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PubMed2006

Statistical models for autocorrelated count data.

A generalized linear mixed model is an increasingly popular choice for the modelling of correlated, non-normal responses in a regression setting. A number of methods are currently available for fitting a generalized linear mixed model including Monte-Carlo Markov-Chain maximum likelihood algorithms, approximate maximum likelihood (PQL), iterative bias correction, and others. Of interest in this paper is to compare the parameter estimation of the various methods in the modelling of a count data set, the incidence of polio in the USA over the period 1970-1983, using a longlinear generalized linear mixed model with an autoregressive correlation structure. Despite the fact that all of these methods are considered valid modelling techniques, we find that parameter estimates and standard errors differ substantially between analyses, particularly in the estimation of the parameters describing the random effects distribution. A small simulation study is helpful in understanding some of these differences. The methods lead to reasonably similar predictions for future observations, with small differences observed in some monthly counts.

Algorithms↗

PubMed2002

Estimated genetic parameters for carcass traits of Brahman cattle.

Heritabilities and genetic and phenotypic correlations were estimated from feedlot and carcass data collected from Brahman calves (n = 504) in central Florida from 1996 to 2000. Data were analyzed using animal models in MTDFREML. Models included contemporary group (n = 44; groups of calves of the same sex, fed in the same pen, slaughtered on the same day) as a fixed effect and calf age in days at slaughter as a continuous variable. Estimated feedlot trait heritabilities were 0.64, 0.67, 0.47, and 0.26 for ADG, hip height at slaughter, slaughter weight, and shrink. The USDA yield grade estimated heritability was 0.71; heritabilities for component traits of yield grade, including hot carcass weight, adjusted 12th rib backfat thickness, loin muscle area, and percentage kidney, pelvic, and heart fat were 0.55, 0.63, 0.44, and 0.46, respectively. Heritability estimates for dressing percentage, marbling score, USDA quality grade, cutability, retail yield, and carcass hump height were 0.77, 0.44, 0.47, 0.71, 0.5, and 0.54, respectively. Estimated genetic correlations of adjusted 12th rib backfat thickness with ADG, slaughter weight, marbling score, percentage kidney, pelvic, and heart fat, and yield grade (0.49, 0.46, 0.56, 0.63, and 0.93, respectively) were generally larger than most literature estimates. Estimated genetic correlations of marbling score with ADG, percentage shrink, loin muscle area, percentage kidney, pelvic, and heart fat, USDA yield grade, cutability, retail yield, and carcass hump height were 0.28, 0.49, 0.44, 0.27, 0.45, -0.43, 0.27, and 0.43, respectively. Results indicate that sufficient genetic variation exists within the Brahman breed for design and implementation of effective selection programs for important carcass quality and yield traits.

Animals↗

PubMed2005

Estimation of parameter kmax in fractal analysis of rat brain activity.

We recorded electrocortical activity in anesthetized rats and constructed k(max) new self-similar time series, applying Higuchi's algorithm. The aim of this study was to estimate value of the parameter k(max) in order to obtain fractal dimension values as an optimum measure of biosignal change. After our analysis, electrocortical activity recordings resulted in a family of curves f(k(max)). Three regions could be distinguished 2 < or = k(max) < 8, with a U-shape; 8 < or = k(max) < or = 30, with a steeper quasilinear increase; and k(max) > or = 30, with a smaller slope quasilinear increase. We suggest the optimum region for k(max): 8 < k(max) < 18, specifically k(max) = 8.

Algorithms↗

PubMed1998

Optimal experimental design for precise estimation of the parameters of the axial dispersion model of hepatic elimination.

The axial dispersion model of hepatic drug elimination is characterized by two dimensionless parameters, the dispersion number, DN, and the efficiency number, RN, corresponding to the relative dispersion of material on transit through the organ and the relative efficiency of elimination of drug by the organ, respectively. Optimal design theory was applied to the estimation of these two parameters based on changes in availability (F) of drug at steady state for the closed boundary condition model, with particular attention to variations in the fraction of drug unbound in the perfusate (fuB). Sensitivity analysis indicates that precision in parameter estimation is greatest when F is low and that correlation between RN and DN is high, which is desirable for parameter estimation, when DN lies between 0.1 and 100. Optimal design points were obtained using D-optimization, taking into account the error variance model. If the error variance model is unknown, it is shown that choosing Poisson error model is reasonable. Furthermore, although not optimal, geometric spacing of fuB values is often reasonable and definitively superior to a uniform spacing strategy. In practice, the range of fuB available for selection may be limited by such practical considerations as assay sensitivity and acceptable concentration range of binding protein. Notwithstanding, optimal design theory provides a rational approach to precise parameter estimation.

