PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Linear Regression”

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 91 records · Page 5Linked to original sources
PubMed2003

Linear regression and two-class classification with gene expression data.

MOTIVATION: Using gene expression data to classify (or predict) tumor types has received much research attention recently. Due to some special features of gene expression data, several new methods have been proposed, including the weighted voting scheme of Golub et al., the compound covariate method of Hedenfalk et al. (originally proposed by Tukey), and the shrunken centroids method of Tibshirani et al. These methods look different and are more or less ad hoc. RESULTS: We point out a close connection of the three methods with a linear regression model. Casting the classification problem in the general framework of linear regression naturally leads to new alternatives, such as partial least squares (PLS) methods and penalized PLS (PPLS) methods. Using two real data sets, we show the competitive performance of our new methods when compared with the other three methods.

Algorithms↗
PubMed2001

Conditional local influence in case-weights linear regression.

The local influence approach proposed by Cook (1986) makes use of the normal curvature and the direction achieving the maximum curvature to assess the local influence of minor perturbation of statistical models. When the approach is applied to the linear regression model, the result provides information concerning the data structure different from that contributed by Cook's distance. One of the main advantages of the local influence approach is its ability to handle the simultaneous effect of several cases, namely, the ability to address the problem of 'masking'. However, Lawrance (1995) points out that there are two notions of 'masking' effects, the joint influence and the conditional influence, which are distinct in nature. The normal curvature and the direction of maximum curvature are capable of addressing effects under the category of joint influences but not conditional influences. We construct a new measure to define and detect conditional local influences and use the linear regression model for illustration. Several reported data sets are used to demonstrate that new information can be revealed by this proposed measure.

Humans↗
PubMedDate not supplied

Comparison of linear regression and probit analysis for detecting H-reflex threshold in individuals with and without spinal cord injury.

A major challenge to understanding spinal reflex organization in health and disease is identifying sensitive measures of reflex excitability. The purpose of this study was to determine whether linear regression or probit analysis techniques are more sensitive for detecting H-reflex and M-wave threshold and for identifying differences in H-reflex threshold in individuals with and without spinal cord injury (SCI). Soleus H-reflex recruitment curves were generated in 9 individuals with SCI and 20 able-bodied individuals. H-reflex and M-wave threshold was estimated using three different methods, two that used linear regression of H-reflex peak-to-peak amplitude and one that used probit analysis of quantal H-reflexes. Results indicate that in both groups all three techniques were equally sensitive for detecting H-reflex but not M-wave threshold. When H-reflex threshold was normalized to M-wave threshold, different techniques provided different estimates of H-reflex threshold. However, between-group differences (SCI vs. able-body) in H-reflex and M-wave threshold were not affected by the measurement techniques that were compared in this study. We conclude that these techniques provide equally sensitive estimates of H-reflex but not M-wave threshold in persons with and without SCI. Hence, caution should be used when interpreting normalized and non-normalized values of H-reflex threshold.

Adult↗
PubMed1989

The use of a non-linear regression approach for the analysis of the ouabain-K+ interaction with (Na+ + K+)-ATPase from guinea pig and rat hearts.

1. The interaction between ouabain and K+ and their effects on (Na+ + K+)-ATPase activity were studied using microsomes from guinea pig and rat heart. 2. Microsomes were incubated in the presence of various concentrations of K+ and ouabain and ATPase activity was estimated by measuring the inorganic phosphate liberated. The experimental data were analyzed statistically by micro-computer, using a non-linear regression program based on the steepest descent technique. 3. The experimental data were best fitted by a model which assumes that ouabain acts like a mixed inhibitor with respect to the apparently cooperative K+ activation of (Na+ + K+)-ATPase. This quantitative approach provided estimates (with approximate standard deviations) of all the parameters involved in the model. 4. The inhibition constant for the uncompetitive term of the effect was 7- to 9-fold higher than the inhibition constant for the competitive term for both the guinea pig and rat heart preparations. 5. The present results indicate that graphical analyses are helpful for illustrative purposes but suggest that a computerized, non-linear regression program simultaneously analyzing all the non-linearized data should be used to quantify the complex kinetic parameters and to discriminate objectively among possible models.

Animals↗
PubMed1984

Linear regression analysis of binary response data with mixed covariates - a simulation study.

In a clinical trial with binary outcome, analyses are required for treatment or study group comparisons adjusted for covariate effects. A special problem arises with "mixed binary and Gaussian covariates", i.e., when some covariates are binary and some are continuous and may be assumed to be Gaussian. The correct model for such a data structure is of the logistic form. In the past, analyses of such data have been carried out by linear regression as well as by logistic regression methods. In this article, computer simulation was used to study the type I error level of linear regression analysis tests for treatment comparisons, when applied to a binary outcome variate obeying a logistic model with mixed binary and Gaussian covariates. It was found that the true type I error level depends on the distribution of covariates among treatment groups and on the magnitudes of the actual covariate effects, and can differ importantly from that assumed under Gaussian theory. Some recommendations are made for developing computer package programs for this problem.

