The Effects of Selection on Linkage Analysis for Quantitative Traits

The effects of within-sample selection on the outcome of analyses detecting linkage between genetic markers and quantitative traits were studied. It was found that selection by truncation for the trait of interest significantly reduces the differences between marker genotype means thus reducing the power to detect linked quantitative trait loci (QTL). The size of this reduction is a function of proportion selected, the magnitude of the QTL effect, recombination rate between the marker locus and the QTL, and the allele frequency of the QTL. Proportion selected was the most influential of these factors on bias, e.g., for an allele substitution effect of one standard deviation unit, selecting the top 80%, 50% or 20% of the population required 2, 6 or 24 times the number of progeny, respectively, to offset the loss of power caused by this selection. The effect on power was approximately linear with respect to the size of gene effect, almost invariant to recombination rate, and a complex function of QTL allele frequency. It was concluded that experimental samples from animal populations which have been subjected to even minor amounts of selection will be inefficient in yielding information on linkage between markers and loci influencing the quantitative trait under selection.     

Parameter Estimation in Systematic Sampling

First it is shown that an estimate of the variance of the sample-mean in systematic sampling from a non-autocorrelated population with linear trend, which is published in textbooks, isn't a suitable estimate: It is biased and not dependent on the essential parameter, the slope of the linear trend. In section 2 an unbiased estimate of the variance is given. As estimate of the sample-mean we take the same as usually used in literature. In section 3 a centric estimate of the sample-mean is introduced, which takes into consideration the slope of the trendline. It is shown that this estimate is unbiased; an unbiased estimate of its variance is given.     

Testimation in Regression Parameter Estimation

Testimation is considered in the problem of estimation of regression parameters. The first stage sample is used to test a (null) hypothesis that specifies initial (preassumed) values for some of the regression parameters. Linear combination of the preassumed values and the ordinary least square (OLS) estimates is considered as the estimate if the data agree with the hypothesis. Otherwise, a second sample is taken and parameters are estimated only by using OLS, based on the combined sample. The procedure protects against type II error and against taking larger samples when inference can be made from a smaller sample.     

Parameter Estimation of the Gompertz Population

The Gompertz distribution has been used to model human mortality and fit actuarial tables. In the recent years, this distribution has been studied by some authors. The MLE estimates for the parameters of the Gompertz distribution were disucssed by GARG, RAO and REDMOND (1970). The purpose of this paper is to develop an exact confidence interval and an exact joint confidence region for the parameters of the Gompertz distribution.     

Parameter Estimation for the Compartmental Model

An estimation procedure is obtained for a stochastic compartmental model. Compartmental analysis assumes that a system may be divided into homogeneous components, or compartments. The main theory for the compartmental system was studied by Matis and Hartley (1971) with a discrete population in a steady state. All the transitions among the particles are considered to be stochastic in nature. An estimation procedure, Regular Best Asymptotic Normal (RBAN), discussed by Chiang (1956) is investigated for a stochastic m-compartmental system. The detailed proof of the procedure is provided here. Asymptotic properties for the estimator has been studied and computation has been carried out on our proposed nonlinear model. The downhill simplex search method, originally developed by Nelder and Mead (1965), and applied to minimize our quadratic form is inherently nonlinear in nature, thus avoiding the need to evaluate any derivative for point estimation of the parameters. The procedure applied to an experimental situation involving two compartments gives very encouraging results.     

Parameter Estimation and Model Selection in Computational Biology

A central challenge in computational modeling of biological systems is the determination of the model parameters. Typically, only a fraction of the parameters (such as kinetic rate constants) are experimentally measured, while the rest are often fitted. The fitting process is usually based on experimental time course measurements of observables, which are used to assign parameter values that minimize some measure of the error between these measurements and the corresponding model prediction. The measurements, which can come from immunoblotting assays, fluorescent markers, etc., tend to be very noisy and taken at a limited number of time points. In this work we present a new approach to the problem of parameter selection of biological models. We show how one can use a dynamic recursive estimator, known as extended Kalman filter, to arrive at estimates of the model parameters. The proposed method follows. First, we use a variation of the Kalman filter that is particularly well suited to biological applications to obtain a first guess for the unknown parameters. Secondly, we employ an a posteriori identifiability test to check the reliability of the estimates. Finally, we solve an optimization problem to refine the first guess in case it should not be accurate enough. The final estimates are guaranteed to be statistically consistent with the measurements. Furthermore, we show how the same tools can be used to discriminate among alternate models of the same biological process. We demonstrate these ideas by applying our methods to two examples, namely a model of the heat shock response in E. coli, and a model of a synthetic gene regulation system. The methods presented are quite general and may be applied to a wide class of biological systems where noisy measurements are used for parameter estimation or model selection.     

Modeling the Cardiovascular-Respiratory Control System: Data,Model Analysis,and Parameter Estimation

Several key areas in modeling the cardiovascular and respiratory control systems are reviewed and examples are given which reflect the research state of the art in these areas. Attention is given to the interrelated issues of data collection, experimental design, and model application including model development and analysis. Examples are given of current clinical problems which can be examined via modeling, and important issues related to model adaptation to the clinical setting.     

