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PubMed1996

[Prevalence of porphyria cutanea tarda in Madrid and relationship between urine porphyrin and ethanol intake in a multiple linear regression model].

BACKGROUND: The application of a simple fluorometric analytical method enabled us to quantify the urinary porphyrin excretion and to establish the prevalence of porphyria cutanea tarda (PCT) in the town of Madrid, Spain, in a cross-sectional study. PATIENTS AND METHODS: The study assessed 1,613 subjects from three districts in Madrid, in whom further variables potentially related to porphyrinuria such as ethanol intake or -in women-oral contraceptive use were measured and recorded. RESULTS: The estimated prevalence of the disease was 1.24 cases per 1,000 inhabitants (95% confidence interval 0.15-4.47 per thousand). After excluding from the study sample all cases with existent disease, an analysis was performed to ascertain an unilateral tolerance interval for urinary porphyrin concentration in the adult population; this level was established at 181.2 micrograms/l. The effect of ethanol intake on porphyrinuria was considered significant using a multiple linear regression model adjusted for the control variables gender, age and body mass index. In fertile women, contraceptive use did not attain statistical significance when that variable was included in a multiple regression model. CONCLUSIONS: A high prevalence has been estimated for PCT in the Madrid population. A significant association was further found between alcohol intake and porphyrinuria in non-porphyric adults.

Adolescent↗
PubMed2004

Estimating the input function non-invasively for FDG-PET quantification with multiple linear regression analysis: simulation and verification with in vivo data.

A novel statistical method, namely Regression-Estimated Input Function (REIF), is proposed in this study for the purpose of non-invasive estimation of the input function for fluorine-18 2-fluoro-2-deoxy- d-glucose positron emission tomography (FDG-PET) quantitative analysis. We collected 44 patients who had undergone a blood sampling procedure during their FDG-PET scans. First, we generated tissue time-activity curves of the grey matter and the whole brain with a segmentation technique for every subject. Summations of different intervals of these two curves were used as a feature vector, which also included the net injection dose. Multiple linear regression analysis was then applied to find the correlation between the input function and the feature vector. After a simulation study with in vivo data, the data of 29 patients were applied to calculate the regression coefficients, which were then used to estimate the input functions of the other 15 subjects. Comparing the estimated input functions with the corresponding real input functions, the averaged error percentages of the area under the curve and the cerebral metabolic rate of glucose (CMRGlc) were 12.13+/-8.85 and 16.60+/-9.61, respectively. Regression analysis of the CMRGlc values derived from the real and estimated input functions revealed a high correlation (r=0.91). No significant difference was found between the real CMRGlc and that derived from our regression-estimated input function (Student's t test, P>0.05). The proposed REIF method demonstrated good abilities for input function and CMRGlc estimation, and represents a reliable replacement for the blood sampling procedures in FDG-PET quantification.

Algorithms↗
PubMed1996

QT interval-heart rate relation during exercise in normal men and women: definition by linear regression analysis.

