SEARCH · PubMed Health

Results for “Linear Models”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 757 records · Page 42Linked to original sources

PubMed1982

Sensitivity analysis of biological models.

An inhomogenous linear model of the lung mechanics system was selected for the demonstration of one of the methods of sensitivity analysis. Given the values of state variables, the sensitivity of the model makes possible a safe adjustment of coefficients, without leading to large errors of solution with even a small deviation in adjustment. Any mathematical model only represents a picture of basic and substantial dynamic properties and relations of a real object. By means of sensitivity analysis it is possible to obtain a faithful description of the real object's behavior by computing the simplest model solution, with knowing at the same time, by sensitivity analysis, the range of errors introduced by simplifications and approximations.

Computers↗

PubMed2003

Clines: a reductionist model.

A piecewise linear model is used to provide a caricature of the nonlinear equation describing genetic variation due to migration and local natural selection in an inhomogeneous bounded habitat. The conditions for which nontrivial spatially-dependent steady state solutions exist are analytically determined together with these solutions for three distinct scenarios. For the usual case of no flux (Neumann) boundary conditions, explicit solutions require additional information to fix the genetic frequency within the habitat. This difficulty can be bypassed in two of the scenarios considered (this is an artifact of the model), but in the remaining scenario it is necessary to take into account the connection with the initial data to explicitly determine the steady state frequency. Some numerical examples are considered for each of the scenarios to illustrate the analytical results that are the primary focus of the work presented here.

Gene Frequency↗

PubMed1978

Multifactorial inheritance with cultural transmission and assortative mating. I. Description and basic properties of the unitary models.

A general linear model of familial resemblance is described which allows for cultural transmission from parent to offspring, polygenic inheritance, phenotypic assortative mating, common environment, maternal and paternal effects, and threshold effects. Three special cases are described in detail which are particularly useful when data are only available about a few classes of relatives reared in intact families. The cultural model, the polygenic model, and the pseudopolygenic model share the common feature that all factors which are transmitted from parent to offspring may be represented by one parameter without any loss of information. We introduce a new model, termed the unitary model, which includes these models and is appropriate when combined genetic and cultural transmission is present and when data are available only for individuals reared in intact nuclear families. The basic properties of these models are explored using path analysis and computer simulation, including description of the relationship between parameters under random and assortative mating, rate of approach to equilibrium, and constraints on the magnitude of the parameters. General formulae for familial resemblance in extended pedigrees are given for any ancestor or descendant of either vertical or collateral relatives. Estimation procedures are described and a FORTRAN program TAU, available upon request, is used to provide maximum likelihood estimates of the parameters from reported correlations. A powerful test for detecting the presence of cultural transmission is suggested and applied to simulated data and to data sets reported by others for human stature, for which cultural transmission is suggested. In addition, it is shown that there is no need to postulate dominance to account for available data about height.

Environment↗

PubMed2004

A comparison of the general linear mixed model and repeated measures ANOVA using a dataset with multiple missing data points.

Longitudinal methods are the methods of choice for researchers who view their phenomena of interest as dynamic. Although statistical methods have remained largely fixed in a linear view of biology and behavior, more recent methods, such as the general linear mixed model (mixed model), can be used to analyze dynamic phenomena that are often of interest to nurses. Two strengths of the mixed model are (1) the ability to accommodate missing data points often encountered in longitudinal datasets and (2) the ability to model nonlinear, individual characteristics. The purpose of this article is to demonstrate the advantages of using the mixed model for analyzing nonlinear, longitudinal datasets with multiple missing data points by comparing the mixed model to the widely used repeated measures ANOVA using an experimental set of data. The decision-making steps in analyzing the data using both the mixed model and the repeated measures ANOVA are described.

Analysis of Variance↗

PubMed1993

Relationships between social and health factors and depression in old age in a multivariate analysis.

