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PubMed2004

Application of piecewise hierarchical linear growth modeling to the study of continuity in behavioral development of baboons (Papio hamadryas).

In behavioral science, developmental discontinuities are thought to arise when the association between an outcome measure and the underlying process changes over time. Sudden changes in behavior across time are often taken to indicate that a reorganization in the outcome-process relationship may have occurred. The authors proposed in this article the use of piecewise hierarchical linear growth modeling as a statistical methodology to search for discontinuities in behavioral development and illustrated its possibilities by applying 2-piece hierarchical linear models to the study of developmental trajectories of baboon (Papio hamadryas) mothers' behavior during their infants' 1st year of life. The authors provided empirical evidence that piecewise growth modeling can be used to determine whether abrupt changes in development trajectories are tied to changes in the underlying process.

Age Factors↗
PubMed2006

QTL methodology for response curves on the basis of non-linear mixed models, with an illustration to senescence in potato.

The improvement of quantitative traits in plant breeding will in general benefit from a better understanding of the genetic basis underlying their development. In this paper, a QTL mapping strategy is presented for modelling the development of phenotypic traits over time. Traditionally, crop growth models are used to study development. We propose an integration of crop growth models and QTL models within the framework of non-linear mixed models. We illustrate our approach with a QTL model for leaf senescence in a diploid potato cross. Assuming a logistic progression of senescence in time, two curve parameters are modelled, slope and inflection point, as a function of QTLs. The final QTL model for our example data contained four QTLs, of which two affected the position of the inflection point, one the senescence progression-rate, and a final one both inflection point and rate.

Nonlinear Dynamics↗
PubMed1996

Underprediction of human skin erythema at low doses per fraction by the linear quadratic model.

BACKGROUND AND PURPOSE: The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. MATERIALS AND METHODS: Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). RESULTS AND CONCLUSIONS: Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model.

Aged↗
PubMed1995

Neuroangiographic assessment of aneurysm stability and impending rupture based on a non-linear biomathematical model.

The probability or risk of aneurysm rupture is assessed using conventional angiography by applying the aneurysm radius and systolic blood pressure obtained at examination to a non-linear biomathematical model of an aneurysm. A non-linear biomathematical model was developed based on Laplace's law to represent the viscoelastic relation between the wall tension and the radius. A differential expression of this relation was used to derive the critical radius: Rc = [2Et/P]2At/P where E is the elastic modulus of the aneurysm, t is the wall thickness, P is the pressure, and A is the elastic modulus of collagen. Using average values of E, A, and t, the risk of aneurysm rupture is defined as the area of integration under the curve defined by the minimum value of pressure (50 mmHg) and the patient pressure recorded at examination. This area was normalized by the area of integration defined by the pressure limits: 50 to 300 mmHg. This method of risk assessment was applied to four previously published case studies of patients with documented aneurysm rupture in which both the aneurysm size at rupture and the patient systolic blood pressure were reported. Two additional parameters were calculated to further evaluate aneurysm stability: (1) a ratio given as (Rexp/Rth) where Rexp is the radius of aneurysm rupture measured from angiography and Rth is the critical radius based on the model; and (2) chi 2 analysis defined by chi 2 = (O - E)2/E where O and E are the observed (Rexp) and expected (Rth) variables, respectively. The average systolic blood pressure and radius of aneurysm rupture was 147.2 mmHg and 3.95 mm, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)

Aneurysm, Ruptured↗
PubMed2003

Prognostic significance of biomarkers in squamous cell carcinoma of the tongue: multivariate analysis.

