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Results for “Linear Regression”

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At least 127 records · Page 7Linked to original sources

PubMed1989

Linear regression analysis for enzyme kinetic studies in toxicant interactions.

A new method based on linear regression of per cent modulation in enzyme activity over substrate concentration is proposed to give an interpretative base to the influence of more than one modulator/inhibitor/toxicant, a situation commonly met with in toxicological studies-toxicant interactions. Advantages of this method over the classical kinetic methods are discussed in detail using brain Mg2+ ATPase activity of the fish Tilapia mossambica under in vitro regimes of hexachlorocyclohexane and malathion.

Acetylcholinesterase↗

PubMed2002

Wavelet-generalized least squares: a new BLU estimator of linear regression models with 1/f errors.

Long-memory noise is common to many areas of signal processing and can seriously confound estimation of linear regression model parameters and their standard errors. Classical autoregressive moving average (ARMA) methods can adequately address the problem of linear time invariant, short-memory errors but may be inefficient and/or insufficient to secure type 1 error control in the context of fractal or scale invariant noise with a more slowly decaying autocorrelation function. Here we introduce a novel method, called wavelet-generalized least squares (WLS), which is (to a good approximation) the best linear unbiased (BLU) estimator of regression model parameters in the context of long-memory errors. The method also provides maximum likelihood (ML) estimates of the Hurst exponent (which can be readily translated to the fractal dimension or spectral exponent) characterizing the correlational structure of the errors, and the error variance. The algorithm exploits the whitening or Karhunen-Loéve-type property of the discrete wavelet transform to diagonalize the covariance matrix of the errors generated by an iterative fitting procedure after both data and design matrix have been transformed to the wavelet domain. Properties of this estimator, including its Cramèr-Rao bounds, are derived theoretically and compared to its empirical performance on a range of simulated data. Compared to ordinary least squares and ARMA-based estimators, WLS is shown to be more efficient and to give excellent type 1 error control. The method is also applied to some real (neurophysiological) data acquired by functional magnetic resonance imaging (fMRI) of the human brain. We conclude that wavelet-generalized least squares may be a generally useful estimator of regression models in data complicated by long-memory or fractal noise.

Adult↗

PubMed1994

[Measurement errors and linear regression].

The consequences of a measurement error of known variance in the explanatory variable of a linear regression were assessed. On the average, the ordinary least squares (OLS) method underestimated the regression slope, the bias increasing with the variance of the measurement error and the strength of the relationship. Simulation results showed that the corrected-for-the-error estimate slightly overestimated the slope, the bias increasing with the variance of the measurement error and the strength of the relationship, but rapidly decreasing when the number of observations increased. In all cases the corrected estimate has a larger variance than the OLS estimate, Nevertheless, the mean square deviation of the corrected estimate to the "true" slope value can be smaller than the OLS one, even for a relatively small number of observations (< or = 100). In those conditions, the corrected estimate might be preferred when a "good estimation" of the regression slope is needed. Whereas a measurement error in the dependent variable, does not bias the slope estimator, when it is independent of the error in the explanatory variable, this is not the case when both measurement errors are correlated. An example of the need to correct for such a correlation is given.

Bias↗

PubMed2005

Applying a data duplication technique in linear regression analysis of waiting time to pregnancy.

This analysis demonstrates the application of a data duplication technique in linear regression with censored observations of the waiting time to third pregnancy ending in two outcome types, using data from Malaysia. The linear model not only confirmed the results obtained by the Cox proportional hazards model, but also identified two additional significant factors. The method provides a useful alternative when Cox proportionality assumption of the hazards is violated.

Adult↗

PubMed2001

A multiple imputation approach to linear regression with clustered censored data.

We extend Wei and Tanner's (1991) multiple imputation approach in semi-parametric linear regression for univariate censored data to clustered censored data. The main idea is to iterate the following two steps: 1) using the data augmentation to impute for censored failure times; 2) fitting a linear model with imputed complete data, which takes into consideration of clustering among failure times. In particular, we propose using the generalized estimating equations (GEE) or a linear mixed-effects model to implement the second step. Through simulation studies our proposal compares favorably to the independence approach (Lee et al., 1993), which ignores the within-cluster correlation in estimating the regression coefficient. Our proposal is easy to implement by using existing softwares.

Algorithms↗

PubMed1980

A program for non-linear regression analysis to be used on desk-top computers.

A simple program for non-linear regression analysis, based upon the strategy of evolution, is described. It should run on any minicomputer (even on "personal computers') if a BASIC interpreter is available. It can easily be modified for the both the type of function and the "best fitting' condition.

Anti-Bacterial Agents↗

PubMedDate not supplied

Multiple-dose non-linear regression analysis program. Aminoglycoside dose prediction.