This community-based epidemiological survey concerns relationships between social and health factors and depression in a Finnish population aged 60 years or over. A multivariate analysis based on log-linear models is used in this study. The log-linear model showed five interactions for the depressed men and eight for the depressed women surveyed. These indicated that the depressive persons had experienced detrimental events either of an interpersonal nature or concerning health status more often than those who were not depressed. A positive connection between life stress and depression was found even though no cause-and-effect relationship could be defined. Social stress factors seemed somewhat important prior to the onset of depression in the women studied, whereas stressful health factors played a significant role for the men. Despite this, the log-linear models for the selected variables used here did not point to a combination of interactions between a high incidence of current social stress factors and a high incidence of stressful health factors during the six-month period prior to the onset of depression.

Activities of Daily Living↗

PubMed2000

The weighing of pathological and non-pathological information in clinical judgment.

On the basis of the classic data of Meehl (1959), I examine how clinical psychologists use the MMPI scales to judge the degree of pathology of psychiatric patients by comparing linear models of the judgment to a linear model of the criterion (the actual diagnosis of the patients). This comparison reveals that excessively heavy weight is assigned to pathological information in comparison to non-pathological information. Additional analyses reveal that this biased weighing also influences the actual diagnosis and that it is a major determinant of the accuracy of clinical judgment. It is suggested that these effects arise from a confirmation bias associated with the hypothesis that a patient has severe, rather than mild, pathology.

Adult↗

PubMed2000

Renormalization group analysis of a quivering string model of posture control.

Scaling concepts and renormalization group methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces. The string is driven by uncorrelated white Gaussian noise, intended to model the corrections of the physiological control system. We find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space (representing the dynamics) with various nontrivial fixed points and basins of attraction. The transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon, and the robustness of the linear model with respect to weak nonlinearities is confirmed. Correlations in posture fluctuations are obtained in both time and space domains. There is an attractive fixed point identified with falling. The scaling of the correlations in the front-back displacement, which can be measured in the laboratory, is predicted for both large-separation (along the string) and long-time regimes of posture control.

Humans↗

PubMed2004

Applying linear mixed models to estimate reliability in clinical trial data with repeated measurements.

Repeated measures are exploited to study reliability in the context of psychiatric health sciences. It is shown how test-retest reliability can be derived using linear mixed models when the scale is continuous or quasi-continuous. The advantage of this approach is that the full modeling power of mixed models can be used. Repeated measures with a different mean structure can be used to usefully study reliability, correction for covariate effects is possible, and a complicated variance-covariance structure between measurements is allowed. In case the variance structure reduces to a random intercept (compound symmetry), classical methods are recovered. With more complex variance structures (e.g., including random slopes of time and/or serial correlation), time-dependent reliability functions are obtained. The methodology is motivated by and applied to data from five double-blind randomized clinical trials comparing the effects of risperidone to conventional antipsychotic agents for the treatment of chronic schizophrenia. Model assumptions are investigated through residual plots and by investigating the effect of influential observations.

Analysis of Variance↗

PubMed1999

Gait analysis before and after unilateral total knee arthroplasty. Study using a linear regression model of normal controls -- women without arthropathy.

Stepwise multiple regression analysis (forward method) was performed with 22 gait variables obtained from the free and slow gait of 35 normal controls (women without knee arthropathy). These 22 variables were target variables, and velocity, age, body height, and body weight were explanatory variables. Velocity showed the greatest effect on the gait variables, followed by weight, age, and height. Of the 22 target variables, 16 could be explained by a significant level of difference of P < 0.01. A linear regression model of normal gait was then established, based on the judgment that these 16 gait variables were greatly affected by four variables -- velocity, age, height, and weight. Since this model does not perfectly represent the observed values, we compared the observed value/predicted value ratios in different groups to compensate for their differences. The free gait velocity in 20 osteoarthritic patients, 1 year or more after unilateral total knee arthroplasty (TKA), and who had no pain in the contralateral knee was lower than in the normal controls. In comparisons using linear regression models, step length was shorter, step width was longer, and gait cycle was shorter than in controls. Single support time was shorter and double support time was longer. Of the ground reaction forces, the first peak of the vertical component and the peak of the driving force of the fore-aft component were smaller than in controls. The total range of motion (TRM) in the stance phase was less than in controls. These results show quantitatively not only that the velocity of gait after TKA is lower than in normal controls, but also that gait patterns are different. In eight osteoarthritic patients assessed before and after TKA, and who had no pain in the contralateral knee, free gait velocity increased 6 months post-operation, but showed no further changes at 1 year. A linear regression study comparing the gait before TKA and 6 months post-TKA revealed that step time, single support time, double support time, and step width, and -- with regard to ground reaction forces -- the peaks of the driving force and the braking force of the fore-aft component, and TRM in the stance phase all approached the levels in the normal controls. No further changes were observed 1 year postoperatively. Although our models were not perfect, we were able to clarify the differences in gait variables between a TKA group and normal controls and the improvements from pre- to post TKA by normalizing the influence of the four independent variables, (velocity, age, weight, and height) with particular emphasis on gait velocity.