OBJECTIVES: This study sought to develop a regression-based method for characterization of QT interval behavior during exercise and to define the normal range of the resulting "dynamic" measures of repolarization during submaximal treadmill testing in men and women. BACKGROUND: The Bazett-corrected QT (QTc) interval during exercise has been used as a marker for ischemic disease, arrhythmogenic substrate and the long QT syndrome. However, recent studies indicate that the QTc interval is nonlinear with respect to heart rate during exercise, making the end-exercise QTc interval dependent on peak work load achieved. In contrast, the unadjusted QT interval measured from QRS onset to T wave offset (QTo) and from QRS onset to T wave peak (QTm) appears to vary linearly with heart rate during gently graded effort. METHODS: The QT interval relation to heart rate and cycle length was examined by linear regression in 50 normal men (mean age 48 years) and 30 normal women (mean age 51 years), all of whom had normal rest electrocardiograms. The QTo and QTm measurements were made from digitized lead V5 complexes averaged by computer over 20-s periods, at upright control and after seven 2-min stages of the Cornell modification of the Bruce treadmill protocol (work load equivalent to Bruce stage 3). RESULTS: For each subject, regression of QTo (ms) versus heart rate (beats/min) resulted in a slope (reflecting the "dynamic" change in QTo during effort), an adjusted intercept (reflecting QTo extrapolated to a heart rate of 60 beats/min) and a significant correlation coefficient (r) value. Under these conditions, mean +/- SD (5th to 95th percentile) values for men were -1.45 +/- 0.34 ms/beat per min (-0.90, "less dynamic" to -1.96, "more dynamic") for the slope; 403 +/- 21 ms (365 to 431) for the adjusted intercept; and -0.93 +/- 0.06 (-0.81 to -0.99) for r. Values for women were more dynamic, with a mean slope of -1.74 +/- 0.32 ms/beat per min (-1.23 to -2.18, p < 0.0005 vs. men) and higher adjusted intercept of 426 +/- 23 ms (392 to 462, p < 0.0001 vs. men) at similar strength of correlation (r = -0.95 +/- 0.06). Corresponding normal data were also tabulated for QTm behavior and QT-RR interval behavior during exercise. CONCLUSIONS: These data provide a "dynamic" definition of normal and abnormal repolarization and describe normal limits for the linear relations of the QTo and QTm intervals with respect to heart rate and cycle length during submaximal exercise in normal men and women.

Electrocardiography↗
PubMed1999

[Linear regression analysis of values of the calciuria index, N-telopetide and bone mineral density in patients with osteoporosis].

UNLABELLED: The authors examined 49 patients (n=49) with primary and secndary osteoporosis incl. 37 women aged 41-58 years and 12 men aged 38-56 years. In all they assessed the 24-hour calciuria index (Ca/creatinine), the aminoterminal N-telopetide of collagen I of the organic matrix (NTx24) and the bone mineral density (BMD) in the first three lumbar vertebrae using quantitative computed tomography (QC). OBJECTIVE: To find an answer to the questions:1. Is the calciuria index in the 24-hour diuresis a parameter which provides information on osteresorption? 2. Is there a significant negative correlation between values NTx24 and BMD? 3. Is NTx a sensitive parameter of osteoresorption in men and women with primary or secondary osteoporosis? STATISTICAL ANALYSIS: Linear regression analysis. RESULTS: Correlation coefficients for the correlated groups NTx24 - Ca/creatinine (r = 0.023, p>0.05) and NTx24 - BMD (r = -0.238, p>0.05) were not statistically significant. Statistical significance was recorded in the correlation coefficient for pathologically elevated values of NTx24(zNTx24), correlated with BMD (r = -0.3115, p<0.048). CONCLUSION: 1. The calciuria index in the 24-hour diuresis does not provide information on osteoresorption. 2. Between pathologically elevated values of NTx24 and BMD in L1-L3 is a statistically significant negative correlation. 3. NTx is a sensitive parameter of osteresorptioon in men and women with primary and secondary osteoporosis, it reflects the influence of the bone turnover on the density of the bone mineral.

Adult↗
PubMed2005

Reflections on the use of robust and least-squares non-linear regression to model challenge tests conducted in/on food products.

In this research, we question the straight-forward use of the classical sum of squared error criterion for identifying the typical parameters of a primary model (like growth rate mumax and lag time lambda) when applied to growth curves obtained in and on food products. Firstly, we base our reflections on 62 Listeria monocytogenes laboratory challenge tests collected in various environments (broth, crushed cold-smoked salmon, and surface of cold-smoked salmon slices). Whereas growth data in broth resulted in residual values consistent with a Gaussian distribution, growth data in the crushed product and even more on the surface of slices appeared different. Secondly, we propose the use of an alternative so-called robust non-linear regression method suitable when experimental error is non-normally distributed, which seems, according to this research, typical for microbial challenge tests in/on food products, and which lead to apparent outliers or leverage points in the experimental data. Properties of the robust regression procedure are illustrated on simulated data first, whereafter its use on the considered challenge tests is illustrated. To conclude, reflections on the assumptions and related realism underlying challenge tests and recommendations for fitting growth curves obtained in and on food products are presented.

