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PubMedDate not supplied

Evaluation of alternative statistical methods for linear model analysis to compare two treatments for 24-hour blood pressure response.

This paper evaluates alternative statistical methods for the analysis of 24-hour blood pressure data from a clinical trial which compares two treatments for hypertension. The primary objective of the study discussed here was to determine the time course for the blood pressure lowering effects of a test drug given once daily in the treatment of mild to moderate hypertension when compared with placebo. Thirty-five patients (24 on drug and 11 on placebo) were monitored for 24 hours at baseline and at two weeks post treatment, with diastolic blood pressure (DBP) measurements recorded at 22 time points within each 24-hour visit. The changes in DBP from baseline across the 22 time points are the response variables of interest. Various statistical methods for the assessment of treatment effects over the entire 24-hour dosing interval in a setting with small sample size are discussed and illustrated. The results from a special application of weighted least squares analysis of covariance, which employs a smoothed covariance matrix, support the hypothesis that a once daily dose of the drug significantly reduces DBP over the entire 24-hour dosing interval when compared with placebo. This method has the distinct advantage of enabling evaluation of treatment differences for the change in DBP from baseline at the 22 time points with the corresponding 22 baseline DBP as covariates simultaneously in a situation where the treatment group sample sizes are small.

Antihypertensive Agents↗
PubMed1999

Robust smoothness estimation in statistical parametric maps using standardized residuals from the general linear model.

The assessment of significant activations in functional imaging using voxel-based methods often relies on results derived from the theory of Gaussian random fields. These results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can be estimated. End results (i. e., P values associated with local maxima, clusters, or sets of clusters) critically depend on this assessment, which should be as exact and as reliable as possible. In some earlier implementations of statistical parametric mapping (SPM) (SPM94, SPM95) the smoothness was assessed on Gaussianized t-fields (Gt-f) that are not generally free of physiological signal. This technique has two limitations. First, the estimation is not stable (the variance of the estimator being far from negligible) and, second, physiological signal in the Gt-f will bias the estimation. In this paper, we describe an estimation method that overcomes these drawbacks. The new approach involves estimating the smoothness of standardized residual fields which approximates the smoothness of the component fields of the associated t-field. Knowing the smoothness of these component fields is important because it allows one to compute corrected P values for statistical fields other than the t-field or the Gt-f (e.g., the F-map) and eschews bias due to deviation from the null hypothesis. We validate the method on simulated data and demonstrate it using data from a functional MRI study.

Brain↗
PubMed1990

[Linear model of the etiology of temporomandibular pain dysfunction syndrome].

The investigation searched if a relatively complete, empirically tested model of the etiology of the mandibular dysfunction can be set up. The so-called LISREL- (Linear Structural Relationship) method was used for statistic evaluation. All factors showing a direct connection with the anamnestic and clinical dysfunction index were built into the model. The results led to the conclusion that anxiety and constitutional joint factors also play a role in the occurrence of mandibular dysfunction. The most important etiological factors are given by malocclusions, by occlusal interferences, impaired general state of health and parafunctions.

Cross-Sectional Studies↗
PubMed1995

Estimation of critical power with nonlinear and linear models.

Sixteen young, healthy males each performed five to seven randomly assigned, exhaustive exercise bouts on a cycle ergometer, with each bout on a separate day and at a different power, to compare estimates of critical power (PC) and anaerobic work capacity (W') among five different models: t = W'/(Pmax-PC) (two-parameter nonlinear); t = (W'/P-PC))-(W'/(Pmax-PC)) (three-parameter nonlinear); P.t = W' + (PC.t) (linear (P.t)); P = (W'/t) + PC (linear (P)); P = PC + (Pmax-PC)exp(-t/tau) (exponential). The data fit each of the models well (mean R2 = 0.96 through 1.00 for each model). However, significant differences among models were observed for both PC (mean +/- standard deviation (SD) for each model was 195 +/- 29 W through 242 +/- 21 W) and W' (18 +/- 5 kJ through 58 +/- 19 kJ). PC estimates among models were significantly correlated (r = 0.78 through 0.99). For W', between-model correlations ranged from 0.25 to 0.95. For a group of six subjects, the ventilatory threshold for long-term exercise (LTE Tvent; 189 +/- 34 W) was significantly lower than PC for all models except the three-parameter nonlinear (PC = 197 +/- 30 W); PC for each model was, however, positively correlated with LTE Tvent (r = 0.69 through 0.91).(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗
PubMed2002

[Non-linear model of glottic vibration. Potential clinical implications].

