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PubMed1995

General linear compartment model with zero input: I. Kinetic equations.

The derivation of kinetic equations is described for n-compartment linear models, in which the substance may be simultaneously introduced into one or more compartments at t = 0 and eliminated from any compartment. For a given zero-input, general formulas are derived which describe the amount of tracer in any of the compartments as a function of time and the model parameters. New algorithms have been developed which allow the expression of the kinetic equations.

Algorithms↗

PubMed2003

Using simultaneous equation modeling for defining complex phenotypes.

BACKGROUND: Interactions between multiple biological phenotypes are difficult to model. Simultaneous equation modelling (SEM), as used in econometric modelling, may prove an effective tool for this problem. Generalized linear models were used to derive the structural equations defining the interactions between cholesterol, glucose, triglycerides and high-density lipoprotein cholesterol (HDL-C). These structural equations were then applied, using SEM, to Cohort 2 data (replicates 1-100) to estimate the phenotypic structure underlying the simulation. The goal was to determine if this empiric method of deriving structural equations for use in SEM was able to recover the simulation model better than generalized linear models. RESULTS: First, the underlying structural equations were estimated using generalized linear model techniques, which found strong a relationship between glucose, triglycerides and HDL-C. Using these structural equations, I used SEM to evaluate these relationships jointly. I found that a combination of the empiric structural equations and the SEM method was better at recovering the underlying simulated relationship between biologic measures than generalized linear modelling. CONCLUSION: The empiric SEM procedure presented here estimated different relationships between dependent variables than generalized linear modelling. The SEM procedure using empirically developed structural equations was able to recover the underlying simulation relationship partially and thus holds promise as a technique for complex phenotype analysis. Robust methods for determining the structural equations must be developed for application of SEM to population data.

Cardiovascular Diseases↗

PubMed2001

Graphical representation of a generalized linear model-based statistical test estimating the fit of the single-hit Poisson model to limiting dilution assays.

Standardized statistical and graphical methods for analysis of limiting dilution assays are highly desirable to enable investigators to compare and interpret results and conclusions with greater accuracy and precision. According to these requirements, we present in this work a powerful statistical slope test that estimates the fit of the single-hit Poisson model to limiting dilution experiments. This method is readily amenable to a graphical representation. This slope test is obtained by modeling limiting dilution data according to a linear log-log regression model, which is a generalized linear model specially designed for modeling binary data. The result of the statistical slope test can then be graphed to visualize whether the data are compatible or not with the single-hit Poisson model. We demonstrate this statistical test and its graphical representation by using two examples: a real limiting dilution experiment evaluating the growth frequency of IL-2-responsive tumor-infiltrating T cells in a malignant lymph node involved by a B cell non-Hodgkin's lymphoma, and a simulation of a limiting dilution assay corresponding to a theoretical non-single-hit Poisson model, suppressor two-target Poisson model.

Allergy and Immunology↗

PubMed2003

A biphasic model of limb venous compliance: a comparison with linear and exponential models.

Compliance is not linear within the physiological range of pressures, and linear modeling may not describe venous physiology adequately. Forearm and calf venous compliance were assessed in nine subjects. Venous compliance was modeled by using a biphasic model with high- and low-pressure linear phases separated by a breakpoint. This model was compared with a linear model and several exponential models. The biphasic, linear, and two-parameter exponential models best represented the data. The mean coefficient of determination for the biphasic model was greater than for the linear and exponential models in the calf (biphasic 0.94 +/- 0.04, exponential 0.81 +/- 0.16, P = not significant; and linear 0.54 +/- 0.05, P < 0.05) and forearm (biphasic 0.83 +/- 0.17, exponential 0.79 +/- 0.15, P = not significant; and linear 0.51 +/- 0.06, P < 0.05). The breakpoint pressure in the biphasic model was higher in the calf than the forearm, 34.4 +/- 3.9 vs. 29.1 +/- 4.5 mmHg, P < 0.05. A biphasic model can describe limb venous compliance and delineate differences in venous physiology at high and low pressures. The steep low-pressure phase of the compliance curve extends to higher pressures in the calf than in the forearm, thereby enlarging the range of pressures over which hemodynamic regulation by the calf venous circulation occurs.

Adult↗

PubMed2000

[Ionizing radiation].

