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PubMedDate not supplied

Evaluation of preservative systems in a sunscreen formula by linear regression method.

A sunscreen formula with eight different preservative systems was evaluated by linear regression, pharmacopeial, and the CTFA (Cosmetic, Toiletry and Fragrance Association) methods. The preparations were tested against Staphylococcus aureus, Burkholderia cepacia, Shewanella putrefaciens, Escherichia coli, and Bacillus sp. The linear regression method proved to be useful in the selection of the most effective preservative system used in cosmetic formulation.

Anti-Infective Agents↗

PubMed1994

Fourier analysis versus multiple linear regression to analyse pressure-flow data during artificial ventilation.

Respiratory resistance (Rrs) and elastance (Ers) are commonly measured in artificially-ventilated patients or animals by multiple linear regression of airway opening pressure (Pao) versus flow (V') and volume (V), according to the first order model: Pao = P0 + Ers.V + Rrs.V', where P0 is the static recoil pressure at end-expiration. An alternative way to obtain Rrs and Ers is to derive them from the Fourier coefficients of Pao and V' at the breathing frequency. A potential advantage of the second approach over the first is that it should be insensitive to a zero offset on V' and to the corresponding volume drift. The two methods were assessed comparatively in six tracheotomized, paralysed and artificially ventilated rabbits with and without adding to V' an offset equal to 5% of the mean unsigned flow. The 5% flow offset did not modify the results of Fourier analysis, but increased Rrs and Ers from linear regression by 15.8 +/- 4.6% and 4.55 +/- 0.64%, respectively. Without additional offset, differences between the two methods averaged 30.2 +/- 14.0% for Rrs and 9.3 +/- 6.2% for Ers. The differences almost completely disappeared (2.47 and 0.61%, respectively) when the flow signal was zero-corrected using the assumption that inspired and expired volumes were the same. After induced bronchoconstriction, however, Ers was still slightly larger by linear regression than by Fourier analysis, which may result from nonlinearities and/or frequency dependence of the parameters. We conclude that the regression method requires zero flow correction and that Fourier analysis is an attractive alternative.

Algorithms↗

PubMed2005

Comparison of methods for calculating serum osmolality: multivariate linear regression analysis.

BACKGROUND: There are several methods for calculating serum osmolality, and their accordance with measured osmolality is the subject of controversy. METHODS: The concentrations of sodium, potassium, glucose, blood urea nitrogen (BUN) and osmolalities of 210 serum samples were measured. Two empirical equations were deduced for the calculation of serum osmolality by regression analysis of the data. To choose the best equation, chemical concentrations were also used to calculate osmolalities according to our formulas and 16 different equations were taken from the literature and compared with the measured osmolalities. Correlation and linear regression analyses were performed using Excel and SPSS software. RESULTS: Multiple linear regression analysis showed that serum concentrations of sodium (beta = 0.778, p< or = 0.000), BUN (beta = 0.315, p < or = 0.000), glucose (beta = 0.0.089, p < or = 0.007) and potassium (beta = 0.109, p < or = 0.008) are strong predictors of serum osmolality. The data were also analyzed by manual linear regression to yield the equations: osmolality = 1.897[Na + ]+glucose+BUN+13.5, and osmolality = 1.90[Na+ + K+]+glucose+BUN+5.0. The osmotic coefficient for sodium and potassium solutes was deduced to be 0.949 from the slope of the curves of measured osmolality vs. [Na+] and [Na+ + K+], respectively. The inclusion of a BUN value in the equation for osmolality increased the correlation coefficient by approximately 450% and decreased the SD of difference by approximately 35% (p < or = 0.002). Inclusion of the osmotic coefficient for sodium solutes caused an underestimation of measured osmolality and positive osmolal gap unless an appropriate coefficient, constant value and/or the potassium value were included in the equation. The agreement was not improved when molal chemical concentrations were used instead of molar values. The formula presented by Dorwart and Chalmers gave inferior results to those obtained with our formulas. CONCLUSIONS: Our data suggest use of the Worthley et al. formula Osm = 2[Na +]+glucose+BUN for rapid mental calculation and the formulas of Bhagat et al. or ours for calculation of serum osmolality by equipment linked to a computer.

