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At least 667 records · Page 37Linked to original sources
PubMed2003

Detection of suppressor T lymphocytes and estimation of their frequency in limiting dilution assays by generalized linear regression modeling.

The estimate of the frequency of suppressor T lymphocytes in unfractionated cell populations remains challenging, mainly because these regulatory cells do not display specific immunophenotypic markers. In this paper, we describe a novel theoretical approach for quantifying the frequency of suppressor cells. This method is based on limiting dilution data modeling, and allows the simultaneous estimation of the frequencies of both proliferating and suppressor cells. We used previously published biological data, characterizing the inhibiting activity of suppressor T cell clones. Starting from these data, we propose a mathematical model describing the interaction between suppressor and proliferating T cells, and applied to a Poisson process. Limiting dilution data corresponding to this non-single-hit, suppressor two-target Poisson model were artificially generated, then modeled according to a generalized linear regression procedure. Deviation from the single-hit Poisson model was revealed by a statistical slope test, and a stepwise analysis of the regression appeared to be an efficient method that strongly argued in favor of the presence of suppressor cells. By using the frequency of proliferating T cells calculated in the first step of the regression, we demonstrated the possibility to provide a reasonable estimate of the frequency of suppressor T cells. Based on these findings, a practical decision-making procedure is given to perform standard analyses of limiting dilution data.

Animals↗
PubMedDate not supplied

Predicting the cost of illness: a comparison of alternative models applied to stroke.

Predictions of cost over well-defined time horizons are frequently required in the analysis of clinical trials and social experiments, for decision models investigating the cost-effectiveness of interventions, and for macro-level estimates of the resource impact of disease. With rare exceptions, cost predictions used in such applications continue to take the form of deterministic point estimates. However, the growing availability of large administrative and clinical data sets offers new opportunities for a more general approach to disease cost forecasting: the estimation of multivariable cost functions that yield predictions at the individual level, conditional on intervention(s), patient characteristics, and other factors. This raises the fundamental question of how to choose the "best" cost model for a given application. The central purpose of this paper is to demonstrate how to evaluate competing models on the basis of predictive validity. This concept is operationalized according to three alternative criteria: 1) root mean square error (RMSE), for evaluating predicted mean cost; 2) mean absolute error (MAE), for evaluating predicted median cost; and 3) a logarithmic scoring rule (log score), an information-theoretic index for evaluating the entire predictive distribution of cost. To illustrate these concepts, the authors conducted a split-sample analysis of data from a national sample of Medicare-covered patients hospitalized for ischemic stroke in 1991 and followed to the end of 1993. Using test and training samples of about 500,000 observations each, they investigated five models: single-equation linear models, with and without log transform of cost; two-part (mixture) models, with and without log transform, to directly address the problem of zero-cost observations; and a Cox proportional-hazards model stratified by time interval. For deriving the predictive distribution of cost, the log transformed two-part and proportional-hazards models are superior. For deriving the predicted mean or median cost, these two models and the commonly used log-transformed linear model all perform about the same. The untransformed models are dominated in every instance. The approaches to model selection illustrated here can be applied across a wide range of settings.

Cerebrovascular Disorders↗
PubMed1999

The use of mixed logit models to reflect heterogeneity in capture-recapture studies.

We examine issues in estimating population size N with capture-recapture models when there is variable catchability among subjects. We focus on a logistic-normal mixed model, for which the logit of the probability of capture is an additive function of a random subject and a fixed sampling occasion parameter. When the probability of capture is small or the degree of heterogeneity is large, the log-likelihood surface is relatively flat and it is difficult to obtain much information about N. We also discuss a latent class model and a log-linear model that account for heterogeneity and show that the log-linear model has greater scope. Models assuming homogeneity provide much narrower intervals for N but are usually highly overly optimistic, the actual coverage probability being much lower than the nominal level.

Animals↗
PubMed2006

Effects of unmeasured heterogeneity in the linear transformation model for censored data.

We investigate the effect of unobserved heterogeneity in the context of the linear transformation model for censored survival data in the clinical trials setting. The unobserved heterogeneity is represented by a frailty term, with unknown distribution, in the linear transformation model. The bias of the estimate under the assumption of no unobserved heterogeneity when it truly is present is obtained. We also derive the asymptotic relative efficiency of the estimate of treatment effect under the incorrect assumption of no unobserved heterogeneity. Additionally we investigate the loss of power for clinical trials that are designed assuming the model without frailty when, in fact, the model with frailty is true. Numerical studies under a proportional odds model show that the loss of efficiency and the loss of power can be substantial when the heterogeneity, as embodied by a frailty, is ignored.