Everyone is exposed to radiation from natural, man-made and medical sources, and world-wide average annual exposure can be set at about 3.5 mSv. Exposure to natural sources is characterised by very large fluctuations, not excluding a range covering two orders of magnitude. Millions of inhabitants are continuously exposed to external doses as high as 10 mSv per year, delivered at low dose rates, very few workers are exposed above the legal limit of 50 mSv/year, and referring to accidental exposures, only 5% of the 116,000 people evacuated following the Chernobyl disaster encountered doses above 100 mSv. Epidemiological survey of accidentally, occupationally or medically exposed groups have revealed radio-induced cancers, mostly following high dose-rate exposure levels, only above 100 mSv. Risk coefficients were derived from these studies and projected into linear models of risk (linear non-threshold hypothesis: LNT), for the purpose of risk management following exposures at low doses and low dose-rates. The legitimacy of this approach has been questioned, by the Academy of sciences and the Academy of medicine in France, arguing: that LNT was not supported by Hiroshima and Nagasaki studies when neutron dose was revisited; that linear modelling failed to explain why so many site-related cancers were obviously non-linearly related to the dose, and especially when theory predicted they ought to be; that no evidence could be found of radio-induced cancers related to natural exposures or to low exposures at the work place; and that no evidence of genetic disease could be shown from any of the exposed groups. Arguments were provided from cellular and molecular biology helping to solve this issue, all resulting in dismissing the LNT hypothesis. These arguments included: different mechanisms of DNA repair at high and low dose rate; influence of inducible stress responses modifying mutagenesis and lethality; bystander effects allowing it to be considered that individual cellular responses reflected in fact the results of multiple cellular interactions. Following the conclusion of the French Academy of medicine, LNT modelling resulted in public anxiety by changing an hypothetical residual risk at low doses into a real one, calling on regulators, continuously, for a more and more severe control of tiny sources which may result in considerable collective doses when considered as being exposed to billions of people for hundreds of years. Examples were provided that showed that the perception of risk of radioactive sources was not related to the severity of the risk itself but to the importance attributed to the situation by the media. In some instances, such as those resulting from the loss of gammagraphy sources, it resulted in a dangerous underestimate of the necessary remedial actions.

Dose-Response Relationship, Radiation↗

PubMed2004

Evaluation of community-intervention trials via generalized linear mixed models.

In community-intervention trials, communities, rather than individuals, are randomized to experimental arms. Generalized linear mixed models offer a flexible parametric framework for the evaluation of community-intervention trials, incorporating both systematic and random variations at the community and individual levels. We propose here a simple two-stage inference method for generalized linear mixed models, specifically tailored to the analysis of community-intervention trials. In the first stage, community-specific random effects are estimated from individual-level data, adjusting for the effects of individual-level covariates. This reduces the model approximately to a linear mixed model with the unit of analysis being community. Because the number of communities is typically small in community-intervention studies, we apply the small-sample inference method of Kenward and Roger (1997, Biometrics53, 983-997) to the linear mixed model of second stage. We show by simulation that, under typical settings of community-intervention studies, the proposed approach improves the inference on the intervention-effect parameter uniformly over both the linearized mixed-effect approach and the adaptive Gaussian quadrature approach for generalized linear mixed models. This work is motivated by a series of large randomized trials that test community interventions for promoting cancer preventive lifestyles and behaviors.

Biometry↗

PubMed1999

Neighborhoods and child maltreatment: a multi-level study.

OBJECTIVE: To better understand how neighborhood and individual factors are related to child maltreatment. METHOD: Using an ecological framework, a multi-level model (Hierarchical Linear Modeling) was used to analyze neighborhood structural conditions and individual risk factors for child abuse and neglect. Parents (n = 400) of children under the age of 18 were systematically selected from 20 randomly selected census-defined block groups with different risk profiles for child maltreatment report rates. Parents were administered the Neighborhood Environment for Children Rating Scales, the Child Abuse Potential Inventory, the Zimet measure of social support, and the Conflict Tactics Scales as a measure of childhood experience with violence. RESULTS: Neighborhood factors of impoverishment and child care burden significantly affect child abuse potential after controlling for individual risk factors. However, neighborhood effects are weaker than they appear to be in aggregate studies of official child maltreatment reports. Variation in child abuse potential within neighborhoods is greater than between neighborhoods. However, adverse neighborhood conditions weakend the effects of known individual risk and protective factors, such as violence in the family of origin. CONCLUSIONS: If individual potential for child maltreatment is more evenly distributed across neighborhoods than reported maltreatment, then neighborhood and community play an important, if as yet unspecified, role in child maltreatment. Multi-level models are a promising research strategy for disentangling the complex interactions of individual and contextual factors in child maltreatment.

