimate the parameters of these distributions and of finite mixtures of these distributions. In addition, left and/or right censoring or truncation may be imposed. Censoring and truncation are useful methods by which to accommodate outlying observations, which are a pervasive problem in RT research. We consider five RT distributions: the Weibull, the ex-Gaussian, the gamma, the log-normal, and the Wald. We employ quasi-Newton optimization to obtain ML estimates. Multicase distributional analyses can be carried out, which enable one to conduct detailed (across or within subjects) comparisons of RT data by means of loglikelihood difference tests. Parameters may be freely estimated, estimated subject to boundary constraints, constrained to be equal (within or over cases), or fixed. To demonstrate the feasibility of ML estimation and to illustrate some of the possibilities offered by the present approach, we present three small simulation studies. In addition, we present three illustrative analyses of real data.

Humans↗

PubMed1991

An evolutionary model for maximum likelihood alignment of DNA sequences.

Most algorithms for the alignment of biological sequences are not derived from an evolutionary model. Consequently, these alignment algorithms lack a strong statistical basis. A maximum likelihood method for the alignment of two DNA sequences is presented. This method is based upon a statistical model of DNA sequence evolution for which we have obtained explicit transition probabilities. The evolutionary model can also be used as the basis of procedures that estimate the evolutionary parameters relevant to a pair of unaligned DNA sequences. A parameter-estimation approach which takes into account all possible alignments between two sequences is introduced; the danger of estimating evolutionary parameters from a single alignment is discussed.

Algorithms↗