Linear Models↗

PubMed2006

Analysis of longitudinal health-related quality of life data with terminal events.

Longitudinal health-related quality of life data arise naturally from studies of progressive and neurodegenerative diseases. In such studies, patients' mental and physical conditions are measured over their follow-up periods and the resulting data are often complicated by subject-specific measurement times and possible terminal events associated with outcome variables. Motivated by the "Predictor's Cohort" study on patients with advanced Alzheimer disease, we propose in this paper a semiparametric modeling approach to longitudinal health-related quality of life data. It builds upon and extends some recent developments for longitudinal data with irregular observation times. The new approach handles possibly dependent terminal events. It allows one to examine time-dependent covariate effects on the evolution of outcome variable and to assess nonparametrically change of outcome measurement that is due to factors not incorporated in the covariates. The usual large-sample properties for parameter estimation are established. In particular, it is shown that relevant parameter estimators are asymptotically normal and the asymptotic variances can be estimated consistently by the simple plug-in method. A general procedure for testing a specific parametric form in the nonparametric component is also developed. Simulation studies show that the proposed approach performs well for practical settings. The method is applied to the motivating example.

Health Status↗

PubMed2001

Tree stem diameter variations and transpiration in Scots pine: an analysis using a dynamic sap flow model.

A dynamic model for simulating water flow in a Scots pine (Pinus sylvestris L.) tree was developed. The model is based on the cohesion theory and the assumption that fluctuating water tension driven by transpiration, together with the elasticity of wood tissue, causes variations in the diameter of a tree stem and branches. The change in xylem diameter can be linked to water tension in accordance with Hookeâ s law. The model was tested against field measurements of the diurnal xylem diameter change at different heights in a 37-year-old Scots pine at Hyytiälä, southern Finland (61 degrees 51' N, 24 degrees 17' E, 181 m a.s.l.). Shoot transpiration and soil water potential were input data for the model. The biomechanical and hydraulic properties of wood and fine root hydraulic conductance were estimated from simulated and measured stem diameter changes during the course of 1 day. The estimated parameters attained values similar to literature values. The ratios of estimated parameters to literature values ranged from 0.5 to 0.9. The model predictions (stem diameters at several heights) were in close agreement with the measurements for a period of 6 days. The time lag between changes in transpiration rate and in sap flow rate at the base of the tree was about half an hour. The analysis showed that 40% of the resistance between the soil and the top of the tree was located in the rhizosphere. Modeling the water tension gradient and consequent woody diameter changes offer a convenient means of studying the link between wood hydraulic conductivity and control of transpiration.

Models, Biological↗

PubMed1996

Realized sampling variances of estimates of genetic parameters and the difference between genetic and phenotypic correlations.

A data set of 1572 heritability estimates and 1015 pairs of genetic and phenotypic correlation estimates, constructed from a survey of published beef cattle genetic parameter estimates, provided a rare opportunity to study realized sampling variances of genetic parameter estimates. The distribution of both heritability estimates and genetic correlation estimates, when plotted against estimated accuracy, was consistent with random error variance being some three times the sampling variance predicted from standard formulae. This result was consistent with the observation that the variance of estimates of heritabilities and genetic correlations between populations were about four times the predicted sampling variance, suggesting few real differences in genetic parameters between populations. Except where there was a strong biological or statistical expectation of a difference, there was little evidence for differences between genetic and phenotypic correlations for most trait combinations or for differences in genetic correlations between populations. These results suggest that, even for controlled populations, estimating genetic parameters specific to a given population is less useful than commonly believed. A serendipitous discovery was that, in the standard formula for theoretical standard error of a genetic correlation estimate, the heritabilities refer to the estimated values and not, as seems generally assumed, the true population values.

Analysis of Variance↗

PubMed1998

Litter, permanent environmental, ram-flock, and genetic effects on early weight gain of lambs.