Adult↗

PubMedDate not supplied

Characteristics and trajectories of treatment foster care youth.

Using cross-sectional analyses in conjunction with dynamic modeling (hierarchical linear modeling), the authors profiled 119 treatment foster care youth and constructed behavioral change trajectories for a subset of 97 children. Children generally showed improvements in internalizing and critical pathology problem domains but remained the same on measures of externalizing behaviors and total problem score. The number of previous out-of-home placements was positively associated with increased levels of psychiatric symptomatology and served as the most robust predictor for modeling treatment response trajectories across problem domains. Placement instability places the well-being of children at heightened risk, therefore, accurate assessment of child need and risk in relation to caregiver capacities is critical.

Adolescent↗

PubMedDate not supplied

[Multilevel model applications to the analysis of longitudinal data].

This work is an introduction to repeated measurement analysis for longitudinal studies. It uses a two stage modelling framework, using hierarchical linear models with two levels. The first level pertains to the repeated measures, the second level pertains to the individual. For the last 25 years, hierarchical linear models have been used in the Social Sciences to analyse data coming from organizations with multiple levels. Their applications have been extended to the study of change in populations, both to describe the average change in an outcome variable in a population and to analyse the factors associated with variability in the individual trajectories of change. In this article, the basic concepts are introduced: between subjects and within subjects variability, the person-specific model for the individual trajectory and the between person model to describe how individuals vary in their trajectories, fixed and random effects, linear and quadratic growth models. At the end of each section, an illustration is given for the study of cognitive function of the older people cohort "Aging in Leganés", followed in four occasions between 1993 and 1999. Results from fitting the models to answer the most frequently asked research questions in the descriptions and analysis of individual change are presented. Lastly, we present possible generalizations of these linear models to non linear situations which arise when outcomes are dichotomous, nominal or ordinal.

Aging↗

PubMed2001

Local influence to detect influential data structures for generalized linear mixed models.

This article discusses the generalization of the local influence measures for normally distributed responses to local influence measures for generalized linear models with random effects. For these models, it is shown that the subject-oriented influence measure is a special case of the proposed observation-oriented influence measure. A two-step diagnostic procedure is proposed. The first step is to search for influential subjects. A search for influential observations is proposed as the second step. An illustration of a two-treatment, multiple-period crossover trial demonstrates the practical importance of the detection of influential observations in addition to the detection of influential subjects.

Aspartame↗

PubMed1998

Neural network subtyping of depression.

OBJECTIVE: To examine the applicability of a neural network classification strategy to examine the independent contribution of psychomotor disturbance (PMD) and endogeneity symptoms to the DSM-III-R definition of melancholia. METHOD: We studied 407 depressed patients with the clinical dataset comprising 17 endogeneity symptoms and the 18-item CORE measure of behaviourally rated PMD. A multilayer perception neural network was used to fit non-linear models of varying complexity. A linear discriminant function analysis was also used to generate a model for comparison with the non-linear models. RESULTS: Models (linear and non-linear) using PMD items only and endogeneity symptoms only had similar rates of successful classification, while non-linear models combining both PMD and symptoms scores achieved the best classifications. CONCLUSIONS: Our current non-linear model was superior to a linear analysis, a finding which may have wider application to psychiatric classification. Our non-linear analysis of depressive subtypes supports the binary view that melancholic and non-melancholic depression are separate clinical disorders rather than different forms of the same entity. This study illustrates how non-linear modelling with neural networks is a potentially fruitful approach to the study of the diagnostic taxonomy of psychiatric disorders and to clinical decision-making.

Behavioral Symptoms↗

PubMed2006

Glucose dynamics in Type I diabetes: insights from the classic and linear minimal models.