Blood Glucose↗

PubMed1994

Characterization and analysis of skin wealing by computerized non-linear regression.

Weal formation in human skin may be induced by histamine, histamine releasers and other inflammatory mediators. Weals occur spontaneously in chronic urticaria, and in response to frictional pressure in dermographic urticaria. We present an improved method for the analysis of wealing in human skin by the use of non-linear regression. The method has the advantage of speed, and by the use of non-linear regression permits the full characterization of the response curves. The time course of histamine-induced wealing is a double exponential function corresponding to the separate components of weal appearance and disappearance. Dermographic wealing corresponds to an increasing exponential function with increasing pressure. The method of computerized non-linear regression is a considerable advance on previous methods for the analysis of urticarial wealing, the effect of vasoactive agents, and their therapeutic action.

Cetirizine↗

PubMed1998

Power and sample size calculations for studies involving linear regression.

This article presents methods for sample size and power calculations for studies involving linear regression. These approaches are applicable to clinical trials designed to detect a regression slope of a given magnitude or to studies that test whether the slopes or intercepts of two independent regression lines differ by a given amount. The investigator may either specify the values of the independent (x) variable(s) of the regression line(s) or determine them observationally when the study is performed. In the latter case, the investigator must estimate the standard deviation(s) of the independent variable(s). This study gives examples using this method for both experimental and observational study designs. Cohen's method of power calculations for multiple linear regression models is also discussed and contrasted with the methods of this study. We have posted a computer program to perform these and other sample size calculations on the Internet (see http://www.mc.vanderbilt.edu/prevmed/psintro+ ++.htm). This program can determine the sample size needed to detect a specified alternative hypothesis with the required power, the power with which a specific alternative hypothesis can be detected with a given sample size, or the specific alternative hypotheses that can be detected with a given power and sample size. Context-specific help messages available on request make the use of this software largely self-explanatory.

Bacterial Vaccines↗

PubMed2000

[Simultaneous determination of iron, cobalt and nickel in oil by multiwavelength linear regression spectrophotometry].

A method for simultaneous determination of iron, cobalt and nickel, using multiwavelength linear regression spectrophotometry, is proposed. Since there were no interferences caused by cobolt and nickel complexes at the peak of iron complex compound formed with 5-Br-PADAP at 750 nm, the content of iron was determined by working-curve method at 750 nm. Cobalt and nickel were simultaneously determined by multiwavelength linear regression method over the range 550-600 nm. The method was applied to the analysis of iron, cobalt and nickel in synthetic mixtures and oil samples with satisfactory results. The recovery was 97.5%-104.3% and the RSD% was 1.4%-3.8%.

English Abstract↗

PubMed2005

Predicting protein secondary structure and solvent accessibility with an improved multiple linear regression method.

We have improved the multiple linear regression (MLR) algorithm for protein secondary structure prediction by combining it with the evolutionary information provided by multiple sequence alignment of PSI-BLAST. On the CB513 dataset, the three states average overall per-residue accuracy, Q(3), reached 76.4%, while segment overlap accuracy, SOV99, reached 73.2%, using a rigorous jackknife procedure and the strictest reduction of eight states DSSP definition to three states. This represents an improvement of approximately 5% on overall per-residue accuracy compared with previous work. The relative solvent accessibility prediction also benefited from this combination of methods. The system achieved 77.7% average jackknifed accuracy for two states prediction based on a 25% relative solvent accessibility mode, with a Mathews' correlation coefficient of 0.548. The improved MLR secondary structure and relative solvent accessibility prediction server is available at http://spg.biosci.tsinghua.edu.cn/.

Algorithms↗

PubMed2002

A comparison of combinatorial partitioning and linear regression for the detection of epistatic effects of the ACE I/D and PAI-1 4G/5G polymorphisms on plasma PAI-1 levels.