Aged↗

PubMed1991

On using the linear-quadratic model in daily clinical practice.

To facilitate its use in the clinic, Barendsen's formulation of the Linear-Quadratic (LQ) model is modified by expressing isoeffect doses in terms of the "Standard Effective Dose," Ds, the isoeffective dose for the "standard" fractionation schedule of 2 Gy fractions given once per day, 5 days per week. For any arbitrary fractionation schedule, where total dose D is given in N fractions of size d in a total time T, the corresponding "Standard Effective Dose," Ds, will be proportional to the total dose D and the proportionality constant will be called the "Standard Relative Effectiveness," SRE, to distinguish it from Barendsen's "Relative Effectiveness," RE. Thus, Ds = SRE.D. The constant SRE depends on the parameters of the fractionation schedule, and on the tumor or normal tissue being irradiated. For the "simple" LQ model with no time dependence, which is applicable to late reacting tissue, SRE = [(d + delta)/(2 + delta)], where d is the fraction size and delta = alpha/beta is the alpha/beta ratio for the tissue of interest, with both d and delta expressed in units of Gy. Application of this method to the Linear Quadratic model with a time dependence, the "LQ + time" model, and to low dose rate brachytherapy will be discussed. To clarify the method of calculation, and to demonstrate its simplicity, examples from the clinical literature will be used.

Brachytherapy↗

PubMed1978

Prediction of gentamicin serum levels using a one-compartment open linear pharmacokinetic model.

The accuracy of predicting serum gentamicin levels based on a one-compartment open linear pharmacokinetic model was studied. Twenty-two patients accounted for 59 serum gentamicin levels which were measured by microbiologic assay and compared with predicted serum levels determined by pharmacokinetic calculation. Seventeen serum levels were collected at peak times, 15 at trough time and 27 at times between peak and trough. Forty-nine of the levels were obtained from patients with impaired renal function. Predicated gentamicin levels correlated well with measured serum levels (r = 0.85, p less than 0.001). Of the measured levels, 56% were within +/- 1 microgram/ml of the predicted levels. Of 49 levels collected from patients with impaired renal function, 59% were within +/- 1 microgram/ml of the predicted level. In 13 patients from whom multiple serum gentamicin levels were collected and predictions based on half-life or elimination rate obtained by fitting the first level, 83% of the measured levels were within +/- 1 microgram/ml of the predicted level. The one-compartment open linear pharmacokinetic calculations can be used to adequately predict serum gentamicin levels. In patients with changing or diminished renal function, pharmacokinetic predictions may not be accurate, and actual serum level determinations may be needed to monitor gentamicin therapy.

Adult↗

PubMedDate not supplied

Determination of the 1,3- and 2-positional distribution of fatty acids in olive oil triacylglycerols by 13C nuclear magnetic resonance spectroscopy.