Clinical Trials as Topic↗
PubMed2004

The use of linear mixed models to estimate variance components from data on twin pairs by maximum likelihood.

It is shown that maximum likelihood estimation of variance components from twin data can be parameterized in the framework of linear mixed models. Standard statistical packages can be used to analyze univariate or multivariate data for simple models such as the ACE and CE models. Furthermore, specialized variance component estimation software that can handle pedigree data and user-defined covariance structures can be used to analyze multivariate data for simple and complex models, including those where dominance and/or QTL effects are fitted. The linear mixed model framework is particularly useful for analyzing multiple traits in extended (twin) families with a large number of random effects.

Algorithms↗
PubMed2006

The prediction of stress-relaxation of ligaments and tendons using the quasi-linear viscoelastic model.

Recent studies have questioned the ability of the quasi-linear viscoelastic (QLV) model to predict stresses and strains in response to loading conditions other than those used to fit the model. The objective of this study was to evaluate the ability of several models in the literature to predict the elastic stress response of ligament and tendon at strain levels higher than the levels used to fit the model. The constitutive models were then used to evaluate the ability of the QLV model to predict the overall stress response during stress relaxation. The models expressing stress as an exponential function of strain significantly overestimated stress when used at higher strain levels. The polynomial formulation of the Mooney-Rivlin model more accurately predicted the stress-strain behavior of ligament and tendon. The results demonstrate that the ability of the QLV model to accurately predict the stress-relaxation response is dependent in part on the accuracy of the function used to model the elastic response of the soft tissue.

Elasticity↗
PubMed2001

An alternative parameterization of the general linear mixture model for longitudinal data with non-ignorable drop-outs.

This paper considers the mixture model methodology for handling non-ignorable drop-outs in longitudinal studies with continuous outcomes. Recently, Hogan and Laird have developed a mixture model for non-ignorable drop-outs which is a standard linear mixed effects model except that the parameters which characterize change over time depend also upon time of drop-out. That is, the mean response is linear in time, other covariates and drop-out time, and their interactions. One of the key attractions of the mixture modelling approach to drop-outs is that it is relatively easy to explore the sensitivity of results to model specification. However, the main drawback of mixture models is that the parameters that are ordinarily of interest are not immediately available, but require marginalization of the distribution of outcome over drop-out times. Furthermore, although a linear model is assumed for the conditional mean of the outcome vector given time of drop out, after marginalization, the unconditional mean of the outcome vector is not, in general, linear in the regression parameters. As a result, it is not possible to parsimoniously describe the effects of covariates on the marginal distribution of the outcome in terms of regression coefficients. The need to explicitly average over the distribution of the drop-out times and the absence of regression coefficients that describe the effects of covariates on the outcome are two unappealing features of the mixture modelling approach. In this paper we describe a particular parameterization of the general linear mixture model that circumvents both of these problems.

Anti-Asthmatic Agents↗
PubMed1977

[Model building in pharmacokinetics/Part II: Generalized theoretical presentation of complete integration of linear compartment models of optional structure (author's transl)].

The method of Laplace transformation is used to obtain the integral of linear differential equations for pharmacokinetic models. A general solution uniform in structure for all types of models (mammillary, catenary, mixed) was established. Choice of one more application compartments, of kinetics describing the input procedure and of elimination pathways is free.

Kinetics↗
PubMed1992

Using follow-up data to avoid omitted variable bias: an application to cardiovascular epidemiology.

Omitted variable bias is discussed in the context of linear models. It is shown that the effect of omitted variables can be controlled in linear models for metric dependent variables by using data from follow-up studies. Two different models for analysing such data are proposed. In the first model the omitted variables are assumed to be uncorrelated with the explanatory variables in the model and to be constant over time. These assumptions lead to a special structure of the covariance matrix of the errors over time. Efficient estimation of the parameters in the linear model has to take this special covariance matrix of the errors into account by using appropriate generalized least squares or maximum likelihood methods. In the second model the omitted variables are assumed to be time constant. Additionally, they are allowed to be correlated with the explanatory variables, that is these variables are omitted confounders in the usual epidemiological sense. It is shown that even in this case the parameters of the linear model can be estimated consistently with ordinary least squares if a follow-up study is available. The differences between the parameter estimates under the first and the second model may be used to construct a Hausman test for misspecification. The models, the estimation methods and the Hausman test are illustrated by the example that explores the determinants of serum cholesterol in German adoloscents of both sexes.

Adolescent↗
PubMed2005

Is it possible to predict the average surface hydrophobicity of a protein using only its amino acid composition?