Joint Multipoint Linkage Analysis of Multivariate Qualitative and Quantitative Traits. II. Alcoholism and Event-Related Potentials

The availability of robust quantitative biological markers that are correlated with qualitative psychiatric phenotypes can potentially improve the power of linkage methods to detect quantitative-trait loci influencing psychiatric disorders. We apply a variance-component method for joint multipoint linkage analysis of multivariate discrete and continuous traits to the extended pedigree data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate analysis of qualitative alcoholism phenotypes and quantitative event-related potentials. Joint consideration of the DSM-IV diagnosis of alcoholism and the amplitude of the P300 component of the Cz event-related potential significantly increases the evidence for linkage of these traits to a chromosome 4 region near the class I alcohol dehydrogenase locus ADH3. A likelihood-ratio test for complete pleiotropy is significant, suggesting that the same quantitative-trait locus influences both risk of alcoholism and the amplitude of the P300 component.     

Parameter Estimation Methods for Single Neuron Models

With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.     

Parameter Estimation Methods for Chaotic Intercellular Networks

We have investigated simulation-based techniques for parameter estimation in chaotic intercellular networks. The proposed methodology combines a synchronization–based framework for parameter estimation in coupled chaotic systems with some state–of–the–art computational inference methods borrowed from the field of computational statistics. The first method is a stochastic optimization algorithm, known as accelerated random search method, and the other two techniques are based on approximate Bayesian computation. The latter is a general methodology for non–parametric inference that can be applied to practically any system of interest. The first method based on approximate Bayesian computation is a Markov Chain Monte Carlo scheme that generates a series of random parameter realizations for which a low synchronization error is guaranteed. We show that accurate parameter estimates can be obtained by averaging over these realizations. The second ABC–based technique is a Sequential Monte Carlo scheme. The algorithm generates a sequence of “populations”, i.e., sets of randomly generated parameter values, where the members of a certain population attain a synchronization error that is lesser than the error attained by members of the previous population. Again, we show that accurate estimates can be obtained by averaging over the parameter values in the last population of the sequence. We have analysed how effective these methods are from a computational perspective. For the numerical simulations we have considered a network that consists of two modified repressilators with identical parameters, coupled by the fast diffusion of the autoinducer across the cell membranes.     

Noninvasive Characterization of Locally Advanced Breast Cancer Using Textural Analysis of Quantitative Ultrasound Parametric Images

PURPOSE: The identification of tumor pathologic characteristics is an important part of breast cancer diagnosis, prognosis, and treatment planning but currently requires biopsy as its standard. Here, we investigated a noninvasive quantitative ultrasound method for the characterization of breast tumors in terms of their histologic grade, which can be used with clinical diagnostic ultrasound data. METHODS: Tumors of 57 locally advanced breast cancer patients were analyzed as part of this study. Seven quantitative ultrasound parameters were determined from each tumor region from the radiofrequency data, including mid-band fit, spectral slope, 0-MHz intercept, scatterer spacing, attenuation coefficient estimate, average scatterer diameter, and average acoustic concentration. Parametric maps were generated corresponding to the region of interest, from which four textural features, including contrast, energy, homogeneity, and correlation, were determined as further tumor characterization parameters. Data were examined on the basis of tumor subtypes based on histologic grade (grade I versus grade II to III). RESULTS: Linear discriminant analysis of the means of the parametric maps resulted in classification accuracy of 79%. On the other hand, the linear combination of the texture features of the parametric maps resulted in classification accuracy of 82%. Finally, when both the means and textures of the parametric maps were combined, the best classification accuracy was obtained (86%). CONCLUSIONS: Textural characteristics of quantitative ultrasound spectral parametric maps provided discriminant information about different types of breast tumors. The use of texture features significantly improved the results of ultrasonic tumor characterization compared to conventional mean values. Thus, this study suggests that texture-based quantitative ultrasound analysis of in vivo breast tumors can provide complementary diagnostic information about tumor histologic characteristics.     

Joint Multipoint Linkage Analysis of Multivariate Qualitative and Quantitative Traits. I. Likelihood Formulation and Simulation Results

We describe a variance-components method for multipoint linkage analysis that allows joint consideration of a discrete trait and a correlated continuous biological marker (e.g., a disease precursor or associated risk factor) in pedigrees of arbitrary size and complexity. The continuous trait is assumed to be multivariate normally distributed within pedigrees, and the discrete trait is modeled by a threshold process acting on an underlying multivariate normal liability distribution. The liability is allowed to be correlated with the quantitative trait, and the liability and quantitative phenotype may each include covariate effects. Bivariate discrete-continuous observations will be common, but the method easily accommodates qualitative and quantitative phenotypes that are themselves multivariate. Formal likelihood-based tests are described for coincident linkage (i.e., linkage of the traits to distinct quantitative-trait loci [QTLs] that happen to be linked) and pleiotropy (i.e., the same QTL influences both discrete-trait status and the correlated continuous phenotype). The properties of the method are demonstrated by use of simulated data from Genetic Analysis Workshop 10. In a companion paper, the method is applied to data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate linkage analysis of alcoholism diagnoses and P300 amplitude of event-related brain potentials.     