Glottic vibration is governed by a certain number of physical laws which in general correspond, as far as myo-elastic theory is concerned, with the laws of passive vibration of an elastic body under the influence of the expired air. Some of these laws are non-linear, especially those that deal with the exchange of energy between the expired air and the vocal folds. This non-linearity is specially important when it comes to the key concepts of the phonatory threshold and the passive synchronisation of the vocal cords. Based on their experimental work, which has been presented previously, the authors propose a mixed model, which is both linear and non-linear, like the oscillators of Van der Pool. This model is known as Slip-Stick.

Glottis↗
PubMed1996

Piecewise linear models for the quasiperiodic transition to chaos.

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode locking and the quasiperiodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic "sine-circle" map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction. (c) 1996 American Institute of Physics.

Journal Article↗
PubMed2004

Qualitative simulation of genetic regulatory networks using piecewise-linear models.

In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewise-linear (PL) differential equations that has been well-studied in mathematical biology. The simulation method is well-adapted to state-of-the-art measurement techniques in genomics, which often provide qualitative and coarse-grained descriptions of genetic regulatory networks. Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system. The qualitative simulation method has been implemented in Java in the computer tool Genetic Network Analyzer.

Computer Simulation↗
PubMed2002

Mode-doubling and tripling in reaction-diffusion patterns on growing domains: a piecewise linear model.

Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper we have shown that incorporation of domain growth in a reaction-diffusion model generates a sequence of quasi-steady patterns and can provide a mechanism for increased reliability of pattern selection. In this paper we analyse the model to examine the transitions between patterns in the sequence. Introducing a piecewise linear approximation we find closed form approximate solutions for steady-state patterns by exploiting a small parameter, the ratio of diffusivities, in a singular perturbation expansion. We consider the existence of these steady-state solutions as a parameter related to the domain length is varied and predict the point at which the solution ceases to exist, which we identify with the onset of transition between patterns for the sequence generated on the growing domain. Applying these results to the model in one spatial dimension we are able to predict the mechanism and timing of transitions between quasi-steady patterns in the sequence. We also highlight a novel sequence behaviour, mode-tripling, which is a consequence of a symmetry in the reaction term of the reaction-diffusion system.

Animals↗
PubMed1978

Convexity theorem for subthreshold stimuli in linear models of visual contrast detection.

Under the general assumption that visual contrast detection occurs by a parallel array of linear detectors, either without probability summation or with probability summation of a commonly assumed type, it is shown that the set of functions representing subthreshold stimuli must be convex. Thus, for example, a planar plot of the threshold locus using multiples of any two functions as axes, must be convex (cannot bulge inward). If experimental evidence to the contrary were discovered, it would rule out detection by parallel linear detectors of the above type. One possible kind of such evidence would be an inward cusp of the threshold locus corresponding to one of a special class of stimuli to which the visual system might be specifically sensitive.

Humans↗
PubMed2002

Traveling kinks in discrete media: exact solution in a piecewise linear model.

We present an exact integral representation of a traveling kink solution in a reaction-diffusion equation with a piecewise linear reaction function, complementing existence proofs and numerical observations of such solutions in discrete excitable media. The kink speed is determined through a matching condition, and is worked out explicitly in two limiting situations: the pinning limit, and the opposite limit of infinitely fast kink. Results on the pinning limit agree with those in a recent paper by Fath [Physica D 116, 176 (1998)]. The model includes a "recovery parameter" for a possible extension to a discrete FitzHugh-Nagumo-type system.