Clinical Trials as Topic↗
PubMed2006

A comparative study of linear and non-linear regression analysis for ammonium exchange by clinoptilolite zeolite.

Ammonium ion exchange from aqueous solution using clinoptilolite zeolite was investigated at laboratory scale. Batch experimental studies were conducted to evaluate the effect of various parameters such as pH, zeolite dosage, contact time, initial ammonium concentration and temperature. Freundlich and Langmuir isotherm models and pseudo-second-order model were fitted to experimental data. Linear and non-linear regression methods were compared to determine the best fitting of isotherm and kinetic model to experimental data. The rate limiting mechanism of ammonium uptake by zeolite was determined as chemical exchange. Non-linear regression has better performance for analyzing experimental data and Freundlich model was better than Langmuir to represent equilibrium data.

Hydrogen-Ion Concentration↗
PubMedDate not supplied

Linear regression analysis and its application to multivariate chromatographic calibration for the quantitative analysis of two-component mixtures.

Multivariate chromatographic calibration technique was developed for the quantitative analysis of binary mixtures enalapril maleate (EA) and hydrochlorothiazide (HCT) in tablets in the presence of losartan potassium (LST). The mathematical algorithm of multivariate chromatographic calibration technique is based on the use of the linear regression equations constructed using relationship between concentration and peak area at the five-wavelength set. The algorithm of this mathematical calibration model having a simple mathematical content was briefly described. This approach is a powerful mathematical tool for an optimum chromatographic multivariate calibration and elimination of fluctuations coming from instrumental and experimental conditions. This multivariate chromatographic calibration contains reduction of multivariate linear regression functions to univariate data set. The validation of model was carried out by analyzing various synthetic binary mixtures and using the standard addition technique. Developed calibration technique was applied to the analysis of the real pharmaceutical tablets containing EA and HCT. The obtained results were compared with those obtained by classical HPLC method. It was observed that the proposed multivariate chromatographic calibration gives better results than classical HPLC.

Calibration↗
PubMed2004

Multiple linear regression analysis of bacterial deposition to polyurethane coatings after conditioning film formation in the marine environment.

Many studies have shown relationships of substratum hydrophobicity, charge or roughness with bacterial adhesion, although bacterial adhesion is governed by interplay of different physico-chemical properties and multiple regression analysis would be more suitable to reveal mechanisms of bacterial adhesion. The formation of a conditioning film of organic compounds adsorbed from seawater affects the properties of substratum surfaces prior to bacterial adhesion, which is a complicating factor in studying the mechanism of bacterial adhesion. In this paper, the impact of conditioning films adsorbed from natural seawater to four polyurethane coatings with different hydrophobicity, elasticity and roughness was studied for three different marine bacterial strains in a multiple linear regression analysis. The water contact angle on hydrophobic coatings decreased on average by 8 degrees and increased on average by the same amount on hydrophilic coatings. These changes were accompanied by increased concentrations of oxygen and nitrogen on the surface as determined by X-ray photoelectron spectroscopy, indicative of adsorption of proteinaceous material. Furthermore, the mean surface roughness increased on average by 4 nm after conditioning film formation. Multiple linear regression analysis revealed that changes in deposition due to conditioning film formation of Marinobacter hydrocarbonoclasticus, Psychrobacter sp. SW5H and Halomonas pacifica in a stagnation-point flow chamber could be explained in a model comprising hydrophobicity and the prevalence of nitrogen-rich components on the surface for the most hydrophobic strain. For the two more hydrophilic strains, deposition was governed by a combination of surface roughness and hydrophobicity. Elasticity was not a factor in bacterial adhesion to conditioning films.

Bacterial Adhesion↗
PubMed1988

Multiple linear regression is a useful alternative to traditional analyses of variance.

Physiologists often wish to compare the effects of several different treatments on a continuous variable of interest, which requires an analysis of variance. Analysis of variance, as presented in most statistics texts, generally requires that there be no missing data and often that each sample group be the same size. Unfortunately, this requirement is rarely satisfied, and investigators are confronted with the problem of how to analyze data that do not strictly fit the traditional analysis of variance paradigm. One can avoid these pitfalls by recasting the analysis of variance as a multiple linear regression problem. When there are no missing data, the results of a traditional analysis of variance and the corresponding multiple regression problem are identical; when the sample sizes are unequal or there are missing data, one can use a regression formulation to analyze data that cannot be easily handled in a traditional analysis of variance paradigm and thus overcome a practical computational limitation of traditional analysis of variance. In addition to overcoming practical limitations of traditional analysis of variance, the multiple linear regression approach is more efficient because in one run of a statistics routine, not only is the analysis of variance done but also one obtains estimates of the size of the treatment effects (as opposed to just an indication of whether such effects are present or not), and many of the pairwise multiple comparisons are done (they are equivalent to t tests for significance of the regression parameter estimates). Finally, interaction between the different treatment factors is easier to interpret than it is in traditional analysis of variance.

