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PubMed2005

Variation in precaecal amino acid and energy digestibility between pea (Pisum sativum) cultivars determined using a linear regression approach.

An experiment was conducted to study the variation in the precaecal amino acid (AA) and energy digestibility of 4 cultivars of white-flowering peas (Pisum sativum) for broiler chickens. The 4 cultivars were grown and harvested under the same agronomic and environmental conditions. One basal diet and 8 diets including each pea cultivar at inclusion rates of either 150 or 300 g/kg were used. Peas were included at the expense of starch. Hence, the differences in dietary crude protein and AA concentrations resulted only from the inclusion of peas. Titanium dioxide was included as an indigestible marker. Crude protein concentrations in the complete diets ranged from 164 to 244 g/kg. All diets were fed ad libitum to broiler chickens between 14 and 21 d of age. Seven pens of 12 chickens were allocated to each treatment. Digesta were sampled on a pen basis from the section of the gastrointestinal tract between Meckel's diverticulum and 2 cm anterior to the ileo-caeco-colonic junction. The proportions of crude protein and AAs digested responded linearly to increased intake and the relationships between quantitative intake and digested amounts of AAs were described by multiple linear regressions. The slope determined for each pea cultivar was taken as a measure of AA digestibility without the need for consideration of basal endogenous crude protein and AA secretions. Digestibility of AAs in peas ranged from 0.60 to 0.91. One cultivar had significantly lower AA digestibilities than the other three cultivars. This could be explained neither by the trypsin inhibitor activity nor by tannin levels. The AAs with the highest digestibilities in all cultivars were arginine > glutamic acid > lysine > methionine > phenylalanine > leucine. The AAs with the consistently lowest digestibilities were cystine < threonine. The ranking of the remaining AAs varied slightly between cultivars. The multiple linear regression approach is suitable to study differences in AA digestibilities without the need for consideration of basal endogenous AA losses. Diets containing 300 g/kg of peas had significantly lower energy digestibilities than the pea-free basal diet. The pea cultivar with the lowest AA digestibility caused the lowest energy digestibility at both levels of pea inclusion.

Amino Acids↗

PubMed2001

[Determination of naoning pian by multi-wavelength linear regression method].

Assay of naoning pian was reported by multi-wavelength linear regression method in this paper. The program was edited by BASIC. The recoveries and RSD of pyramidon and caffeine were 98.03%-100.9%, 1.0% and 97.77%-99.39%, 0.61%, respectively. This method could be used for the determination of two components in naoning pian without separation. The method was simple, rapid, and results were satisfactory.

Analgesics, Non-Narcotic↗

PubMed1988

Families of lines: random effects in linear regression analysis.

Laboratory experiments often involve two groups of subjects, with a linear phenomenon observed in each subject. Simple linear regression as propounded in standard textbooks is inadequate to treat this experimental design, particularly when it comes to dealing with random variation of slopes and intercepts among subjects. The author describes several techniques that can be used to compare two independent families of lines and illustrates their use with laboratory data. The methods are described tutorially, compared, and discussed in the context of more sophisticated and more naive approaches to this common data-analytic problem. Technical details are supplied in APPENDIX A.

Adolescent↗

PubMedDate not supplied

[Determination of the affinity of high- and low-affinity antibodies, which are in a mixture, using ELISA and the method of non-linear regression].

It was shown that application of the method of non-linear regression for the solution of the equation, which relates the fraction of free antibodies in a mixture and antigen concentrations, allows to determine the affinity constants for two antibodies in a mixture. Such method is easier and more accurate than the suggested by us earlier method, which use the numerical solution of the appropriate four equations, that describe the relations between the experimental data obtained by ELISA, competing antigen concentration, and values of antibody affinity. In addition, the proposed method allows using much less quantity of experimental measurements without diminishing of the accuracy for the affinity constants evaluations.

Antibodies, Monoclonal↗

PubMed1980

Estimation of the reliability of parameters obtained by non-linear regression.

Four methods for estimating the reliability of parameters obtained by non-linear regression are compared. Matrix inversion demands the lest computational effort, but can be unreliable for overdetermined models. The 'jack-knife' technique was found to give results of the right magnitude, but some unexplained discrepancies suggest that this method should be used with caution. A Monte Carlo method and the method of support planes were found to be in good agreement with matrix inversion, but both involve a substantial computational investment. The method of support planes is preferred as it gives information on the degree of non-linearity of the equation which is fitted to the data.

Computers↗

PubMed1993

Further results on the non-parametric linear regression model in survival analysis.