Journal Article↗
PubMed2001

Components of insulin resistance syndrome in a community-based population assessed by log-linear models.

BACKGROUND AND PURPOSE: To investigate the clustering of insulin resistance syndrome with hyperinsulinemia, hypertriglyceridemia, low high-density lipoprotein (HDL) cholesterol, hypertension, and obesity, we conducted this cross-sectional study and analyzed the patterns of conditional independence among these five elements. METHODS: Fasting insulin, lipid profiles, blood pressure, and anthropometric data from 2165 Taiwanese older than 35 years in the Chin-Shan community were examined. The cut-off points of these five factors (all binary variables) were defined. The hierarchical log-linear regression with nested effects model was applied to fit this higher-order contingency table of five variables, and likelihood ratio (chi2) statistics were used to test the goodness of fit. RESULTS: Hyperinsulinemia was independently correlated with obesity (odds ratio [OR] 5.7, 95% confidence interval [CI] 4.5-7.3), low HDL (OR 2.3, 95% CI 1.8-2.9), and hypertriglyceridemia (OR 1.6, 95% CI 1.2-2.2). Hypertriglyceridemia was significantly associated with low HDL (OR 3.6, 95% CI 2.7-4.8), and non-significantly associated with hypertension (OR 1.3, 95% CI 0.9-1.7) and obesity (OR 1.1, 95% CI 0.8-1.6). In persons with normal triglyceride levels, hypertension was positively associated with obesity (OR 2.8, 95% CI 2.1-3.7) and low HDL (OR 2.0, 95% CI 1.5-2.8). Analyses from forward and backward selection methods gave similar results. Graphical models with conditional independence relationships among these five variables were demonstrated. CONCLUSIONS: The components of insulin resistance syndrome have intricate relationships. Hyperinsulinemia was most related to obesity, and hypertriglyceridemia was most related to low HDL.

Adult↗
PubMed1980

A non-linear model for visual-vestibular interaction during body rotation in man.

A mathematical model for visual-vestibular interaction during body rotation in an illuminated visual surround is obtained by combining a previous model of the optokinetic reflex (OKR) with a simplified model of the vestibulo-ocular reflex (VOR). OKR is activated by the slip of the image of the external world on the retina, and represents a negative feedback loop around VOR. For large retinal slip velocities OKR behaves as a basically non-linear system. The validity of the model is proved via computer simulation by comparing predicted responses with the experimental results obtained in man by Koenig et al. (1978) in different situations of visual-vestibular interaction.

Eye Movements↗
PubMed1990

Singular value decomposition--a general linear model for analysis of multivariate structure in the electroencephalogram.

The application of Singular Value Decomposition (SVD) to analysis of EEG and evoked potential data has led to a hypothesis concerning the underlying structure of the EEG recorded from multiple channels. Based on the SVD algorithm the EEG is considered to be the linear combination of a sufficient number of features, each of which is defined in terms of its spatial distribution, temporal distribution, and amplitude. Use of this model leads to clear concepts concerning sampling, data reduction, normalization, and calculation of statistical significance, some of which are less evident when analysis is restricted to a single domain of interest.

Brain↗
PubMed1981

Linear models for calculating digestibile energy for sheep diets.