The detection and characterization of epistasis or non-additive gene-gene interactions remains a statistical challenge in genetic epidemiology. The recently developed combinatorial partitioning method (CPM) may overcome some of the limitations of linear regression for the exploratory analysis of non-additive epistatic effects. The goal of this study was to compare CPM with linear regression analysis for the exploratory analysis of non-additive interactive effects of the angiotensin converting enzyme (ACE) insertion/deletion (I/D) and plasminogen activator inhibitor 1 (PAI-1) 4G/5G polymorphisms on plasma PAI-1 levels in a sample of 50 unrelated African Americans and 117 unrelated Caucasians. Using linear regression, we documented the additive effects of the ACE and PAI-1 genes on plasma PAI-1 levels in African American females (R(2) = 0.10), African American males (R(2) = 0.16), Caucasian females (R(2) = 0.11), and Caucasian males (R2 = 0.09). Using CPM, we found evidence for non-additive effects of the ACE and PAI-1 genes in both African American females (R(2) = 0.22) and African American males (R(2) = 0.24) but not in Caucasian females (R(2) = 0.10) or Caucasian males (R(2) = 0.11). The results of this exploratory data analysis support previous experimental, clinical, and epidemiological studies that have proposed as a working hypothesis that the ACE gene mediates interaction effects of the fibrinolytic and renin-angiotensin systems on plasma levels of PAI-1.

Black People↗

PubMed2001

How useful is linear regression analysis in detecting the existence of dose-response relationships in large-scale epidemiologic studies when only a fraction of the population is sensitive? The case of methylmercury.

The existence of a dose response in epidemiologic studies is generally determined from the linear regression slope after controlling for covariates. This approach assumes the entire population is equally sensitive to the toxicant and that response is a function only of dose and a random error function. However, sensitive subpopulations have been identified for a variety of toxicants possibly including methylmercury (MeHg). The study of MeHg exposure in the Seychelles Islands has failed to find significant effects (dose-response slope not significantly different from zero) while other studies have found such effects. Using data on the error function in developmental test scores and MeHg exposure distributions from that study, and assuming plausible dose-response relationships for sensitive subpopulations, we conducted Monte-Carlo simulations of the power of linear regression analysis to detect a dose-response relationship from the total sample (n=700), and to compare dose-response slopes in the total and sensitive populations. Linear regression did not reliably detect a dose-response relationship for most scenarios when sensitives were 5% of the total and for some scenarios when sensitives were 10% of the total. We also found that the dose-response slope for the total population underestimated the sensitive dose-response slope in all cases by about an order of magnitude. These findings may have important implications for detection and quantification of dose-response relationships from epidemiologic studies.

Child↗

PubMed1985

Simple linear regression in medical research.

This article discusses the method of fitting a straight line to data by linear regression and focuses on examples from 36 Original Articles published in the Journal in 1978 and 1979. Medical authors generally use linear regression to summarize the data (as in 12 of 36 articles in my survey) or to calculate the correlation between two variables (21 of 36 articles). Investigators need to become better acquainted with residual plots, which give insight into how well the fitted line models the data, and with confidence bounds for regression lines. Statistical computing packages enable investigators to use these techniques easily.

Humans↗

PubMed2006

Scoring and staging systems using cox linear regression modeling and recursive partitioning.

OBJECTIVES: Scoring and staging systems are used to determine the order and class of data according to predictors. Systems used for medical data, such as the Child-Turcotte-Pugh scoring and staging systems for ordering and classifying patients with liver disease, are often derived strictly from physicians' experience and intuition. We construct objective and data-based scoring/staging systems using statistical methods. METHODS: We consider Cox linear regression modeling and recursive partitioning techniques for censored survival data. In particular, to obtain a target number of stages we propose cross-validation and amalgamation algorithms. We also propose an algorithm for constructing scoring and staging systems by integrating local Cox linear regression models into recursive partitioning, so that we can retain the merits of both methods such as superior predictive accuracy, ease of use, and detection of interactions between predictors. The staging system construction algorithms are compared by cross-validation evaluation of real data. RESULTS: The data-based cross-validation comparison shows that Cox linear regression modeling is somewhat better than recursive partitioning when there are only continuous predictors, while recursive partitioning is better when there are significant categorical predictors. The proposed local Cox linear recursive partitioning has better predictive accuracy than Cox linear modeling and simple recursive partitioning. CONCLUSIONS: This study indicates that integrating local linear modeling into recursive partitioning can significantly improve prediction accuracy in constructing scoring and staging systems.