This paper gives further developments of a non-parametric linear regression model in survival analysis. Three subjects are studied. First, martingale residuals, originally developed for the Cox model, are introduced for our linear model. Their theory is developed and they are shown to be useful for judging goodness of fit. The second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation. In particular, this is applied to judging whether the effect of a covariate disappears over time, a problem for which no formal test exists. The third subject is density type, or kernel, estimation of the regression functions themselves. This might give more direct information than the cumulative plots. The approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx, and by survival times of grafts in renal patients.

Computer Simulation↗

PubMed1992

Prediction in censored survival data: a comparison of the proportional hazards and linear regression models.

Although the analysis of censored survival data using the proportional hazards and linear regression models is common, there has been little work examining the ability of these estimators to predict time to failure. This is unfortunate, since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a Kaplan-Meier plot obtained by discretizing the variable. In this paper the predictive power of the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-202) proportional hazards estimator and the Buckley-James (1979, Biometrika 66, 429-436) censored regression estimator are compared. Using computer simulations and heuristic arguments, it is shown that the choice of method depends on the censoring proportion, strength of the regression, the form of the censoring distribution, and the form of the failure distribution. Several examples are provided to illustrate the usefulness of the methods.

Biometry↗

PubMedDate not supplied

Longitudinal principal components and non-linear regression models of early childhood growth.

The Jenss curve is a non-linear regression model which describes quite well the longitudinal length or weight measurements of an individual child from three months to six years. It is contrasted with modelling growth by longitudinal principal components analysis, an approach developed by Kent which is not restricted to any particular curve type or age range, and which can be thought of as providing the best fit among linear models having kappa parameters. Thus, in addition to being a model itself, it can be used to evaluate the success of other models. It is shown how this method differs from classical principal components. Data from Longitudinal Studies of Child Health and Development are used to explore these issues.

Child↗

PubMed2006

A novel simple QSAR model for the prediction of anti-HIV activity using multiple linear regression analysis.

A quantitative-structure activity relationship was obtained by applying Multiple Linear Regression Analysis to a series of 80 1-[2-hydroxyethoxy-methyl]-6-(phenylthio) thymine (HEPT) derivatives with significant anti-HIV activity. For the selection of the best among 37 different descriptors, the Elimination Selection Stepwise Regression Method (ES-SWR) was utilized. The resulting QSAR model (R (2) (CV) = 0.8160; S (PRESS) = 0.5680) proved to be very accurate both in training and predictive stages.

Anti-HIV Agents↗

PubMed1997

Estimation of excess risk from case-control data using Aalen's linear regression model.

We introduce methods for statistical inference in Aalen's non-parametric linear regression model of disease incidence (Aalen, 1989, Statistics in Medicine 8, 907-925) from nested case-control data. These methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history. The methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case-control samples from the Colorado Plateau uranium miners cohort.

Adult↗

PubMed2001

Using step-wise linear regression to detect "functional" sequence variants: application to simulated data.

Step-wise linear regression was used to detect the "functional" sequence variant in gene 6 responsible for phenotypic variation in traits Q1 and Q2. Prior to analysis, single-nucleotide polymorphisms (SNPs) that were in complete or near complete linkage disequilibrium were binned. In total, we identified 11 separate alleles (or allelic bins). Analyses were performed on all 50 replicates. The "functional" allele variant in gene 6 (at position 5782) accounted for 24% of the variation in Q1 and 11% of the variation in Q2. We detected a significant association between this SNP and Q1 in 90% of the replicates (i.e., in 45 of 50 replicates) and between this SNP and Q2 in 78% of the replicates. Although significant associations were also observed with some nonfunctional SNPs, our results nevertheless suggest that simple step-wise regression may play a useful role in analyzing sequence data. Some additional extensions to this approach are suggested.

Adult↗

PubMed1977

The analysis of progress curves for enzyme-catalysed reactions by non-linear regression.

A procedure, based on the Gauss-Newton method for non-linear regression, has been developed to obtain enzyme kinetic constants from the analysis of progress curve data. Rules are presented which greatly simplify the derivation of the necessary equations. The method has been applied to the reactions catalysed by prephenate dehydratase, acid phosphatase and lactate dehydrogenase and has yielded values for kinetic parameters which agree well with those obtained from steady-state rate measurements.

Acid Phosphatase↗

PubMed1985

An interactive computer program for the determination of the binding constants of monoclonal antibodies by non-linear regression analysis of radioimmunoassay data.