Linear models were selected from a large data set acquired for Italian olive oil samples by quantitative 13C nuclear magnetic resonance (NMR) spectroscopy with distortionless enhancement by polarization transfer (DEPT). The models were used to determine the composition of the 2 fatty acid pools esterifying the 1,3- and 2-positions of triacylglycerols. The linear models selected proved that the 1,3- and 2-distribution of saturated, oleate, and linoleate chains in olive oil triacylglycerols deviated from the random distribution pattern to an extent that depended on the concentration of the fatty acid in the whole triacylglycerol. To calculate the fatty acid composition of the 1,3- and 2-positions of olive oil triacylglycerols, the equations of the selected linear models were applied to the fatty acid percentages determined by gas chromatography. These data were compared with the values predicted by the computer method (used to determine the theoretical amounts of triacylglycerols), which is based on the 1,3-random-2-random theory of the fatty acid distribution in triacylglycerols. The biggest differences were found in the linoleate chain, which is the chain that deviated the most from a random distribution pattern. The results confirmed that the 1,3-random-2-random distribution theory provides an approximate method for determining the structure of triacylglycerols; however, the linear models calculated by the direct method that applies 13C NMR spectroscopy represent a more precise measurement of the composition of the 2 fatty acid pools esterifying the 1,3- and 2-positions of triacylglycerols.

Chemistry Techniques, Analytical↗

PubMed1998

Observer variation in the assessment of resin composite.

OBJECTIVES: The aim of this study was to compare the type of information obtained from log-linear modelling vs Cohen's kappa statistics on observer variation in the assessment of marginal adaptation in composite inlays and amalgam restorations. METHODS: Marginal adaptation of Class II resin composite inlays and amalgam restorations was clinically assessed by two observers, four years after placement. Each of 52 patients received 4 different restorations, three composite (Herculite XR, Clearfil CR Inlay and Visiomolar) inlays and one Tytin restoration. The results were evaluated by Cohens Kappa statistics and log-linear modelling. RESULTS: The overall Cohen's kappa was 0.45, ranging from poor to good for the four materials. Log-linear modelling confirmed that the observers agreed beyond chance but this agreement depended on the performance of the material. Marginal adaptation of Visiomolar (ESPE) inlays was somewhat inferior compared to the other materials. The assessment of Clearfil CR (Kuraray) inlay was difficult using this clinical evaluation procedure. SIGNIFICANCE: Using log-linear modelling it is possible to look at observer agreement and material performance at the same time. This combined approach is important because agreement may depend on material performance.

Chi-Square Distribution↗

PubMed1992

Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord.

The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. This paper describes experiments in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spinal cord. The first group of rats were given doses in 1, 2, 4, 8 and 40 daily fractions. The second group of animals received three initial "top-up" doses of 9 Gy given once daily, representing three-quarters of tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 daily fractions. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of the forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 daily fractions (25.0-1.98 Gy per fraction) indicated consistency with the LQ model yielding an alpha/beta value of 2.41 Gy. Analysis of data from experiments in which the three "top-up" doses were followed by up to 10 fractions (10.0-1.64 Gy per fraction) gave an alpha/beta value of 3.41 Gy. However, data from "top-up" experiments with 20, 30 and 40 fraction (1.60-0.55 Gy per fraction) were inconsistent with the LQ model and gave a very small alpha/beta value of 0.48 Gy. It is concluded that the LQ model based on data from large doses per fraction underestimates the sparing effect of small doses per fraction provided sufficient time is allowed between each fraction for repair of sublethal damage.

Animals↗

PubMed1993

A comparison of the generalized estimating equation approach with the maximum likelihood approach for repeated measurements.