Humans↗

PubMed2004

Multiple linear regression analysis of the seasonal changes in the serum concentration of beta-cryptoxanthin.

Beta-cryptoxanthin (beta-CRX) is a carotenoid pigment found in Satsuma mandarin (Citrus unshiu Marc.) fruit, which is heavily produced in Japan. In this study, we evaluated the seasonal changes in the serum beta-CRX level and investigated predictors of serum beta-CRX level by multiple linear regression analysis. Blood tests and self-administered questionnaires were used every other month for one year. The subjects were healthy volunteers, 15 males and 12 females. The serum beta-CRX levels increased dramatically as the intake of Satsuma mandarin increased; the maximum increase was noted in January. Multiple linear regression analysis showed that, in males, the serum beta-CRX level could be predicted by Satsuma mandarin intake, age and the month of blood sampling; however, it was inversely associated with alcohol and smoking habits. Conversely, in females, the serum beta-CRX concentration could be predicted by Satsuma mandarin intake, the month of blood sampling and age; however, it was inversely associated with body mass index. The results of multiple linear regression analysis suggest that the serum beta-CRX levels can be used to evaluate the intake volume of Satsuma mandarin. Furthermore, beta-CRX is a useful biomarker to estimate the beneficial effects of Satsuma mandarin intake in epidemiological studies.

Adult↗

PubMed1997

Pointwise univariate linear regression of perimetric sensitivity against follow-up time in glaucoma.

PURPOSE: The authors compared pointwise univariate linear regression (ULR) of sensitivity against follow-up as an indicator of visual field progression with that of the corresponding ULR of mean deviation (MD) and with the Glaucoma Change Probability (GCP) analysis. The authors determined the influence of the number and sequence of prior examinations on the slope of the pointwise function. METHODS: Univariate linear regression was undertaken at each stimulus location on the arbitrarily assigned left eyes of 38 patients with glaucoma examined with the Humphrey Field Analyzer Programs 30-2 or 24-2 (stimulus size III, Humphrey Instruments Inc, San Leandro, CA). The mean age was 59.0 years (standard deviation [SD] = 12.9), the mean number of fields per patients was 12.0 (SD = 2.8), and the mean duration of follow-up was 6.0 years (SD = 1.6). RESULTS: Four patients showed statistically significant MD slopes. Of the 34 patients exhibiting a nonsignificant MD slope, 15 exhibited clusters of at least two contiguous progressing locations. Less than half of these locations were designated as progressing by GCP. The GCP detected less than one third of the locations considered progressing by ULR for the last six fields in the series: this was attributed to the nonlinear nature of the decline in sensitivity. CONCLUSIONS: The degree of agreement between the outcomes of ULR and GCP was dependent on the quality of the collected data, the magnitude of the baseline sensitivity, the extent and type of the subsequent visual field progression, and the position of the fields within the examination series. Good agreement was illustrated at those locations where the deterioration fell outside the limits of expected variability in stable glaucoma.

Female↗

PubMed1994

Non-linear regression models to estimate the size of DNA fragments.

The least-squares, hyperbolic regression model is frequently used to estimate the size of unknown DNA fragments. This model avoids problems associated with semilog-plot interpolation, is computationally easy to use and provides an excellent fit to many experimental data sets. However, the methods commonly used to solve the hyperbolic regression model perform an inappropriate linearization of the original non-linear model. In this note, we describe advantages offered by standard, non-linear regression techniques, and provide computer code for a common statistical package to do these analyses.

Algorithms↗

PubMed1979

A user's experience with a standard non-linear regression program (BMDP3R).