Twelve models were fitted to early growth data of two Swiss sheep breeds to investigate their suitability for evaluation of breeding values. Models were identical for fixed parity, litter size, sex and lambing season effects, random flock-year, and direct genetic effects but differed for combinations of random litter, permanent environmental, ram-flock, and maternal genetic effects. Records of average daily gain to 30 d of 25,564 lambs of the Black-Brown Mountain Sheep (SBS) and of 26,391 lambs of the White Alpine Sheep (WAS) born 1989 to 1995 and their pedigrees were available. A single-trait animal model was fitted by the restricted maximum likelihood method. The information criterion of a particular model (i.e., the maximum of the likelihood function adjusted for the number of independently estimated parameters) was used to evaluate the models for their fitting power. The litter effect accounted for between 26 and 31% of the phenotypic variance, with little variation within breed. Models containing the ram-flock effect provided a better fit of the data than otherwise identical models. This effect contributed 6 and 4% to the phenotypic variance in the two breeds and strongly influenced estimates of other components. The proportion of phenotypic variance due to the flock-year effect was 23 and 25% without and 19 and 23% including the ram-flock effect in the model in the two breeds. Including permanent environmental effect of the ewe in addition to litter effect led to a better fit of the data. Depending on the model, it then contributed between 3 and 6% to the phenotypic variance. Fitting the ram-flock effect reduced heritability considerably and increased the breed difference of the estimates of this parameter. Estimates ranging from .16 to .10 and from .08 to .14 were obtained for the SBS and WAS breeds, respectively. For models without the ram-flock effect, negative estimates of the direct-maternal correlation of between -.38 and -.45 were observed. Including the ram-flock effect reduced this correlation substantially to between -.08 and -.17. Including the direct-maternal covariance in addition to the ram-flock effect did not improve the fit any further in either breed. Ranking of the models investigated differed between breeds, but the same model provided the best fit. It contained the random litter, permanent environmental, ram-flock, direct, and maternal genetic effects, but not the covariance between the last two.

Aging↗

PubMed1984

RECFIT: a microcomputer-based nonlinear regression curve-fitting package for the quantitative resolution of beta-adrenoceptor subtypes and estimation of nonspecific binding.

A dedicated nonlinear regression based curve-fitting packages has been developed for quantitative analysis of beta-adrenoceptor subtypes. A feature of this package is the provision to obtain initial parameter estimates using a conversational graphical technique where the user is prompted for parameter estimates, and the resulting curve is displayed over the data. Data are then fitted to a one- or two-binding site model with user-selected weighting and constraints on the parameters. A novel feature is the provision to estimate the nonspecific binding component in the assays as a parameter in the model. The printout for each model consists of the parameters and their standard deviations, estimates of the goodness of fit, an analysis of residuals, and a graph of the data points overlayed with the fitted curve. The nonlinear regression algorithm is based on that of Gauss-Newton. When unweighted, the values determined by RECFIT are essentially the same as those found using the BMDPAR programs on an ICL 2976 mainframe computer. The implementation is reasonably efficient; a typical run for a two-site fit, using nine data points and estimating nonspecific binding, took a total time of about 8 min, excluding data entry and derivation of initial estimates, 4 min for the fitting, 30 sec for graph generation, and 2-3 min for printing of the graph and data.

Binding Sites↗

PubMed1996

Estimating mechanical parameters of leg segments in individuals with and without physical disabilities.

Methods are described for estimating the inertia, viscosity, and stiffness of the lower leg around the knee and of the whole leg around the hip that are applicable even to persons with considerable spasticity. These involve: 1) a "pull" test in which the limb is slowly moved throughout its range of motion while measuring angles (with an electrogoniometer) and torques (with a hand-held dynamometer) to determine passive stiffness and 2) a "pendulum" test in which the limb is moved against gravity and then dropped, while again measuring angles and torques. By limiting the extent of the movement and choosing a direction (flexion or extension) that minimizes reflex responses, the mechanical parameters can be determined accurately and efficiently using computer programs. In the sample of subjects studied (nine with disability related to spinal cord injury, head injury, or stroke, and nine with no neurological disability), the inertia of the lower leg was significantly reduced in the subjects with disability (p < 0.05) as a result of atrophy, but the stiffness and viscosity were within normal limits. The values of inertia were also compared with anthropometric data in the literature. The identification of these passive parameters is particularly important in designing systems for functional electrical stimulation of paralyzed muscles, but the methods may be widely applicable in rehabilitation medicine.