A computer program is presented for non-linear regression analysis of radioimmunoassay data, which allows the determination of the binding parameters of monoclonal antibodies, i.e., affinity constant and number of available binding sites. The program is based on the median method and gives the values of the binding constants and their 95% confidence limits, without the necessity for their preliminary, approximate evaluation. The program may also be used to determine the binding constants for the interaction of receptors with labelled ligands.

Antibodies, Monoclonal↗

PubMed2000

Linear regression analysis of censored medical costs.

This paper deals with the problem of linear regression for medical cost data when some study subjects are not followed for the full duration of interest so that their total costs are unknown. Standard survival analysis techniques are ill-suited to this type of censoring. The familiar normal equations for the least-squares estimation are modified in several ways to properly account for the incompleteness of the data. The resulting estimators are shown to be consistent and asymptotically normal with easily estimated variance-covariance matrices. The proposed methodology can be used when the cost database contains only the total costs for those with complete follow-up. More efficient estimators are available when the cost data are recorded in multiple time intervals. A study on the medical cost for ovarian cancer is presented.

Journal Article↗

PubMed1988

A general regression procedure for method transformation. Application of linear regression procedures for method comparison studies in clinical chemistry, Part III.

The biometrical treatment of laboratory data may require the estimation of a regression line for the transformation of one set of measurements to another. The regression procedure introduced in part I (1) of our work does not always yield unbiased results in such situations, since its estimators are not scale invariant. In part III we present the parameter estimation of a general regression equation which is scale invariant and retains all properties of the method comparison procedure, in particular its robustness. Its application is demonstrated by several examples, and the results are compared with other robust biometrical procedures. The mathematical aspects are explained in the appendix.

Biometry↗

PubMed2006

Some statistical issues related to multiple linear regression modeling of beach bacteria concentrations.

As a fast and effective technique, the multiple linear regression (MLR) method has been widely used in modeling and prediction of beach bacteria concentrations. Among previous works on this subject, however, several issues were insufficiently or inconsistently addressed. Those issues include the value and use of interaction terms, the serial correlation, the criteria for model selection, and model assessment. The present work shows that serial correlations, as often present in sequentially observed data records, deserve full attention from the modeler. The testing and adjustment for the time-series effect should be implemented in a statistically rigorous framework. The R(2) and Cp-statistic as joint criteria are recommended for the model selection process, while using the t-statistics associated with the full model is erroneous. During model selection, using interaction terms can often help to decrease the bias in reduced models, although the resulting improvement in the numerical performance may be limited. For the assessment of the model predictive capacity, which is different from testing the goodness of fit, a comprehensive set of statistics are advocated to allow for an objective evaluation of different models. Results obtained from the data at Huntington Beach, OH, show that erroneous conclusions could be drawn if only the model R(2) and the count of type I and type II errors are considered. In this sense, several previous works deserve further investigation.

Bathing Beaches↗

PubMed1990

Application of a variance-stabilizing transformation approach to linear regression of calibration lines.

A variance-stabilizing transformation (VST) was applied to the linear regression of calibration standards of different drugs in plasma. This transformation involved the normalization of the dependent variable peak height or peak area ratio (Y), and the independent variable, plasma drug concentration (C). This transformation led to a constant variance in the regression error term across the measured concentration range and allowed the evaluation of the unbiased slope and y intercept with minimum variance. The utility of the VST procedure in comparison with the ordinary least squares (OLS) approach, routinely used in pharmaceutical studies for constructing calibration lines, is described. The principal advantage of the VST approach is allowing a lower minimum level of drug quantification while using a single calibration line over a wide range of drug concentrations. The VST method is especially useful to quantify drug plasma levels in pharmacokinetic evaluation of sustained-release dosage forms, where the precise quantification of low levels of drug is critical. The application of the VST method was explored and evaluated in comparison with the OLS method for pharmacokinetic assays of diltiazem, gallopamil, nitroglycerin, and nicotine.

Calibration↗

PubMedDate not supplied

A free derivative program for non-linear regression analysis of enzyme kinetics to be used on small computers.

A non-linear regression program, written in BASIC, is described. The program uses the Marquardt 's algorithm as modified by Reich et al. (Eur. J. Biochem., 26 (1972) pp. 368-379). The user only supplies the expression to fit, since the program uses numerical differentiation. It is possible to fit models of 1 substrate, 2 substrates, 1 substrate and 1 inhibitor, and 2 substrates and 1 inhibitor. Likewise, several weighting patterns, as well as a simple or robust regression, can be selected.

Computers↗