Hydrophobicity is one of the most important physicochemical properties of proteins. Moreover, it plays a fundamental role in hydrophobic interaction chromatography, a separation technique that, at present time, is used in most industrial processes for protein purification as well as in laboratory scale applications. Although there are many ways of assessing the hydrophobicity value of a protein, recently, it has been shown that the average surface hydrophobicity (ASH) is an important tool in the area of protein separation and purification particularly in protein chromatography. The ASH is calculated based on the hydrophobic characteristics of each class of amino acid present on the protein surface. The hydrophobic characteristics of the amino acids are determined by a scale of aminoacidic hydrophobicity. In this work, the scales of Cowan-Whittaker and Berggren were studied. However, to calculate the ASH, it is necessary to have the three-dimensional protein structure. Frequently this data does not exist, and the only information available is the amino acid sequence. In these cases it would be desirable to estimate the ASH based only on properties extracted from the protein sequence. It was found that it is possible to predict the ASH from a protein to an acceptable level for many practical applications (correlation coefficient > 0.8) using only the aminoacidic composition. Two predictive tools were built: one based on a simple linear model and the other on a neural network. Both tools were constructed starting from the analysis of a set of 1982 non-redundant proteins. The linear model was able to predict the ASH for an independent subset with a correlation coefficient of 0.769 for the case of Cowan-Whittaker and 0.803 for the case of Berggren. On the other hand, the neural model improved the results shown by the linear model obtaining correlation coefficients of 0.831 and 0.836, respectively. The neural model was somewhat more robust than the linear model particularly as it gave similar correlation coefficients for both hydrophobicity scales tested, moreover, the observed variabilities did not overcome 6.1% of the mean square error. Finally, we tested our models in a set of nine proteins with known retention time in hydrophobic interaction chromatography. We found that both models can predict this retention time with correlation coefficients only slightly inferior (11.5% and 5.5% for the linear and the neural network models, respectively) than models that use the information about the three-dimensional structure of proteins.

Amino Acids↗
PubMed1998

The detection of residual serial correlation in linear mixed models.

Diggle (1988) described how the empirical semi-variogram of ordinary least squares residuals can be used to suggest an appropriate serial correlation structure in stationary linear mixed models. In this paper, this approach is extended to non-stationary models which include random effects other than intercepts, and will be applied to prostate cancer data, taken from the Baltimore Longitudinal Study of Aging. A simulation study demonstrates the effectiveness of this extended variogram for improving the covariance structure of the linear mixed model used to describe the prostate data.

Analysis of Variance↗
PubMed2005

General linearized biexponential model for QSAR data showing bilinear-type distribution.

A major impediment of many QSAR-type analyses is that the data show a maximum or minimum and can no longer be adequately described by linear functions that provide unrivaled simplicity and usually give good description over more restricted ranges. Here, a general linearized biexponential (LinBiExp) model is proposed that can adequately describe data showing bilinear-type distribution as a function of not just often-employed lipophilicity descriptors (e.g., log P) but as a function of any descriptor (e.g., molecular volume). Contrary to Hansch-type parabolic models, LinBiExp allows the natural extension of linear models and fitting of asymmetrical data. It is also more general and intuitive than Kubinyi's model as it has a more natural functional form. It was obtained by a differential equation-based approach starting from very general assumptions that cover both static equilibria and first-order kinetic processes and that involve abstract processes through which the concentration of the compound of interest in an assumed "effect" compartment is connected to its "external" concentration. Physicochemical aspects placing LinBiExp within the framework of linear free energy relationship (LFER) approaches are presented together with illustrative applications in various fields such as toxicity, antimicrobial activity, anticholinergic activity, and glucocorticoid receptor binding.

Alcohols↗
PubMed2003

Random effects selection in linear mixed models.

We address the important practical problem of how to select the random effects component in a linear mixed model. A hierarchical Bayesian model is used to identify any random effect with zero variance. The proposed approach reparameterizes the mixed model so that functions of the covariance parameters of the random effects distribution are incorporated as regression coefficients on standard normal latent variables. We allow random effects to effectively drop out of the model by choosing mixture priors with point mass at zero for the random effects variances. Due to the reparameterization, the model enjoys a conditionally linear structure that facilitates the use of normal conjugate priors. We demonstrate that posterior computation can proceed via a simple and efficient Markov chain Monte Carlo algorithm. The methods are illustrated using simulated data and real data from a study relating prenatal exposure to polychlorinated biphenyls and psychomotor development of children.

Algorithms↗
PubMed1999

The Linear Index Model for establishing nutrient goals in the Dietary Approaches to Stop Hypertension trial. DASH Collaborative Research Group.