This study demonstrates that the classic minimal model (MM) and the linear minimal model (LMM) are able to follow the dynamics of glucose in Type I diabetes. LMM precision is better than the MM with systematic lower mean values for the coefficient of variation (CV) in all characteristic model parameters. LMM S(I)(L)=7.40 is not significantly different from MM S(I)=10.71 (units 1/min per muU/ml, alpha=0.001) with a strong correlation (R(s) = 0.83, alpha=0.01). LMM S(G)(L)=0.0407 appears to be significantly different to S(G)=0.0266 (units 1/min, alpha=0.001) but correlates very well (R(s)=0.91,alpha=0.01). Since residuals appear to be heteroscedastic, further work is required to address the effect of modeling and signal processing on them. For the data under study, the models are not able to fit two-thirds of the data windows available. This is because none of the models are able to follow complex situations such as the presence of several bolus injections, the absence of insulin supply or inappropriate insulin dosage. A synthesis of the patterns found in these windows is presented which would be useful for the development of new models for fitting these data.

Absorption↗

PubMed2003

Evaluation models and genetic parameters for calving difficulty in beef cattle.

Calving difficulty was analyzed under threshold and linear models considering either a fixed or random herd-year effect. The aim of the study was to compare models for predicting breeding values according to the size of herd-year groups. When simulating data sets with small herds, in order to obtain an unbiased evaluation under a nonrandom and negative association of sire and herd effects, the best model for a practical evaluation was the fixed linear model. Field data included 246,576 records of the largest Charolais herds in France. Models were compared using the correlations of estimated breeding values between the different models. Although the best model from a theoretical point of view was a threshold model with a fixed herd-year effect, a linear model with a fixed herd-year effect was the best choice from a practical point of view for predicting direct effects for calving difficulty in beef cattle and was a sufficient choice for predicting the associated maternal effects for data set with large herds. Correlations between direct estimated breeding values under the reference model and the fixed linear model and the random threshold model were 0.94 and 0.91, respectively. Correlations between the corresponding maternal estimated breeding values were 0.94 and 0.98. Heritabilities of direct effects were 0.27 and 0.14 under fixed threshold and fixed linear models, respectively. The corresponding heritabilities of maternal effects were 0.18 and 0.13, and the genetic correlation between direct and maternal effects were -0.36 and -0.34, respectively.

Animal Husbandry↗

PubMed1998

Evaluation of selected mathematical approaches to the kinetics of protein degradation in situ.

A linear model, two mathematical nonlinear models, and a curve-peeling procedure were used to estimate rate and extent of ruminal CP degradation of meat and bone meal (MBM) and soybean meal (SBM) from data obtained using the in situ Dacron polyester bag technique. Most of the values for extent of CP degradation of MBM were lowest when determined using curve peeling or the nonlinear models. In general, rates and extents of CP degradation of MBM estimated using the linear model and including ruminal incubations up to 12 h were greater than those obtained with the linear model and including ruminal incubations up to 24 h or up to 72 h. In addition, the models ranked the MBM samples differently for rate and extent of CP degradation. The results of the lack-of-fit test indicated that the linear model was inappropriate for estimating rate of degradation of MBM. However, CP degradation for SBM could be described by the linear model if long ruminal incubation times (greater than 48 h) were included in the calculations. Regression analyses were conducted to evaluate various compositional characteristics as predictors of CP degradation for MBM. Most of the correlation coefficients between CP degradation and the same independent variables were greater when the nonlinear models and curve peeling were used compared with the linear model. In general, the correlation coefficients between extent of CP degradation and the independent variables obtained with the linear model increased as the duration of ruminal incubations included in the model increased. Lysine concentrations, followed by CP solubility and ash content, were the best predictors of ruminal degradation of MBM protein. When using a specific mathematical model to predict CP degradation, analysis of residuals vs fitted and lack-of-fit tests should be performed to assess the validity of the model to describe the degradation patterns of the protein source under consideration. Also, long (at least 48 h) ruminal incubation times may be needed to correctly describe the pattern of CP degradation for MBM.

Animal Feed↗

PubMed1989

A class of linear spectral models and analyses for the study of longitudinal data.

Longitudinal data can always be represented by a time series with a deterministic trend and randomly correlated residuals, the latter of which do not usually form a stationary process. The class of linear spectral models is a basis for the exploratory analysis of these data. The theory and techniques of factor analysis provide a means by which one component of the residual series can be separated from an error series, and then partitioned into a sum of randomly scaled metameters that characterize the sample paths of the residuals. These metameters, together with linear modelling techniques, are then used to partition the nonrandom trend into a determined component, which is associated with the sample paths of the residuals, and an independent inherent component. Linear spectral models are assumption-free and represent both random and nonrandom trends with fewer terms than any other mixed-effects linear model. Data on body-weight growth of juvenile mice are used in this paper to illustrate the application of linear spectral models, through a relatively sophisticated exploratory analysis.