BACKGROUND AND OBJECTIVES: Expression of a panel of biomarkers, such as p53, Bcl-2, Cyclin D1, c-myc, p21ras, c-erb B2, cytokeratin-19 (CK-19), and factor VIII-related antigen (FVIII-RA), was studied together in anterior tongue tumors from the oral cavity and in posterior tongue tumors from the oropharynx of patients with early- and locally advanced-stage disease, to evaluate their prognostic value. METHODS: The expression of the above-mentioned biomarkers was studied by immunohistochemical localization. RESULTS: In this study, 18%, 26%, 62%, 75%, 73%, 50%, and 29% of the tumors exhibited p53, Bcl-2, Cyclin D1, c-myc, p21ras, c-erb B2, and CK-19 expression, respectively. Twenty percent of the tumors had a microvessel count of >0.0. The expression of these biomarkers was also correlated with clinicopathologic parameters. In early-stage patients with a tobacco habit, who showed borderline significance for relapse-free survival by Kaplan-Meier survival analysis, this turned out to be significant, with the general linear model univariate survival analysis. In the total group, disease stage emerged as the most significant prognostic factor, followed by c-myc, when Cox forward stepwise regression and general linear model multivariate survival analysis were performed. However, Cyclin D1, which was significant by Cox forward stepwise regression analysis, lost its significance by general linear model multivariate analysis. In patients with early-stage disease, MVC, which was a significant predictor of disease relapse by Cox forward stepwise regression analysis, lost its significance by general linear model analysis because of small number of patients. In patients with locally advanced tongue cancer, multivariate survival analysis of individual biomarkers by both Cox forward stepwise regression and general linear model analysis indicated c-myc expression to be strongly indicative of poor prognosis. However, multivariate analysis of individual markers along with a combination of markers showed that only by Cox forward stepwise regression analysis did the combined expression of markers c-myc, Cyclin D1, and p21ras emerge as a significant independent prognosticator. CONCLUSIONS: Overall stage emerged as the most significant prognostic indicator of disease outcome. Tobacco habit also affected relapse-free survival in patients with early-stage disease. However, immunostaining of c-myc in the tumors of locally advanced-stage tongue cancer patients might be a potential adjunct to clinical stage in the pathologic evaluation of tongue specimens.

Adult↗
PubMed2005

Psychotropic combination in schizophrenia.

OBJECTIVE: To study adjunctive medications used with antipsychotic agents in schizophrenia via comparisons of antidepressant, anxiolytic and antiparkinsonian co-prescribing. METHOD: In the context of a national naturalistic prospective observational study, a database containing all the prescriptions from 100 French psychiatrists during the year 2002 was analysed. The inclusion criteria were a diagnosis of schizophrenia or schizoaffective disorder and age over 18. A log-linear model and generalised linear mixed models were used. RESULTS: In all 5,257 prescriptions for 922 patients were analysed. The proportion of patients who were prescribed an antiparkinsonian drug was 32.9%. Amisulpride, haloperidol, phenothiazines with a sedative action and depot typical antipsychotics proved more likely to be prescribed with antiparkinsonians. The frequency of antidepressant and anxiolytic prescriptions was 51.2% and 52.3%, respectively. Associations between atypical antipsychotics (except clozapine) and antidepressants were positive while associations between typical antipsychotics and antidepressants were not. There were no differences among antipsychotics for the prescription of anxiolytics. CONCLUSIONS: Atypical antipsychotics can be expected to be less likely associated with antiparkinsonians. This result is indeed found for olanzapine, clozapine and to a limited extent for risperidone. Furthermore, a trend towards a positive association between atypical antipsychotics and antidepressants appears. In view of the antidepressive action of certain atypical antipsychotics, this result is surprising. The increase in the prescriptions of anxiolytics concerns all types of antipsychotics. In view of the increase in associated medications in schizophrenia and the difficulty of estimating it in randomised trials, this study underlines the contribution of naturalistic studies on this score.

Adult↗
PubMed2005

Differential gene expression detection and sample classification using penalized linear regression models.

Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p >> n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-differentially expressed genes that can classify the samples very well. The idea of shrinkage is to regularize the model parameters to reduce the effects of noise and produce reliable inferences. Shrinkage has been successfully applied in the microarray data analysis. The SAM statistics proposed by Tusher et al. and the 'nearest shrunken centroid' proposed by Tibshirani et al. are ad hoc shrinkage methods. Both methods are simple, intuitive and prove to be useful in empirical studies. Recently Wu proposed the penalized t/F-statistics with shrinkage by formally using the (1) penalized linear regression models for two-class microarray data, showing good performance. In this paper we systematically discussed the use of penalized regression models for analyzing microarray data. We generalize the two-class penalized t/F-statistics proposed by Wu to multi-class microarray data. We formally derive the ad hoc shrunken centroid used by Tibshirani et al. using the (1) penalized regression models. And we show that the penalized linear regression models provide a rigorous and unified statistical framework for sample classification and differential gene expression detection.

Algorithms↗
PubMed1978

The analysis of pair-matched case-control studies, a multivariate approach.