Animals↗
PubMed2003

Accuracy of contrast-enhanced MR angiography in predicting angiographic stenosis of the internal carotid artery: linear regression analysis.

BACKGROUND AND PURPOSE: We sought to assess whether contrast-enhanced MR angiography is able to predict the degree of angiographic stenosis of the internal carotid artery within a clinically acceptable margin of error, thereby decreasing the need for angiography. In addition, we sought to assess whether adding ultrasound peak systolic velocity (PSV) as an additional regressor improves the accuracy of prediction. METHODS: A retrospective review of our institution's records for a 4-year period was conducted to identify all patients who had undergone evaluation of their carotid arteries using digital subtraction angiography, contrast-enhanced MR angiography, and ultrasonography. All internal carotid artery stenoses ranging from 10% to 90% at carotid angiography were selected (n = 22). Measurements were then obtained based on the North American Symptomatic Carotid Endarterectomy Trial style by using the digital subtraction angiograms and contrast-enhanced MR angiograms in a blinded fashion. The correlation between digital subtraction angiography data and contrast-enhanced MR angiography data was assessed by conducting linear regression analysis. Multiple regression analysis was then conducted to determine whether the inclusion of ultrasound PSV as an additional regressor increased the accuracy of prediction. RESULTS: The correlation between the degree of stenosis measured by digital subtraction angiography and that measured by contrast-enhanced MR angiography was r = 0.967. The 95% confidence interval for the line of means showed low errors bounds, ranging as low as +/-2.8%. The 95% confidence interval for individual prediction of angiographic stenosis based on a given contrast-enhanced MR angiographic measurement, however, was significantly larger, being no less than +/-13.6%. With the inclusion of PSV, the adjusted correlation was r = 0.965. CONCLUSION: A clear linear relationship exists between digital subtraction angiographic and contrast-enhanced MR angiographic measurements of carotid stenosis. Increasing severity of stenosis as measured by contrast-enhanced MR angiography corresponds to increasing severity at angiography. Although the predictive value of contrast-enhanced MR angiography is excellent in the mean, it is less reliable for predicting the degree of angiographic stenosis in the individual patient, showing rather wide confidence intervals. Furthermore, the inclusion of PSV as an additional regressor does not improve the predictive accuracy beyond that of contrast-enhanced MR angiography alone.

Angiography, Digital Subtraction↗
PubMed1986

Relative contribution of various expressions of cAMP excretion to other indices of parathyroid function, as tested by discriminant multivariate linear regression analysis.

We evaluated the relative contribution to the diagnosis of hyperparathyroid disease from current laboratory indices of parathyroid function--plasma calcium (I), phosphate (II), carboxy-terminal (III) and predominantly amino-terminal (IV) radioimmunoassays of parathyrin, the urinary excretion ratios of cyclic adenosine monophosphate (cAMP) to creatinine (V) or to glomerular filtrate (VI), and the ratio of the nephrogenous fraction of cAMP to glomerular filtrate (VII)--in 224 subjects: 40 with surgically proven hyperparathyroid disease, the others normoparathyroid. The decreasing order of sensitivity was I greater than VI greater than VII greater than V greater than III greater than IV greater than II; all these indices differed significantly between normoparathyroid and hyperparathyroid patients. The decreasing order of specificity was VII, III greater than I greater than IV greater than V, II greater than VI. Discriminant multivariate linear regression analysis was performed in a subset of 58 subjects (17 hyper- and 41 normoparathyroid) from the population studied here, chosen because all of the laboratory indices were determined for each subject. The classification accuracy was 98.3% for combining I, VII, and III (r = 0.908), or I and V (r = 0.893), or I and VII (r = 0.889). The other variables did not add to the precision of classification.

Adult↗
PubMed2004

Microemulsion electrokinetic chromatography of drugs varying in charge and hydrophobicity: I. Impact of parameters on separation performance evaluated by multiple linear regression models.