Equations for estimating the digestible energy (DE) content of sheep diets were generated from the chemical contents and a factorial description of diets fed to lambs in digestion trials. The diet factors were two forages (alfalfa and grass hay), harvested at three stages of maturity (late vegetative, early bloom and full bloom), fed in two ingredient combinations (all hay or a 50:50 hay and corn grain mixture) and prepared by two forage texture processes (coarsely chopped or finely chopped and pelleted). The 2 x 3 x 2 x 2 factorial arrangement produced 24 diet treatments. These were replicated twice, for a total of 48 lamb digestion trials. In model 1 regression equations, DE was calculated directly from chemical composition of the diet. In model 2, regression equations predicted the percentage of digested nutrient from the chemical contents of the diet and then DE of the diet was calculated as the sum of the gross energy of the digested organic components. Expanded forms of model 1 and model 2 were also developed that included diet factors as qualitative indicator variables to adjust the regression constant and regression coefficients for the diet description. The expanded forms of the equations accounted for significantly more variation in DE than did the simple models and more accurately estimated DE of the diet. Information provided by the diet description proved as useful as chemical analyses for the prediction of digestibility of nutrients. The statistics indicate that, with model 1, neutral detergent fiber and plant cell wall analyses provided as much information for the estimation of DE as did model 2 with the combined information from crude protein, available carbohydrate, total lipid, cellulose and hemicellulose. Regression equations are presented for estimating DE with the most currently analyzed organic components, including linear and curvilinear variables and diet factors that significantly reduce the standard error of the estimate. To estimate De of a diet, the user utilizes the equation that uses the chemical analysis information and diet description most effectively.

Animals↗
PubMed1988

A linear model of muscle respiration explains monoexponential phosphocreatine changes.

Phosphocreatine (PCr) content was measured by phosphorus nuclear magnetic resonance spectroscopy in the gastrocnemius muscles of pentobarbital-anesthetized rats during and after twitch stimulation at rates up to 0.75 Hz. The monoexponential time constant for PCr changes was similar at the onset of vs. during recovery after stimulation and was not significantly different for different stimulation rates (mean time constant 1.44 min). Steady-state PCr level during stimulation was linearly related to the product of stimulation rate times peak twitch force. These results are shown to be consistent with a simple first-order electrical analog model of oxidative metabolism that is applicable at submaximal oxidative rates. The model assumes equilibrium of the creatine kinase reaction, which is modeled as a chemical capacitor, with capacitance proportional to the total creatine level, and PCr level proportional to the cytosolic free energy of ATP hydrolysis.

Animals↗
PubMed1996

A non-linear model of growth in the first year of life.

Weight gain curves in infancy and childhood show valleys and hills which cannot be simplistically ascribed to random variations, so that they are referred to as pulsatile or pulse growth. Classical mathematical models of human growth, upon which the statistical percentiles are based, do not account for these oscillations. Moreover, statistical curves can hide individual patterns of growth. In the present paper a system dynamics approach to modelling the first year weight gain is suggested which simultaneously accounts for the oscillations of weight gain, for its decreasing trend, and for a more or less marked initial spurt observed approximately in the second month of life. It is suggested that the overall weight growth in the first year is the output of complex hidden non-linear dynamics.

Anthropometry↗
PubMed1997

Acoustic streaming: comparison of low-amplitude linear model with streaming velocities measured by 32-MHz Doppler.

The pressure gradient along the ultrasonic beam results in medium streaming. Following Nyborg's analysis of the Navier-Stokes equation, Wu and Du developed an approximate solution for the streaming velocity generated by flat and weakly focused transducers. We have modified their solution of the Poisson equation by directly deriving the Dirichlet boundary conditions to be applied for this type of equation. Our numerical results (for the linear case) were about one half smaller for flat and weakly focused on Gaussian beam transducers compared to the results by Wu and Du. The theoretical calculations were verified using a purpose-designed 32-MHz pulsed Doppler unit. The applied average acoustic power was changed from 1 microW to 6 mW, the burst width was 0.5 microseconds and the pulse repetition frequency was 32 kHz. The experiments were done on 4-mm-diameter flat and focused (focal distance = 8 and 12 mm) transducers. The streaming was measured along the ultrasonic beam from 0-20 mm; at all positions, the maximum Doppler frequency was estimated from the recorded spectra. Streaming was induced in a solution of water and corn starch. The experimental results showed that, for a given acoustic power, the streaming velocity was independent of the starch density in water changed from 0.3-40 g of starch in 1 l of distilled water. For applied acoustic powers, the streaming velocity changed linearly from 0.2-40 mm/s. Both the theoretical solutions for plane and focused waves and the experimental results were in good agreement.

Acoustics↗