Analysis of Variance↗
PubMed1997

Evaluation of logistic versus linear regression models for predicting pulmonary hypertension syndrome (ascites) using cold exposure or pulmonary artery clamp models in broilers.

Syndromes such as ascites (pulmonary hypertension syndrome) present difficulties both in the interpretation of associated physiological observations and in their analyses. The ability to predict which physiological variables have the greatest influence on survival or, more importantly, which individuals are most susceptible or resistant to ascites would be very useful selection tools. When addressed in this manner, ascites data become binary data sets (healthy or affected). Binary data can be problematic in that they do not meet all of the assumptions necessary for more traditional analyses such as ANOVA and linear regression. Binary data are discrete and do not have normally distributed errors, which violates a fundamental assumption of linear models. The predictive abilities of linear and logistic regression were evaluated in two replicated experiments using two methods to induce ascites, cold exposure (COLD) and surgical clamping of one pulmonary artery (PAC). The logistic and linear predictive models were derived using the same data and variables. The first data set from PAC and COLD were used to develop the predictive models and the replicate data sets of PAC and COLD were used as "test data sets" for the prediction of ascites. The linear models developed were complex, using four or five variables and requiring up to seven different measurements. On average, the linear models predicted ascites correctly 87.6% of the time. The logistic models were simple (single variable) models that predicted ascites correctly 92.0% of the time. The variables used in the logistic models were derivations of the ratio of right ventricular weight to total ventricular weight, either corrected for age or the body weight of the bird. Although linear regression predicted the incidence of ascites almost as well as logistic regression did, logistic regression is the more appropriate test statistic to use.

Analysis of Variance↗
PubMed1991

Multiple linear regression modeling of furosemide renal clearance and urinary excretion rate.

Multiple linear regression techniques were utilized to determine models for the renal clearance and urinary excretion rate of furosemide. Models for the renal clearance were formulated based on data collected from the literature. The best model predicted that the weight-normalized renal clearance was a function of the weight-normalized creatinine clearance, with coefficient values dependent on the presence or absence of heart, liver, and/or kidney failure. The predictive performance of this model was evaluated using a separate verification data set, and, prospectively, for a group of cardiac patients. The urinary excretion rate of furosemide is the primary determinate of response. Models for the furosemide excretion rate were formulated from data collected prospectively from a group of patients with cardiac disease. The best model predicted that the dose-normalized morning urinary excretion rate was a function of the blood urea nitrogen concentration (BUN), with modifications for the presence of liver failure and/or decompensated heart failure. The oral dosage required to produce a clinically optimal furosemide excretion rate in cardiac patients without liver disease was dose (mg) = 42.1/(0.925-0.0151 BUN).

Aged↗
PubMed1984

Linear regression analysis with repeated measurements.

The statistical aspects of repeated measures linear regression, in which each subject contributes several pairs of measurements to the analysis, are discussed. It is shown that the standard error of a regression coefficient computed from the ordinary least squares analysis can either underestimate or overestimate the true standard error, depending on how values of the independent variable are selected. The application of generalized least squares analysis to repeated measures data is also discussed. Two examples are given.

Adolescent↗
PubMed1990

Physicochemical factors associated with binding and retention of compounds in ocular melanin of rats: correlations using data from whole-body autoradiography and molecular modeling for multiple linear regression analyses.

The relationship between the physicochemical characteristics of 27 new drug candidates and their distribution into the melanin-containing structure of the rat eye, the uveal tract, was examined. Tissue distribution data were obtained from whole-body autoradiograms of pigmented Long-Evans rats sacrificed at 5 min and 96 hr after dosing. The physicochemical parameters considered include molecular weight, pKa, degree of ionization, octanol/water partition coefficient (log Po/w), drug-melanin binding energy, and acid/base status of the functional groups within the molecule. Multiple linear regression analysis was used to describe the best model correlating physicochemical and/or biological characteristics of these compounds to their initial distribution at 5 min and to the retention of residual radioactivity in ocular melanin at 96 hr post-injection. The early distribution was a function primarily of acid/base status, pKa, binding energy, and log P(o/w), whereas uveal tract retention in rats was a function of volume of distribution (V1), log P(o/w), pKa, and binding energy. Further, there was a relationship between the initial distribution of a compound into the uveal tract and its retention 96 hr later. More specifically, the structures most likely to be distributed and ultimately retained at high concentrations were those containing strongly basic functionalities, such as piperidine or piperazine moieties and other amines. Further, the more lipophilic and, hence, widely distributed the basic compound, the greater the likelihood that it interacts with ocular melanin. In summary, the use of multiple linear regression analysis was useful in distinguishing which physicochemical characteristics of a compound or group of compounds contributed to melanin binding in pigmented rats in vivo.