Establishing target levels of nutrients in feeding studies presents a challenge to dietitians. Although researchers studying energy-containing nutrients, such as protein and fat, commonly establish target levels according to body weight or as a percentage of energy, it is less clear how to establish levels of micronutrients. Typically, a constant target level is used regardless of energy requirements. Alternatively, nutrients could be provided at a fixed level per 1,000 kcal. Such an approach, however, could result in absolute levels of nutrient intakes that are difficult to achieve through foods alone, particularly for persons with high energy requirements. This report describes the Linear Index Model, a new approach for establishing target levels of selected micronutrients in the Dietary Approaches to Stop Hypertension trial. This model indexes micronutrient levels to energy levels to achieve a linear range of targeted intake in proportion to the energy intake. The Linear Index Model has several benefits: it takes advantage of indexing nutrients according to energy requirements, thus providing levels of nutrient intakes that can be readily achieved by foods; it is based on population consumption data, thus providing a realistic range of intakes for the experimental conditions; and it ensures distinct contrasts in experimental conditions. The Linear Index Model is a feasible and practical approach for establishing target levels of nutrients in feeding studies.

Blood Pressure↗
PubMed2005

Clustering expressed genes on the basis of their association with a quantitative phenotype.

Cluster analyses of gene expression data are usually conducted based on their associations with the phenotype of a particular disease. Many disease traits have a clearly defined binary phenotype (presence or absence), so that genes can be clustered based on the differences of expression levels between the two contrasting phenotypic groups. For example, cluster analysis based on binary phenotype has been successfully used in tumour research. Some complex diseases have phenotypes that vary in a continuous manner and the method developed for a binary trait is not immediately applicable to a continuous trait. However, understanding the role of gene expression in these complex traits is of fundamental importance. Therefore, it is necessary to develop a new statistical method to cluster expressed genes based on their association with a quantitative trait phenotype. We developed a model-based clustering method to classify genes based on their association with a continuous phenotype. We used a linear model to describe the relationship between gene expression and the phenotypic value. The model effects of the linear model (linear regression coefficients) represent the strength of the association. We assumed that the model effects of each gene follow a mixture of several multivariate Gaussian distributions. Parameter estimation and cluster assignment were accomplished via an Expectation-Maximization (EM) algorithm. The method was verified by analysing two simulated datasets, and further demonstrated using real data generated in a microarray experiment for the study of gene expression associated with Alzheimer's disease.

Algorithms↗
PubMed1989

Linear-quadratic model isoeffect relations for proliferating tumor cells for treatment with multiple fractions per day.

A modified linear-quadratic model isoeffect relation that includes the effect of proliferation is proposed. As for a planned course of therapy, the treatment time T and the number of fractions N are not independent variables; the new isoeffect relation involves only the fraction size d and the total dose D, but differs from the unmodified linear-quadratic model isoeffect relation and predicts higher isoeffect doses for small dose fractions. Using the new isoeffect relation it is explicitly shown, for a simple model, that decreasing the fraction size will improve the therapeutic ratio only if multiple fractions per day are given.

Cell Division↗
PubMed1995

Modelling series of visual fields to detect progression in normal-tension glaucoma.

BACKGROUND: Use of statistical modelling techniques to identify models that both describe glaucomatous sensitivity decay and allow predictions of future field status. METHOD: Twelve initially normal fellow eyes of untreated patients with confirmed normal tension glaucoma were studied. All had in excess of 15 Humphrey fields (mean follow-up 5.7 years). From this cohort individual field locations were selected for analysis if they demonstrated unequivocal deterioration at the final two fields. Forty-seven locations from five eyes satisfied this criterion and were analysed using curve-fitting software which automatically applies 221 different models to sensitivity (y) against time of follow up (x). Curve-fitting was then repeated on the first five fields, followed by projection to the date of the final field to generate a predicted threshold which was compared to the actual threshold. Competing models were therefore assessed on their performance at adequately fitting the data (R2) and their potential to predict future field status. RESULTS: Models that provide the best fit to the data were all complex polynomial expressions (median R2 0.93). Other simple expressions fitted fewer locations and exhibited lower R2 values. However, accuracy in predicting future deterioration was superior with these less complex models. In this group a linear expression demonstrated an adequate fit to the majority of the data and generated the most accurate predictions of future field status. CONCLUSIONS: A linear model of the pointwise sensitivity values against time of follow-up can provide a framework for detecting and forecasting glaucomatous field progression. Linear modelling allows the clinically important rate of sensitivity loss to be estimated.

Cohort Studies↗