Liang and Zeger proposed an extension of generalized linear models to the analysis of longitudinal data. Their approach is closely related to quasi-likelihood methods and can handle both normal and non-normal outcome variables such as Poisson or binary outcomes. Their approach, however, has been applied mainly to non-normal outcome variables. This is probably due to the fact that there is a large class of multivariate linear models available for normal outcomes such as growth models and random-effects models. Furthermore, there are many iterative algorithms that yield maximum likelihood estimators (MLEs) of the model parameters. The multivariate linear model approach, based on maximum likelihood (ML) estimation, specifies the joint multivariate normal distribution of outcome variables while the approach of Liang and Zeger, based on the quasi-likelihood, specifies only the marginal distributions. In this paper, I compare the approach of Liang and Zeger and the ML approach for the multivariate normal outcomes. I show that the generalized estimating equation (GEE) reduces to the score equation only when the data do not have missing observations and the correlation is unstructured. In more general cases, however, the GEE estimation yields consistent estimators that may differ from the MLEs. That is, the GEE does not always reduce to the score equation even when the outcome variables are multivariate normal. I compare the small sample properties of the GEE estimators and the MLEs by means of a Monte Carlo simulation study.

Clinical Trials as Topic↗

PubMed1998

Global identifiability of linear compartmental models--a computer algebra algorithm.

A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

Algorithms↗

PubMed2000

Anticonvulsant teratogenesis 4: inter-rater agreement in assessing minor physical features related to anticonvulsant therapy.

BACKGROUND: We report on inter-rater agreement in the assessment of newborn infants with respect to a range of minor physical features in a cohort study of the fetal effects of maternal anticonvulsant use during pregnancy. METHODS: Infants from three groups (exposed to anticonvulsants, seizure history but no medication exposure, and unexposed controls) were examined by both a pediatrician/teratologist, who was blinded with respect to the mother's exposure status, and an unblinded research assistant. Agreement on assessments for selected anomalies associated with anticonvulsant therapy was measured by kappa-statistics, as well as by more sensitive log-linear modeling techniques, which allow examination of possible covariate effects on the strength of agreement. Although the physician and research assistant agreed on a high proportion of cases (80-90%), kappa values were modest (0.2-0. 5), partly because of the low prevalence of the anomalies considered. To explore how agreement varies within subgroups, we used recently developed methods for studying agreement based on log-linear models. RESULTS: Log-linear modeling indicated that there was substantial variation in pattern of agreement between different individual research assistants but that other factors (e.g., exposure category, sex, and birthweight) did not appear to be related to agreement. Our results suggest that research assistants with more experience showed the highest degree of agreement with the physicians. CONCLUSIONS: Our results have implications for both clinical practice and epidemiologic research and underline the importance of thorough training of staff in the definitions to be used and also the need for multiple independent assessments of these subtle anomalies.

Abnormalities, Drug-Induced↗

PubMed1993

AIDS anxieties of adolescents: determinants of "state" and "trait" anxiety dimensions in a linear structural model.

This study presents the effects of general psychologic characteristics on acquired immunodeficiency syndrome (AIDS) anxieties and sexual behaviour of adolescents. To this end, data were collected in a complex interview and subsequently subjected to a linear structural model analysis. The questioned adolescents were divided into one representative group (n = 256) and a second group who had participated in a voluntary human immunodeficiency virus (HIV) antibody test (n = 45). AIDS anxieties have to be divided into two independent dimensions: first, a relatively stable feeling of AIDS anxiety (trait anxiety) and second, a manifest personal anxiety toward AIDS experienced in a concrete situation (state anxiety). A principal component analysis of the primary data brought forth four variables described as depression/general anxiety, extent of phobic anxieties, compulsion, and tendency to self-consciousness. The present study reveals that the AIDS trait anxiety is more pronounced among those subjects who are not well informed about AIDS, who tend to phobic anxieties, and who observe themselves in a particularly intensive manner. The AIDS state anxiety however, is stronger among subjects who are well informed about AIDS, have sexual experience, and observe themselves intensively. Among the participants who took part in the HIV test, there were more individuals with a higher manifest AIDS anxiety and stronger tendency to depression. The percentage of adolescents who were indeed exposed to a possible risk of getting infected was relatively low. Generally speaking, those young people who are depressed, anxious, and sexually active agreed more easily to take the test than young people with a pronounced phobia toward the risk of infection and less sexual experience. As a conclusion, we can state that those adolescents with less sexual experience tend to externalize their general sexual anxieties in the form of concrete AIDS anxieties.

Acquired Immunodeficiency Syndrome↗