A study was made to test and compare the behavior of a standard non-linear regression program (BMDP3R) in fitting data from six classical least-squares problems. The use of three program control parameters is discussed and four measures of regression failure are utilized to give a quantitative reference of success. Recommendations are given to aid the user of packaged programs in the parameter estimation of non-linear regression models.

Computers↗

PubMed1994

Alternatives to least squares linear regression analysis for computation of standard curves for quantitation by high performance liquid chromatography: applications to clinical pharmacology.

Standard curves and validation points for high-performance liquid chromatography (HPLC) determination of four drugs (carbamazepine and phenytoin at therapeutic drug monitoring concentrations and deuterium labeled carbamazepine and phenytoin at tracer dose concentrations) were computed using standard least squares linear regressions analysis and six alternative regression techniques (weighted 1/x, 1/y, 1/x2, 1/y2 least squares linear, log/log least squares linear, and robust). The coefficient of determination (R2) and the coefficient of prediction (R2pred) values for standard curves and the computed values for validation points did not differ significantly among the seven methods. The lower limit of quantitation (LLQ) values obtained with all six of the alternative regression methods were significantly (P < .01) lower than the LLQ values obtained with least squares linear regression analysis. The lowest LLQ values were obtained with 1/x2 and 1/y2 weighting and were threefold to tenfold less than the values obtained with unweighted least squares linear regression analysis (P < .001). The authors conclude that alternative regression analysis techniques (especially 1/x2 and 1/y2 weighting) offer significant advantages for clinical pharmacology studies when concentration values being measured by HPLC are near the LLQ of the method determined by unweighted least squares linear regression analysis. In other situations, alternative forms of regression analysis had no significant advantages in our study.

Analysis of Variance↗

PubMed1984

Comparison of several regression procedures for method comparison studies and determination of sample sizes. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part II.

In part I of this series (H. Passing & W. Bablok (1983), J. Clin. Chem. Clin. Biochem. 21, 709-720) we described a new biometrical procedure for the evaluation of method comparison studies. In part II we now discuss its properties and compare them with those of other established procedures by means of a simulation study. We demonstrate that the reliability of the results not only depends on the sample size but also on the sampling distribution, the precision of the methods, and the concentration range covered by the samples. Linear regression and principal component procedures are either inadequate or not as reliable as our new procedure. The appropriate sample size is discussed and recommendations are given.

Chemistry, Clinical↗

PubMed1997

[Experimental study of response latency of visual search processes and premotor decision latency in dyslexic and non-dyslexic children. Model of linear regression: derived parametric estimates].

BACKGROUND: For some time the question of a visual impairment in dyslexic children has been a source of controversy in the literature. Depending on the method used, the findings point either to receptor or neural impairment or to a visual deficit in information processing. The question remains of whether these findings mask retardation in the motor planning and execution of a response. METHOD: In this investigation 61 children (15 dyslexic boys and 15 dyslexic girls aged 8 years 0 months to 10 years 8 months and 16 non-dyslexic boys and 15 non-dyslexic girls aged 8 years 0 months to 10 years 10 months) were tested using a computer-assisted visual display method (visual scan procedure). The results were included into a linear regression model. RESULTS: Compared to the non-dyslexic children the dyslexic children had a significant retardation in the speed of motor response (MANCOVA, Mann-Whitney U-test). For the "pure" visual process no differences in time course were found. Another important findings is the surprisingly wide range of results obtained for individual dyslexic children. In some instances there were deviations as great as 3.6 sigma (SEM). These findings indicate that we may be dealing with an individual partial impairment. It should be noted that the calculation of the linear regression model cannot be detailed for the group of dyslexic children. The prerequisites for a linear regression model are not satisfied. The comparability of the results is therefore limited. CONCLUSIONS: We cannot assume there will be a manifest visuomotor impairment in all dyslexic children when the stimulus is presented at the center and periphery of the field of vision. However, if such an impairment is present it is highly likely that the findings contain a mixture of retardation of pre-motor and visual decision latency. This would have substantial consequences for therapy, as visuomotor perception training would not be indicated in all instances. Some dyslexic children, both boys and girls, achieve completely "normal" results.

Attention↗