The ability of a new multiple-dose non-linear regression analysis program to predict steady-state aminoglycoside peak and trough serum concentrations was evaluated. 30 patients receiving either amikacin (7), gentamicin (10) or tobramycin (13) were studied. A standard method of prediction which requires the collection of 3 or 4 serum samples during a dosing interval and a predictive method which relies upon population-based estimates of pharmacokinetic parameters were compared with the new approach which requires the collection of 2 serum samples. There were no significant differences between the methods which utilised serum concentration data with regard to predictive precision (mean prediction error of about 10%). These methods were more precise than the population-based method (p less than 0.01, mean prediction error 29.1%). None of the methods produced biased estimates. These results indicate that when the regression program is employed, valid estimates of pharmacokinetic parameters and prediction of steady-state serum concentrations can be obtained with fewer serum samples than have been recommended.

Adult↗

PubMed1991

[Multi-center evaluation of Showa disk susceptibility to presumptively determine minimum inhibitory concentrations through linear regression analysis].

To confirm the reliability of minimum inhibitory concentrations (MICs) determined by use of predefined linear regressions to bacterial growth inhibitory zone diameter on Showa disk susceptibility test, the multi-center evaluation along daily routines was performed in comparison with the standard agar dilution method. In total, 4,107 (89.0%) of 4,613 testings gave comparable MICs with 4-fold or less differences to those determined by the standard agar dilutions. The agreement of MICs (less than or equal to 4-fold differences) for gram-negative rods, excluding Pseudomonas aeruginosa, against 10 antimicrobial agents was estimated to 92.1%, and those for gram-positive cocci against 9 agents and for the strains of Pseudomonas aeruginosa against 8 agents were 84.5% and 81.7%, respectively. With these results, we can conclude that, under the well-controlled test procedures, the MIC correlates determined by Showa disk susceptibility test are enough comparable to those determined by the standard agar dilution method.

Anti-Bacterial Agents↗

PubMed1999

Computing minimum description length for robust linear regression model selection.

A minimum description length (MDL) and stochastic complexity approach for model selection in robust linear regression is studied in this paper. Computational aspects and implementation of this approach to practical problems are the focuses of the study. Particularly, we provide both algorithms and a package of S language programs for computing the stochastic complexity and proceeding with the associated model selection. A simulation study is then presented for illustration and comparing the MDL approach with the commonly used AIC and BIC methods. Finally, an application is given to a physiological study of triathlon athletes.

Algorithms↗

PubMed1995

Multiple linear regression analysis of hypertrophy, calcium and cadmium in hypertensive and non-hypertensive states.

Heart disease remains a major public health issue. In this study we aimed to achieve a greater mathematical and mechanistic understanding of the relationship between exposure to heavy metals and heart disease. Measurements of calcium and cadmium levels were made by flame atomic absorption spectrophotometry in tissue from hypertensive and non-hypertensive rabbits. Relationships between hypertrophy, calcium and cadmium were tested using multiple regression analysis. Multiple linear relationships occurred that showed the dependence of hypertrophy on calcium and cadmium levels, and of calcium accumulation on cadmium and hypertrophy. These data provide an insight into the mechanisms of heavy metal accumulation and the development of cardiovascular hypertrophy.

Animals↗

PubMed1997

Multiple linear regression analysis of blood pressure, hypertrophy, calcium and cadmium in hypertensive and non-hypertensive states.

High blood pressure causes heart disease and remains a major public health issue. This paper expands mathematically and mechanically on environmental heavy metal exposure and heart disease. In rabbits, mean blood pressure was measured by direct puncture of the middle ear artery. Measurements of calcium and cadmium levels were made by flame atomic absorption spectrophotometry in tissue from hypertensive and non-hypertensive rabbits. Relationships between blood pressure, hypertrophy, calcium and cadmium were tested using multiple regression analysis. Multiple linear relationships occurred showing the dependence of high blood pressure on hypertrophy, calcium and cadmium: hypertrophy on calcium, cadmium and high blood pressure; and calcium on cadmium, high blood pressure and hypertrophy. These data provide insight into the mechanism of elevated blood pressure on heavy metal and calcium accumulation, and cardiac hypertrophy.

Animals↗

PubMed2003

Weighted estimating equations for linear regression analysis of clustered failure time data.

Estimation of regression parameters in linear survival models is considered in the clustered data setting. One step updates from an initial consistent estimator are proposed. The updates are based on scores that are functions of ranks of the residuals, and that incorporate weight matrices to improve efficiency. Optimal weights are approximated as the solution to a quadratic programming problem, and asymptotic relative efficiencies to various other weights computed. Except under strong dependence, simpler methods are found to be nearly as efficient as the optimal weights. The performance of several practical estimators based on exchangeable and independence working models is explored in simulations.