Adult↗

PubMed2004

An algorithm for molecular dissection of tumor progression.

The volumetric growth of tumor cells as a function of time is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, i.e., quantitative trait loci (QTL), based on polymorphic markers. In this article, we present a novel statistical model for genetic mapping of QTL governing tumor growth trajectories in humans. In principle, this model is a combination of functional mapping proposed to map function-valued traits and linkage disequilibrium mapping designed to provide high resolution mapping of QTL by making use of recombination events created at a historic time. We implement an EM-simplex hybrid algorithm for parameter estimation, in which a closed-form solution for the EM algorithm is derived to estimate the population genetic parameters of QTL including the allele frequencies and the coefficient of linkage disequilibrium, and the simplex algorithm incorporated to estimate the curve parameters describing the dynamic changes of cancer cells for different QTL genotypes. Extensive simulations are performed to investigate the statistical properties of our model. Through a number of hypothesis tests, our model allows for cutting-edge studies aimed to decipher the genetic mechanisms underlying cancer growth, development and differentiation. The implications of our model in gene therapy for cancer research are discussed.

Algorithms↗

PubMed2001

A nonlinear regression approach to estimating signal detection models for rating data.

This paper considers a regression approach to estimating signal detection parameters for rating data. The methodology is based on the statistical modeling of ordinal data and requires only standard statistical software such as SAS (SAS/STAT User's Guide, 1999) for computation. The approach is more efficient than the current practice of extracting the parameter estimates with the use of specialized software and analyzing the estimates with the use of a standard statistical package. It greatly facilitates exploration of the effects of covariates on model parameters. The method is illustrated using a published data set from a single factor multiple-alternative perceptual task, and data from a more complex factorial design examining recognition memory rating data.

Humans↗

PubMed2004

Assessment of two-compartment models as predictive tools for the bioaccumulation of trace metals in the amphipod Gammarus oceanicus Segerstråle, 1947 from Grunnfjord (Northern Norway).

The objective of the present study is to evaluate the suitability of the eulittoral gammaridean amphipod Gammarus oceanicus Segerstråle, 1947 from Grunnfjord (Northern Norway) as a biomonitor for trace metals Cd, Cr, Pb, Cu, Ni and Zn and to analyse whether the two-compartment model could be used as a predictive tool to assess environmental quality. The focus here is on the adjustment of this model to situations where a linear extrapolation of accumulated metals to increasing external metal exposures is not applicable. The amphipods tested accumulated metals upon exposure and it was possible to estimate significant model parameters of two-compartment models, with the sole exception of Zn. These could be used to predict accumulation of Cd, Cr and Pb in a concentration-dependent uptake study, for Cr directly and regarding simultaneous parameter estimation, for Cd and Pb after adjustment taking into account a non-linear relationship between bioconcentration factors (BCFs) and external metal exposures. The elements Cu and Ni need further evaluation, since linear predictions from the two-compartment models were not applicable, whilst a relationship between kinetic parameters and metal exposures could not be established. Kinetic BCFs at theoretical equilibrium were 80-202 for Cd, 80-112 for Cr, 306 for Cu, 251-520 for Pb and 23 for Ni. A tentative estimation showed the following sequence of sensitivity of G. oceanicus to an increase of soluble metal exposure: 0.6 microg Cdl(-1), 0.8 microg Pbl(-1), 2.5-2.9 microg Crl(-1), 8.5 microg Cul(-1) and 11 microg Nil(-1). Available information can be used to quantify a measure of agreement or disagreement between bioaccumulation in different amphipods. This can be regarded as an important step in the calibration of biomonitors, which is necessary to assess the potential for bioaccumulation on a large geographical scale.

Amphipoda↗

PubMed1988

Using jackknife methods for estimating the parameter in dilution series.

Dilution assays are quantal dose-response assays that detect a positive or negative response in each individual culture within groups of replicate cultures that vary in the dose of cells/organisms tested. We propose three jackknife versions of the maximum likelihood estimator of the unknown parameter, i.e., the frequency of a well-defined cell within the context of limiting dilution assays or the density of organisms within the context of serial dilution assays. The methods have been evaluated with artificial data from extensive Monte Carlo experiments. As a result of these experiments and theoretical considerations, the jackknife version based on deleting one individual culture at a time is proposed as the statistical procedure of choice. The next best method is the jackknife version based on leaving out the same replicate from each of the culture groups at a time.

