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At least 271 records · Page 15Linked to original sources
PubMed2000

Development and evaluation of a linear regression method for the prediction of maximal chiral separation of basic drug racemates by cyclodextrin-mediated capillary zone electrophoresis.

An important step in method development of chiral separations with neutral cyclodextrins (CDs) as chiral selectors is the estimation of the CD concentration that gives the highest degree of separation. From the equation [S]opt=1/(K1K2)(1/2) this optimal CD concentration can be calculated if any knowledge is available about the binding constants K1 and K2 of both enantiomer complexes. These values can be obtained by measuring the effective velocities of each enantiomer as a function of the selector concentration and fitting these profiles by non-linear least-square regression. An alternative approach has been developed which makes it possible to predict the optimal CD concentration from a few experiments performed at low CD concentrations. The model is developed using some antimycotic imidazole derivatives (econazole, miconazole and isoconazole) as test substances and hydroxypropyl-beta-CD as chiral selector. The results obtained by this method are in good agreement with those from non-linear least-square regression.

Cyclodextrins↗
PubMed2003

Missing-value estimation using linear and non-linear regression with Bayesian gene selection.

MOTIVATION: Data from microarray experiments are usually in the form of large matrices of expression levels of genes under different experimental conditions. Owing to various reasons, there are frequently missing values. Estimating these missing values is important because they affect downstream analysis, such as clustering, classification and network design. Several methods of missing-value estimation are in use. The problem has two parts: (1) selection of genes for estimation and (2) design of an estimation rule. RESULTS: We propose Bayesian variable selection to obtain genes to be used for estimation, and employ both linear and nonlinear regression for the estimation rule itself. Fast implementation issues for these methods are discussed, including the use of QR decomposition for parameter estimation. The proposed methods are tested on data sets arising from hereditary breast cancer and small round blue-cell tumors. The results compare very favorably with currently used methods based on the normalized root-mean-square error. AVAILABILITY: The appendix is available from http://gspsnap.tamu.edu/gspweb/zxb/missing_zxb/ (user: gspweb; passwd: gsplab).

Algorithms↗
PubMed1976

Testing for a single outlier from a general linear regression.

Several authors have considered the problem of detection of outliers from the general linear model Y = Xbeta + mu. Ellenberg [1973] among others, has advocated use of a detection method which involves examination of the set of internally standardized least squares residuals. Mickey [1974] and Snedecor and Cochran [1968], apparently concerned about the usefulness of an outlier detection method which is based on residual estimates that themselves are biassed by the presence of the outlier, have proposed two other alternatives. It is shown that the three approaches are exactly equivalent. A detection procedure is described which uses as its test statistic the maximum of the internally standardized least squares residuals, and upper and lower bounds for the percentage points of the test statistic are given by Bonferroni inequalities. The computations required to obtain these approximate percentage points are illustrated in a numerical example. Finally, a brief simulation study of the performance of the procedure illustrates that the power of the test can be influenced by the position of the outlier vis-a-vis the structure of the design matrix X.

Mathematics↗
PubMed2002

Strategies to improve neuroreceptor parameter estimation by linear regression analysis.

In an attempt to improve neuroreceptor distribution volume (V) estimates, the authors evaluated three alternative linear methods to Logan graphical analysis (GA): GA using total least squares (TLS), and two multilinear analyses, MA1 and MA2, based on mathematical rearrangement of GA equation and two-tissue compartments, respectively, using simulated and actual PET data of two receptor tracers, [(18)F]FCWAY and [(11)C]MDL 100,907. For simulations, all three methods decreased the noise-induced GA bias (up to 30%) at the expense of increased variability. The bias reduction was most pronounced for MA1, moderate to large for MA2, and modest to moderate for TLS. In addition, GA, TLS, and MA1, methods that used only a portion of the data (T > t*, chosen by an automatic process), showed a small underestimation for [(11)C]MDL 100,907 with its slow kinetics, due to selection of t* before the true point of linearity. These noniterative methods are computationally simple, allowing efficient pixelwise parameter estimation. For tracers with kinetics that permit t* to be accurately identified within the study duration, MA1 appears to be the best. For tracers with slow kinetics and low to moderate noise, however, MA2 may provide the lowest bias while maintaining computational ease for pixelwise parameter estimation.

Basal Ganglia↗
PubMed1985

Comparison of several non-linear-regression methods for fitting the Michaelis-Menten equation.

The known jackknife methods (i.e. standard jackknife, weighted jackknife, linear jackknife and weighted linear jackknife) for the determination of the parameters (as well as of their confidence regions) were tested and compared with the simple Marquardt's technique (comprising the calculation of confidence intervals from the variance-co-variance matrix). The simulated data corresponding to the Michaelis-Menten equation with defined structure and magnitude of error of the dependent variable were used for fitting. There were no essential differences between the results of both point and interval parameter estimations by the tested methods. Marquardt's procedure yielded slightly better results than the jackknives for five scattered data points (the use of this method is advisable for routine analyses). The classical jackknife was slightly superior to the other methods for 20 data points (this method can be recommended for very precise calculations if great numbers of data are available). The weighting does not seem to be necessary in this type of equation because the parameter estimates obtained with all methods with the use of constant weights were comparable with those calculated with the weights corresponding exactly to the real error structure whereas the relative weighting led to rather worse results.

Enzymes↗
PubMed1993

A PC program to aid in the choice of the design matrix in multiple linear regression.