Cluster Analysis↗

PubMed2002

Estimation of sib-pair IBD sharing and multipoint polymorphism information content by linear regression.

A simple method of estimating IBD sharing (pi) of sibling pairs from multipoint genotype data based on linear regression is presented. The new method is an extension of that developed by Fulker, Cherny, and Cardon (1995) and involves a measure of sib-pair specific information, W, defined as the difference between the unconditional variance of pi and the conditional variance of pi given the marker genotype data. When markers are not fully informative, the W method provides estimates closer to those obtained from the exact hidden Markov method (HMM) than the original Fulker method. Using W, we also derive a generalisation for the polymorphism information content (PIC) for multiple markers. This multipoint polymorphism information content (MPIC) can be evaluated at any location along a marker map and is proportional to the noncentrality parameter for linkage. We illustrate MPIC by assessing the relative information content of single nucleotide polymorphism (SNP) and microsatellite markers.

Alleles↗

PubMed1998

An EXCEL template for calculation of enzyme kinetic parameters by non-linear regression.

MOTIVATION: An EXCEL template has been developed for the calculation of enzyme kinetic parameters by non-linear regression techniques. The tool is accurate, inexpensive, as well as easy to use and modify. AVAILABILITY: The program is available from http://www.ebi.ac.uk/biocat/biocat.html CONTACT: agustin. hernandez@bio.kuleuven.ac.be

Computational Biology↗

PubMed1997

A comparison of quantitative structure-activity relationships for the effect of benzoic and cinnamic acids on Listeria monocytogenes using multiple linear regression, artificial neural network and fuzzy systems.

The ability of artificial neural networks (ANN), fuzzy systems (FS) and multiple linear regression (MLR) to fit the biological activity surface describing the inhibition of Listeria monocytogenes by benzoic and cinnamic acid derivatives was compared. MLR and ANN were also compared for their ability to select the properties that best describe the biological activity of the compounds. The criteria used for comparing surface fits of all models were the coefficient of determination r2 and the standard deviation of the error, s(e). The ANN method gave a better correlation, r2 = 0.96, compared with either MLR, r2 = 0.81, or FS, r2 = 0.92, and also a lower standard error, possibly indicating non-linearity in the data. The ANN was shown to generalize better than MLR using the leave-one-out method. The ANN selection algorithm for the selection of the parameters that contributed most to the biological activity of the phenols (log K and pKa) agreed with the selected parameters of the MLR system.

Benzaldehydes↗

PubMed2003

Determinants of waiting time to third pregnancy using censored linear regression.

The intervals between pregnancies have important effects on fertility and maternal and infant health outcomes. This study uses linear regression with censored observation to assess the determinants of the waiting time to third pregnancy. The analysis is applied to data from the Second Malaysian Family Life Survey consisting of 1172 women who had their second delivery ending in a live birth. Contraceptive use, age of the woman, duration of breast-feeding, length of previous pregnancy interval and education of the woman all affect the waiting time to third pregnancy significantly.

Adult↗

PubMed1987

Linear regression analysis of ultrasound follicular growth series: statistical relationship of growth rate and calculated date of growth onset to total growth period.

Linear regression analysis was used to assess the serial growth of carefully measured individual mean follicular diameters as a function of menstrual age in a group of normal volunteers in natural, unstimulated cycles (n = 18). Follicle diameter (FD) growth, as measured with serial pelvic ultrasonography, can be shown to be essentially linear (mean R2, 0.92) with respect to time up to the point of ovulation. Growth rate (k) and the calculated date of growth onset (Do) are obtainable from the individual regression equations. Because an approximation of the date of ovulation (Dov, measured by menstrual age at the date of peak mean follicular size) is an available parameter, total growth period (TGP) is calculated with the equation (TGP = Dov - Do). Do, k, and TGP are highly correlated with one another. The mean parameters (+/- standard deviation) are Do = 4.29 +/- 2.77 day, k = 0.24 +/- 0.07 cm/day, TGP = 10.32 +/- 2.35 day, peak FD = 2.34 +/- 0.28 cm, and Dov = 14.61 +/- 2.00 day. The internal correlation of these parameters predicts that information from the first several scans in an individual series may be used to forecast date of ovulation. This may represent an improvement over the use of follicle size or menstrual age alone in planning for human chorionic gonadotropin administration, insemination timing, follicular aspiration and other interventions.

Adult↗

PubMed2005

Judging the significance of multiple linear regression models.

It is common practice to calculate large numbers of molecular descriptors, apply variable selection procedures to reduce the numbers, and then construct multiple linear regression (MLR) models with biological activity. The significance of these models is judged using the usual statistical tests. Unfortunately, these tests are not appropriate under these circumstances since the MLR models suffer from "selection bias". Experiments with regression using random numbers have generated critical values (Fmax) with which to assess significance.

Antimycin A↗