In matched case-control studies one frequently must consider more than one variable in the analysis and in this paper a log-linear model is presented to meet this objective. A conditional argument yields a method for making inferences on the parameters measuring the association between the variables and disease. The result is similar to the problem of fitting a Bradley-Terry model when one has paired comparisons. Two methods of obtaining maximum conditional likelihood estimates of the parameters are possible: (i) fitting a quasi-independence model in the usual log-linear models context and (ii) fitting a linear logistic model. The results are illustrated with examples.

Adult↗
PubMed2003

An evaluation of the U.S. Department of Agriculture food security measure with generalized linear mixed models.

Over the last decade, new information has been developed and collected to measure the extent of food insecurity and hunger in the United States. Common measurement of the phenomenon of hunger and food insecurity has become possible through efforts of the U.S. Department of Agriculture (USDA) to develop a set of survey questions that can be used to obtain estimates of the prevalence and severity of food insecurity. We evaluated the measurement of food insecurity and the effect of household variables on measured food insecurity. The effects of demographic and survey-specific variables on the food insecurity/hunger scale were evaluated using a generalized linear model with mixed effects. Data came from the 1995, 1997 and 1999 Food Security Module of the Current Population Survey. The results generally validated the model currently used by the USDA. In addition, our approach made it possible to consider the effect of demographics and several survey design variables on food security among measurably food-insecure households, as well as interactions between these factors and the food security questions. The analysis of the expanded model with the 1995 data found results similar to those reported based on the Rasch model used by the USDA. Even though the sample size was reduced and a number of screening and questionnaire changes were introduced in 1997 and 1999, the results for those years appear mostly unchanged and confirm the robustness of the scale in measuring food insecurity. There is some evidence that interpretation of questions may vary among different demographic groups.

Demography↗
PubMed1999

Estimates of essential amino acid requirements from dose-response studies with rainbow trout and broiler chicken: effect of mathematical model.

A total of 37 dose-response experiments with essential amino acids performed with rainbow trout and broiler chicken were re-evaluated with different mathematical approaches: an exponential model, a four-parameter logistic function, the saturation kinetics model and the broken line approach. The different approaches were compared both with regard to the goodness of fit (r2 and sy.x) and with regard to the allowances which were derived regarding the optimal amino acid level in the diet. The experimental design, particularly the chosen range in dietary amino acid concentration was found to be important for the comparison of models. Amongst the non-linear models, the four-parameter logistic function and the saturation kinetics model appeared superior to the exponential approach, when the range in dietary amino acid concentration was very wide and included both a severely deficient basal level and a level that exceeded the needs of the animal by approximately the factor 2. In these cases, allowances derived from individual experiments were considerably different depending on the model. The allowances based on the exponential and the saturation kinetics approach were 27.7 and 20.7 g lysine/kg DM and 8.0 and 6.3 g methionine/kg DM, respectively, for rainbow trout. For other amino acids studied in rainbow trout the difference due to model was less. Consequently, the predicted 'ideal protein' for rainbow trout was considerably different depending on the model used. The maximum deviation found in different experiments with broiler chicken for the exponential vs. the saturation kinetics approach was 13.0 and 9.7 g lysine/kg and 11.4 and 8.2 g sulfur-containing amino acids/kg, respectively. However, the more restricted the range in dietary concentration was, the lesser became the differences between the different non-linear models. No definite recommendation can therefore be extracted regarding the most suitable, generally applicable mathematical model.

Amino Acids, Essential↗
PubMed2004

Generalized linear mixed models with varying coefficients for longitudinal data.

The routinely assumed parametric functional form in the linear predictor of a generalized linear mixed model for longitudinal data may be too restrictive to represent true underlying covariate effects. We relax this assumption by representing these covariate effects by smooth but otherwise arbitrary functions of time, with random effects used to model the correlation induced by among-subject and within-subject variation. Due to the usually intractable integration involved in evaluating the quasi-likelihood function, the double penalized quasi-likelihood (DPQL) approach of Lin and Zhang (1999, Journal of the Royal Statistical Society, Series B61, 381-400) is used to estimate the varying coefficients and the variance components simultaneously by representing a nonparametric function by a linear combination of fixed effects and random effects. A scaled chi-squared test based on the mixed model representation of the proposed model is developed to test whether an underlying varying coefficient is a polynomial of certain degree. We evaluate the performance of the procedures through simulation studies and illustrate their application with Indonesian children infectious disease data.

Biometry↗
PubMed1990

Improving the predictive ability of the signal-averaged electrocardiogram with a linear logistic model incorporating clinical variables.