Biometry↗

PubMed1991

Estimating three-dimensional temperature fields during hyperthermia: studies of the optimal regularization parameter and time sampling period.

During hyperthermia therapy it is desirable to know the entire temperature field in the treatment region. However, accurately inferring this field from the limited number of temperature measurements available is very difficult, and thus state and parameter estimation methods have been used to attempt to solve this inherently ill-posed problem. To compensate for this ill-posedness and to improve the accuracy of this method, Tikhonov regularization of order zero has been used to significantly improve the results of the estimation procedure. It is also shown that the accuracies of the temperature estimates depend upon the value of the regularization parameter, which has an optimal value that is dependent on the perfusion pattern and magnitude. In addition, the transient power-off time sampling period (i.e., the length of time over which transient data is collected and used) influences the accuracy of the estimates, and an optimal sampling period is shown to exist. The effects of additive measurement noise are also investigated, as are the effects of the initial guess of the perfusion values, and the effects of both symmetric and asymmetric blood perfusion patterns. Random perfusion patterns with noisy data are the most difficult cases to evaluate. The cases studied are not a comprehensive set, but continue to show the feasibility of using state and parameter estimation methods to reconstruct the entire temperature field.

Algorithms↗

PubMed2002

Estimating mutation parameters, population history and genealogy simultaneously from temporally spaced sequence data.

Molecular sequences obtained at different sampling times from populations of rapidly evolving pathogens and from ancient subfossil and fossil sources are increasingly available with modern sequencing technology. Here, we present a Bayesian statistical inference approach to the joint estimation of mutation rate and population size that incorporates the uncertainty in the genealogy of such temporally spaced sequences by using Markov chain Monte Carlo (MCMC) integration. The Kingman coalescent model is used to describe the time structure of the ancestral tree. We recover information about the unknown true ancestral coalescent tree, population size, and the overall mutation rate from temporally spaced data, that is, from nucleotide sequences gathered at different times, from different individuals, in an evolving haploid population. We briefly discuss the methodological implications and show what can be inferred, in various practically relevant states of prior knowledge. We develop extensions for exponentially growing population size and joint estimation of substitution model parameters. We illustrate some of the important features of this approach on a genealogy of HIV-1 envelope (env) partial sequences.

Decision Trees↗

PubMed2006

Alternatives to statistical hypothesis testing in ecology: a guide to self teaching.

Statistical methods emphasizing formal hypothesis testing have dominated the analyses used by ecologists to gain insight from data. Here, we review alternatives to hypothesis testing including techniques for parameter estimation and model selection using likelihood and Bayesian techniques. These methods emphasize evaluation of weight of evidence for multiple hypotheses, multimodel inference, and use of prior information in analysis. We provide a tutorial for maximum likelihood estimation of model parameters and model selection using information theoretics, including a brief treatment of procedures for model comparison, model averaging, and use of data from multiple sources. We discuss the advantages of likelihood estimation, Bayesian analysis, and meta-analysis as ways to accumulate understanding across multiple studies. These statistical methods hold promise for new insight in ecology by encouraging thoughtful model building as part of inquiry, providing a unified framework for the empirical analysis of theoretical models, and by facilitating the formal accumulation of evidence bearing on fundamental questions.

Algorithms↗

PubMed1984

Linkage relationships between a major gene for catechol-o-methyltransferase activity and 25 polymorphic marker systems.

Segregation analysis has provided evidence suggesting the existence of a major gene for catechol-o-methyltransferase (COMT) activity in man. Five large families (4 Caucasian, 1 black), with a total of 1,189 individuals, were ascertained as part of a genetic study of blood pressure. Erythrocyte COMT activity and status at 25 polymorphic genetic marker loci were determined on more than 518 individuals in these pedigrees. Genetic linkage analysis of COMT with each of the 25 marker loci was performed in two ways: 1) using parameter estimates from segregation analysis of untransformed COMT activity, and 2) using parameter estimates from segregation analysis of the power transformation of the COMT activity that maximized the likelihood of the genetic hypothesis in each family. Tight and close linkage were excluded at 21 and 15 loci, respectively. A lod score of 1.27 at theta = 0.1 was found between the loci for COMT activity and phosphogluconate dehydrogenase (PGD). Transformation of the data had little effect on the outcome of the linkage analysis.

Catechol O-Methyltransferase↗