A Hidden Markov Model Combining Linkage and Linkage Disequilibrium Information for Haplotype Reconstruction and Quantitative Trait Locus Fine Mapping

Faithful reconstruction of haplotypes from diploid marker data (phasing) is important for many kinds of genetic analyses, including mapping of trait loci, prediction of genomic breeding values, and identification of signatures of selection. In human genetics, phasing most often exploits population information (linkage disequilibrium), while in animal genetics the primary source of information is familial (Mendelian segregation and linkage). We herein develop and evaluate a method that simultaneously exploits both sources of information. It builds on hidden Markov models that were initially developed to exploit population information only. We demonstrate that the approach improves the accuracy of allele phasing as well as imputation of missing genotypes. Reconstructed haplotypes are assigned to hidden states that are shown to correspond to clusters of genealogically related chromosomes. We show that these cluster states can directly be used to fine map QTL. The method is computationally effective at handling large data sets based on high-density SNP panels.ARRAY technology now allows genotyping of large cohorts for thousands to millions of single nucleotide polymorphisms (SNPs), which are becoming available for a growing list of organisms including human and domestic animals. Among other applications, these advances permit systematic scanning of the genome to map trait loci by association (e.g., Wellcome Trust Case Control Consortium 2007; Charlier et al. 2008), to predict genomic breeding values for complex traits (Meuwissen et al. 2001; Goddard and Hayes 2009), or to identify signatures of selection (e.g., Voight et al. 2006).Present-day genotyping platforms do not directly provide information about linkage phase; i.e., co-inherited alleles at adjacent heterozygous markers (haplotypes) are not identified as such. As haplotype information may considerably empower genetic analyses, indirect phasing strategies have been devised: haplotypes can be reconstructed from unphased genotypes using either familial information (Mendelian segregation and linkage) and/or population information (linkage disequilibrium, LD, and surrogate parents) (e.g., Windig and Meuwissen 2004; Scheet and Stephens 2006; Kong et al. 2008).Haplotype-based approaches are routinely applied in animal genetics for combined linkage and LD mapping of QTL (e.g., Meuwissen and Goddard 2000; Blott et al. 2003). In these studies, phasing has so far relied on familial information provided by the extended pedigrees typical of livestock (e.g., Windig and Meuwissen 2004). This approach, however, leaves a nonnegligible proportion of genotypes unphased, especially for the less connected individuals. After phasing, identity-by-descent (IBD) probabilities conditional on haplotype data—needed for QTL mapping—are computed for all chromosome pairs, using familial as well as population information (hence combined linkage and LD mapping – L + LD) (e.g., Meuwissen and Goddard 2001). However, the use of high-density SNP chips and the analysis of ever larger cohorts render the computation of pairwise IBD probabilities a bottleneck.We herein propose a more efficient, heuristic approach based on hidden Markov models (HMM). It simultaneously phases and sorts haplotypes in clusters that can be used directly for mapping or other purposes. The proposed method exploits familial as well as population information, and imputes missing genotypes. We herein describe the accuracy of the proposed method and its use for L + LD mapping of QTL.     

An Improved Parameter Estimation Method for Hodgkin-Huxley Models

We consider whole-cell voltage-clamp data of isolated currents characterized by the Hodgkin-Huxley paradigm. We examine the errors associated with the typical parameter estimation method for these data and show them to be unsatisfactorally large especially if the time constants of activation and inactivation are not sufficiently separated. The size of these errors is due to the fact that the steady-state and kinetic properties of the current are estimated disjointly. We present an improved parameter estimation method that utilizes all of the information in the voltage-clamp conductance data to estimate steady-state and kinetic properties simultaneously and illustrate its success compared to the standard method using simulated data and data from P. interruptus shal channels expressed in oocytes.     

非参数连锁分析

非参数连锁分析是进行复杂疾病连锁分析的有效手段,本通过拟合的数据资料,对目前广泛使用的非参数连锁分析方法进行了探讨,为今后有针对性的选择性连锁分析方法提供依据。     

Genome-Wide Estimation of Linkage Disequilibrium from Population-Level High-Throughput Sequencing Data

Rapidly improving sequencing technologies provide unprecedented opportunities for analyzing genome-wide patterns of polymorphisms. In particular, they have great potential for linkage-disequilibrium analyses on both global and local genetic scales, which will substantially improve our ability to derive evolutionary inferences. However, there are some difficulties with analyzing high-throughput sequencing data, including high error rates associated with base reads and complications from the random sampling of sequenced chromosomes in diploid organisms. To overcome these difficulties, we developed a maximum-likelihood estimator of linkage disequilibrium for use with error-prone sampling data. Computer simulations indicate that the estimator is nearly unbiased with a sampling variance at high coverage asymptotically approaching the value expected when all relevant information is accurately estimated. The estimator does not require phasing of haplotypes and enables the estimation of linkage disequilibrium even when all individual reads cover just single polymorphic sites.