A PC program, DESIGN, which can be used to evaluate and compare alternative choices of the design matrix, X, in the general linear model y = X beta + epsilon is described, illustrated and made available to interested readers. Given X, the program (1) computes various measures of the 'stability' of X and X'X and (2) determines the precisions of estimates of the model parameters, beta, and of predicted values, ŷ, at the given design points. Examples focusing on polynomial regression are given.

Data Interpretation, Statistical↗
PubMed2006

Estimation of postmortem interval from human pericardial fluid electrolytes concentrations in Chandigarh zone of India: log transformed linear regression model.

Estimation of postmortem interval from changes in postmortem pericardial fluid electrolytes concentration is the topic of discussion in the study. Querido [Querido D. Double logarithmic, linear relationship between plasma sodium/potassium concentration ratio and postmortem interval during the 6-96h postmortem period in rats. Forensic Sci Int 1990;44:125-34; Querido D. Linearization of the relationship between postmortem plasma chloride concentration and postmortem interval in rats. Forensic Sci Int 1990;45:117-27] and Singh et al. [Singh D, Prashad R, Parkash C, Bansal YS, Sharma SK, Pandey AN. Linearization of relationship between serum sodium, potassium concentration, their ratio and time since deaths in Chandigarh zone of north west India. Forensic Sci Int 2002;130:107; Singh D, Prashad R, Parkash C, Sharma SK, Pandey AN. Double logarithmic linear relationship between plasma chloride concentration and time since death in humans in Chandigarh zone of north west India. Legal Med 2003;5:49-54] had demonstrated a highly significant double logarithmic linear relationship between the time since death and the plasma sodium/potassium ratio as well as with plasma chloride concentration in Wistar rats and human, respectively. In view of these facts, the present study was carried out to substantiate this propensity in this transcellular extension of blood plasma. Electrolytes analysis in postmortem pericardial fluid obtained from 311 subjects revealed that correlation of time since deaths with potassium, sodium/potassium ratio and phosphorus was highly significant (p<0.001) during 2.5-58h of deaths. Not withstanding, time since death although modulated by ambient temperature could be predicted by log transformed multiple regression equation derived from the combination of potassium, chloride and phosphorus electrolytes concentration with standard error (SE) of prediction (in log hours) of 0.1840h and by double logarithmic model with SE (in log hours) of 0.1959, 0.2068 and 0.2088h from potassium, sodium/potassium ratio and phosphorus electrolytes, respectively.

Electrolytes↗
PubMed1981

Linear regression to approximate longitudinal growth curves: revised standards for velocity of weight and length in infants.

Because of lack of acceptability of the previous log-linear model of slope velocity for the assessment of weight and length in children 1 to 36 months of age, a modified method for least squares determination of velocity of growth by slope has been designed. This model uses a compound logarithmic expression of time and a newly designed graphic scale. The acceptability of the graphic (hand-drawn) line is retained while "goodness of fit" of the model is improved. This improved model makes it possible to revise our standards for velocity of growth of children 1 to 36 months of age.

Anthropometry↗
PubMed2000

Non-linear regression analysis with errors in both variables: estimation of co-operative binding parameters.

Four different parameter estimation criteria, the geometric mean functional relationship (GMFR), the maximum likelihood (ML), the perpendicular least-squares (PLS) and the non-linear weighted least squares (WLS), were used to fit a model to the observed data when both regression variables were subject to error. Performances of these criteria were evaluated by fitting the co-operative drug-protein binding Hill model on simulated data containing errors in both variables. Six types of data were simulated with known variances. Comparison of the criteria was done by evaluating the bias, the relative standard deviation (S.D.) and the root-mean-squared error (RMSE), between estimated and true parameter values. Results show that (1) for data with correlated errors, all criteria perform poorly; in particular, the GMFR and ML criteria. For data with uncorrelated errors, all criteria perform equally well with regard to the RMSE. (2) Use of GMFR and ML lead to lower values for S.D. but higher biases compared with WLS and PLS. (3) WLS performs less well when equal dispersion is applied to the two observed variables.

Binding Sites↗
PubMed2004

Limitations of bi-linear regression analysis for the determination of receptor occupancy with positron emission tomography.

BACKGROUND AND OBJECTIVES: Linear/multilinear regression methods are widely used in quantitative neuroreceptor positron emission tomography. A reference tissue method based on a bi-linear operational equation, the bi-linear reference tissue method, has been introduced in order to overcome the need for arterial blood sampling. The aim of the present paper was to investigate the sensitivity of the bi-linear reference tissue method to statistical noise, with special regard to the assessment of receptor occupancy. In addition, improvement of the bi-linear reference tissue method by regularization using physiological constraints was evaluated. METHODS: Application of the bi-linear method to dynamic positron emission tomography using the serotonin transporter ligand C-(+)McN5652 was considered. Investigations were performed by computer simulations and analysis of 29 patient studies. RESULTS: The equilibrium specific-to-non-specific partition coefficient V"3 was significantly underestimated by the bi-linear reference tissue method. At realistic noise levels the extent of the underestimation ranged from 25% to 75% for partition coefficients ranging from 0.3 to 0.3, respectively. This caused a 15-60% underestimation of changes in receptor occupancy after simulated intervention. The noise dependence of the bias was confirmed in the patient studies. Regularization significantly reduced the underestimation of the occupancy. CONCLUSIONS: When receptor status or noise level vary substantially, as in receptor occupancy studies, the bias of the bi-linear reference tissue method should be taken into account.

Adult↗