Animals↗

PubMed2005

The Mid-Canada Radar Line and First Nations' people of the James Bay region, Canada: an evaluation using log-linear contingency modelling to analyze organochlorine frequency data.

Abandoned radar line stations in the North American arctic and sub-arctic regions are point sources of contamination, especially for PCBs. Few data exist with respect to human body burden of organochlorines (OCs) in residents of communities located in close proximity to these radar line sites. We compared plasma OC concentration (unadjusted for total lipids) frequency distribution data using log-linear contingency modelling for Fort Albany First Nation, the site of an abandoned Mid-Canada Radar Line station, and two comparison populations (the neighbouring community of Kashechewan First Nation without such a radar installation, and Hamilton, a city in southern Ontario, Canada). This type of analysis is important as it allows for an initial investigation of contaminant data without imputing any values. The two-state log-linear model (employing both non-detectable and detectable concentration frequencies and applicable to PCB congeners 28 and 105 and cis-nonachlor) and the four-state log-linear model (using quartile concentration frequencies for Aroclor 1260, PCB congeners [99,118,138,153,156,170,180,183,187], beta-HCH, p,p'-DDT +p,p'-DDE, HCB, mirex, oxychlordane, and trans-nonachlor) revealed that the effects of subject gender were inconsequential. Significant differences (p < 0.05) between the groups examined were attributable to the effect of location on the frequency of detection of OCs or on their differential distribution among the concentration quartiles. In general, people from Hamilton had higher frequencies of non-detections and of concentrations in the first quartile (p < 0.05) for most OCs compared to people from Fort Albany and Kashechewan (who consume a traditional diet of wild meats that does not include marine mammals). An unexpected finding was that, for Kashechewan males, the frequency of many OCs was significantly higher (p < 0.05) in the 4th concentration quartile than that predicted by the four-state log-linear model, but significantly lower than expected in the 1st quartile for beta-HCH. The levels of PCBs found for women in Fort Albany and Kashechewan were greater than those reported for Dene (First Nation people) and Métis (mixed heritage) of the western Northwest Territories (NWT) who did not consume marine mammals, and for Inuit living in the central NWT (occasional consumers of marine mammals). Moreover, the levels of total p,p'-DDT were greater for Fort Albany and Kashechewan women compared to these same aboriginal groups.

Animals↗

PubMed2000

A scaled linear mixed model for multiple outcomes.

We propose a scaled linear mixed model to assess the effects of exposure and other covariates on multiple continuous outcomes. The most general form of the model allows a different exposure effect for each outcome. An important special case is a model that represents the exposure effects using a common global measure that can be characterized in terms of effect sizes. Correlations among different outcomes within the same subject are accommodated using random effects. We develop two approaches to model fitting, including the maximum likelihood method and the working parameter method. A key feature of both methods is that they can be easily implemented by repeatedly calling software for fitting standard linear mixed models, e.g., SAS PROC MIXED. Compared to the maximum likelihood method, the working parameter method is easier to implement and yields fully efficient estimators of the parameters of interest. We illustrate the proposed methods by analyzing data from a study of the effects of occupational pesticide exposure on semen quality in a cohort of Chinese men.

China↗

PubMed2006

Semiparametric models for missing covariate and response data in regression models.

We consider a class of semiparametric models for the covariate distribution and missing data mechanism for missing covariate and/or response data for general classes of regression models including generalized linear models and generalized linear mixed models. Ignorable and nonignorable missing covariate and/or response data are considered. The proposed semiparametric model can be viewed as a sensitivity analysis for model misspecification of the missing covariate distribution and/or missing data mechanism. The semiparametric model consists of a generalized additive model (GAM) for the covariate distribution and/or missing data mechanism. Penalized regression splines are used to express the GAMs as a generalized linear mixed effects model, in which the variance of the corresponding random effects provides an intuitive index for choosing between the semiparametric and parametric model. Maximum likelihood estimates are then obtained via the EM algorithm. Simulations are given to demonstrate the methodology, and a real data set from a melanoma cancer clinical trial is analyzed using the proposed methods.

Algorithms↗