Animals↗
PubMed1997

Respiratory resistive impedance in obstructive patients: linear regression analysis vs viscoelastic modelling.

The aim of this study was to test the ability of a simple two segment model to describe the frequency dependence of resistive impedance in obstructive patients, and to investigate the significance of parameters derived from this model. The study was performed in 38 patients, in the basal state and after inhalation of 200 micrograms salbutamol. Impedance data measured over 4-32 Hz were fitted by a general four parameter viscoelastic model describing gas redistribution, and completed by an inertial component. This model yielded Newtonian resistance (Rmin) and maximal resistance (Rmax = Rmin plus delayed resistance due to gas redistribution). Resistive impedance data were also submitted to linear regression analysis over the 4-16 and 17-32 Hz frequency ranges, which respectively, yielded resistive impedance extrapolated at 0 Hz (R0) and resistive impedance estimated at 32 Hz (R32). R0 and R32 were compared to Rmax and Rmin, respectively. The airway response to salbutamol inhalation was assessed by the percentage changes in these parameters (R0%, R32%, Rmax%, and Rmin%, respectively). Significant linear correlations (p < 0.0001) were found between R0 and Rmax, R32 and Rmin, and R0% and Rmax%. Furthermore, the linear regression lines of R0 vs Rmax, and R0% vs Rmax%, were not significantly different from the identity line. These results demonstrate that resistive impedance extrapolated at zero frequency is equivalent to maximal resistive impedance, and can be proposed as an index, not only of the level of airway obstruction, but also of its reversibility.

Administration, Inhalation↗
PubMed2002

Linear regression of eye velocity on eye position and head velocity suggests a common oculomotor neural integrator.

The oculomotor system produces eye-position signals during fixations and head movements by integrating velocity-coded saccadic and vestibular inputs. A previous analysis of nucleus prepositus hypoglossi (nph) lesions in monkeys found that the integration time constant for maintaining fixations decreased, while that for the vestibulo-ocular reflex (VOR) did not. On this basis, it was concluded that saccadic inputs are integrated by the nph, but that the vestibular inputs are integrated elsewhere. We re-analyze the data from which this conclusion was drawn by performing a linear regression of eye velocity on eye position and head velocity to derive the time constant and velocity bias of an imperfect oculomotor neural integrator. The velocity-position regression procedure reveals that the integration time constants for both VOR and saccades decrease in tandem with consecutive nph lesions, consistent with the hypothesis of a single common integrator. The previous evaluation of the integrator time constant relied upon fitting methods that are prone to error in the presence of velocity bias and saccades. The algorithm used to evaluate imperfect fixations in the dark did not account for the nonzero null position of the eyes associated with velocity bias. The phase-shift analysis used in evaluating the response to sinusoidal vestibular input neglects the effect of saccadic resets of eye position on intersaccadic eye velocity, resulting in gross underestimates of the imperfections in integration during VOR. The linear regression method presented here is valid for both fixation and low head velocity VOR data and is easy to implement.

Animals↗
PubMed1987

Parametrization by non-linear regression and bayesian estimation of bentazepam in a multiple dosage regimen in humans.

The plasma levels of bentazepam were determined by an HPLC technique in a total of 10 patients receiving the drug orally in pill form who were on a dosage regimen with the drug administered every 8, 12 or 24 h. Blood samples were taken three times following the administration of the first and last dose and at times, immediately after the administration of intermediate doses. The parameters corresponding to a one-compartment kinetic model were calculated in each patient by using all the data on plasma levels still corresponding to different administrations by non-linear regression and applying programs with homoscedastic, heteroscedastic and bayesian estimation. The absorption constant had mean values of 2.33, 2.18 and 2.75 h-1. The elimination constant proved to be equal to 0.10, 0.09 and 0.22 h-1 while for the apparent distribution volume mean values of 1.89, 2.89 and 0.80 l/kg were found with each of the estimation programs employed, respectively. The values found for each of the kinetic parameters and with each of the programs were subjected to the non-parametric Kruskal-Wallis test with a view to detecting the presence or absence of statistically significant differences. The discrimination of the program that yielded the best fit was performed by linear regression between the values found for the plasma calculations and those calculated theoretically at the same time with each of the programs.

Adult↗