To improve the predictive accuracy of the signal-averaged electrocardiogram, we created a linear logistic model for predicting ventricular tachycardia during electrophysiologic testing. This signal-averaged electrocardiographic model was created from data obtained from 214 patients undergoing electrophysiologic testing (70 had ventricular tachycardia during electrophysiologic testing) by using stepwise logistic regression to rank eight clinical and nine signal-averaged electrocardiographic variables. The best predictors were ejection fraction, history of infarction, ventricular ectopic pairs or nonsustained ventricular tachycardia on Holter monitoring, QRS duration after 25-Hz filtering, and root mean square voltage of the terminal 40 msec of the QRS complex after 40- and 80-Hz filtering. Cross validation (a statistical technique that can be used to accurately evaluate how a predictive model will perform on a prospective patient population) was used to validate the model. After cross validation, the model's sensitivity was 91% and specificity was 59% for predicting ventricular tachycardia during electrophysiologic testing. This model compared favorably with established 25-Hz late-potential criteria (QRS duration of more than 110 msec and root mean square voltage of less than 25 microV of the terminal 40 msec of the QRS complex; sensitivity, 64%; specificity, 85%) and with established 40-Hz late-potential criteria (QRS duration of more than 114 msec or root mean square voltage of less than 20 microV of the terminal 40 msec of the QRS complex or duration of the low-amplitude signal less than 40 microV at the terminal QRS complex that is greater than 38 msec; sensitivity, 84%; specificity, 54%).(ABSTRACT TRUNCATED AT 250 WORDS)

Aged↗
PubMed2006

Prediction of partitioning between complex organic mixtures and water: application of polyparameter linear free energy relationships.

Equilibrium partitioning between nonaqueous phase liquids (NAPLs) and water is a governing process for contaminants leaching from NAPLs. Conventional prediction methods, such as Raoult's law and single-parameter linear free energy relationship (SP-LFER), are inaccurate for compounds with polar functional groups. Therefore, this study introduces a polyparameter linear free energy relationship (PP-LFER) approach as a more general tool to predict NAPL-water partitioning coefficients. Our approach was evaluated using 441 experimental partitioning data from 30 references. Experimental fuel-water partitioning coefficients were generally well reproduced by existing PP-LFERs for pure solvents using either a volume-fraction weighted sum of partitioning coefficients K (linear model, R2 = 0.983, root-mean-squared error [rmse] = 0.23) or a volume-fraction weighted sum of log K (log linear model, R2 = 0.976, rmse = 0.28). Using the linear model, estimations were, in most cases, within a factor of 2 from the experimental values, regardless of the type of compounds and the presence of a fuel additive. In contrast, the log linear model considerably underestimated partitioning coefficients in the presence of strong solute-solvent hydrogen bonding. For coal tar-water partitioning coefficients (Kcoal tar/w), new PP-LFER equations were calculated based on experimental log Kcoal tar/w values of 35 compounds. The resulting regression equation was log Kcoal tar/w = 0.40(+/-0.33) + 0.34(+/-0.32)E+ 0.61(+/-0.57)S-0.55-(+/-0.61)A-5.07(+/-0.61)B + 3.22(+/-0.35)V with the rmse equal to 0.21, where E, S, A, B, and Vare Abraham's solute descriptors. Partitioning coefficients for phenol and alcohols, calculated by the above equation, were much closer to the experimental values than to those estimated by the SP-LFER approach with octanol-water partitioning coefficients. The values of the coefficients also provide insight into the properties of coal tar in terms of molecular interactions with solutes. Consequently, using the approaches presented in this study, complex organic mixture-water partitioning coefficients of a wide range of organic compounds with varying polarity can be reasonably estimated.

Organic Chemicals↗
PubMed1991

A linear propagation model adapted to the study of fast perturbations in arterial hemodynamics.

The hemodynamic effect of rapid body accelerations is studied in this work using two different models of wave propagation in blood vessels. Simulation curves have been obtained with both models and compared with those measured in vivo on a dog's carotid artery. Results of the first model demonstrate that classic linear theories, based on linearization of the Navier-Stokes and continuity equations, provide a good explanation of the initial effect of body acceleration on pressure. However, the same models significantly underestimate the subsequent pressure perturbation damping. Modified empirical expressions for wave propagation, able to furnish a more accurate description of pressure energy losses occurring during fast hemodynamic phenomena, are thus utilized in the second model and their biophysical significance discussed.

Animals↗
PubMed2003

Non-linear viscoelastic models predict fingertip pulp force-displacement characteristics during voluntary tapping.

We evaluated whether lumped-parameter non-linear viscoelastic models of human fingertip tissue can describe fingertip force-displacement characteristics during a range of rapid, dynamic tapping tasks. Eight human subjects tapped with their index finger on the surface of a rigid load cell while an optical system tracked fingertip position using an infra-red LED attached to the fingernail. Four different tapping conditions were tested: normal and high-speed taps with a relaxed hand, and normal and high-speed taps with the other fingers co-contracted. A non-linear viscoelastic model comprised of an instantaneous stiffness function and viscous relaxation function was capable of predicting fingertip tissue force response due to measured pulp compression under these four different loading conditions. The model could successfully reconstruct very rapid (less than 5 ms) force transients, and forces occurring over time periods greater than 100 ms, with errors of 10%. Model parameters varied by less than 20% over the four conditions, despite almost 3-fold differences in average forces and 38% differences in fingertip velocities. Energy dissipation by the fingertip averaged 81%, and varied little (<3%) across conditions, despite a 1. 5-fold range of energy input. The ability of a lumped-parameter model to describe fingertip force-displacement characteristics during a range of conditions contributes both to understanding the transmission of force through the fingertip to the musculoskeletal system and to predicting the stimulation of mechano-receptors located within the fingertip.

Adult↗
PubMed2004

Rate and amplitude of adaptation to two intensities of exercise in men aged 65-75 yr.

PURPOSE: To test the hypothesis that in males aged 65-75 yr when the total amount of work completed is similar in endurance training three times per week for 12 wk at either 50% or 70% peak oxygen uptake (VO2(peak)), there will be no significant difference in time course and amplitude of selected responses. METHODS: Subjects were randomly assigned to three groups: 70% VO2(peak), N = 19; 50% VO2(peak), N = 16; or control group, N = 19. Subjects underwent a maximal cycle exercise test and blood volume (Evans Blue) determination at 0, 4, 8, and 12 wk. A submaximal exercise test (50 W) was conducted at weeks 0 and 12 where cardiac output was determined. The exercise groups maintained the same exercise relative intensity throughout the 12 wk and completed a similar total amount of work. RESULTS: There were significant and similar increases in peak VO2, power and heart rate (HR) for both exercise groups. Linear models best described the time course for peak power and HR in both exercise groups. In the 70% VO2(peak) group, a quadratic model for VO2 and a linear model for VE were the best fit. There were no significant changes in blood or plasma volume for any groups over the 12 wk. Significant increases in stroke volume and significant decreases in HR at 50 W were found in both exercise groups after training. CONCLUSION: Moderate-intensity cycle exercise (50% VO2(peak)) to achieve 180-200 kJ per session, three times a week for 12 wk is a safe and effective stimulus for healthy asymptomatic men aged 65-75 yr to improve functional capacity in a primarily linear manner.

Adaptation, Physiological↗
PubMed2005

Are there limits to running world records?

PURPOSE: Previous researchers have adopted linear models to predict athletic running world records, based on records recorded throughout the 20th century. These linear models imply that there is no limit to human performance and that, based on projected estimates, women will eventually run faster than men. The purpose of this article is to assess whether a more biologically sound, flattened "S-shaped" curve could provide a better and more interpretable fit to the data, suggesting that running world records could reach their asymptotic limits some time in the future. METHODS: Middle- and long-distance running world record speeds recorded during the 20th century were modeled using a flattened S-shaped logistic curve. RESULTS: The logistic curves produce significantly better fits to these world records than linear models (assessed by separating/partitioning the explained variance from the logistic and linear models using ANOVA). The models identify a slow rise in world-record speeds during the early year of the century, followed by a period of "acceleration" in the middle of the century (due to the professionalization of sport and advances in technology and science), and a subsequent reduction in the prevalence of record-breaking performances towards the end of the century. The model predicts that men's world records are nearing their asymptotic limits (within 1-3%). Indeed, the current women's 1500-m world record speed of 6.51 m x s(-1) may well have reached its limit (time 3:50.46). CONCLUSIONS: Many of the established men's and women's endurance running world records are nearing their limits and, consequently, women's world records are unlikely to ever reach those achieved by men.

Competitive Behavior↗