The separation of anionic, cationic and neutral drugs in microemulsion electrokinetic chromatography (MEEKC) was studied with a statistical experimental design. The concentration of sodium dodecyl sulfate (SDS, surfactant), 1-butanol (co-surfactant) and borate buffer and the factors Brij 35 (surfactant), 2-propanol (organic solvent) and cassette temperature were varied simultaneously, while the parameters pH (9.2), the concentration of octane (oil, 0.8% w/w), the voltage (10 kV) and the dimension of the fused-silica capillary, were kept constant. Eight different model substances were chosen with different hydrophobicities. Two of the analytes were positively charged, two were negatively charged, and the remaining four were neutral or close to neutral at the pH explored. The importance of each parameter on the separation window, the plate height and the retention factor for each of the analytes was studied by means of multiple linear regression (MLR) models. A new response was evaluated for anions, the quotient between the effective mobility in the microemulsion and the effective mobility in the corresponding buffer. Factors affecting selectivity changes were also explored, and it was found that SDS and 2-propanol had the largest effect on selectivity.

2-Propanol↗
PubMed2003

Evaluating dissolution profiles of an anti-HIV agent using ANOVA and non-linear regression models in JMP software.

A powerful statistical method was designed using JMP software to detect factors contributing to differences in the dissolution process of an antiviral drug delivered in an oral dosage form. Due to the large number of dissolution media available for solid dosage forms, a statistical method to choose the appropriate medium is critical for testing solid dosage forms. We have developed an analysis of variance model to analyze the overall dissolution profile obtained from the various media. In vitro tests were performed using a standard USP basket apparatus (Vankel Inc., Cary, NC), and the analysis used the restricted/residual maximum likelihood method (JMP software) to partition the variance due to media (pH 1.2 and 6.8, +SDS, water alone and at pH 1.2 with pepsin), time (repeated measure) and capsule (random effect). This allowed correct standard error estimates to be used to compare dissolution in different media using planned linear contrasts. The model provided us with statistically powerful criteria to identify significant differences in capsule dissolution across time and to quantify capsule-to-capsule population variance estimate. The time specific linear contrasts showed the largest sum of square values (SS) occurred at 180 min (SS=0.268) for the simulated SIF (pH 6.8) versus SGF (pH 1.2) comparison (DF=166, MSE=3.92 x 10(-3)). The dissolution processes were further characterized using a non-linear regression fit of a power law function to the data for each capsule. This resulted in a method to statistically differentiate between the dissolution processes of the capsules in different media.

Analysis of Variance↗
PubMedDate not supplied

Superoxide dismutase, catalase and glutathione peroxidase activities in the liver of young and old mice: linear regression and correlation.

Activities of superoxide dismutase (SOD), catalase (CAT), and glutathione peroxidase (GP) were determined in the liver of 15 young (3-5 months) and 15 old (23-26 months) female CBA mice. Although, the activities of all three enzymes decreased in aging, only the SOD decline was statistically significant (P<0.01). The pair wise correlation analysis exhibited an almost identical positive correlation between SOD and CAT in the liver of both young and old mice (r=0.57), whereas the correlative links between the enzymatic pairs of SOD-GP and CAT-GP were increased in aging. Close to zero in the young group (r=-0.08), the coefficient of correlation between SOD and GP became highly significant in the group of old mice (r=0.66; P<0.01). When the coefficients of pair wise and partial correlation were compared, practically no differences were found for the young mice, whereas all three partial coefficients were decreased in the group of old animals. Estimation of the linear regression between the enzymatic pairs revealed higher coefficients of regression and lower intercepts in the group of old mice. The results imply stronger correlative links between the antioxidant enzymes in the liver of old mice, compared with the same indices in the liver of young animals.

Journal Article↗
PubMed1994

Random-effects linear regression meta-analysis models with application to the nitrogen dioxide health effects studies.

As the field of epidemiology grows and multiple studies of the same topic are more frequently available, increased focus is placed on quantitative methods for synthesis of results to yield an overall conclusion. A major difficulty encountered in practice has been the lack of convenient methodology for addressing groups of studies which are similar, but not exactly alike, in features which may affect study results. The age group from which subjects were selected, the general health of subjects when selected, and the specific health endpoint examined are examples of such features. Some previous investigators have addressed the problem using iterative techniques, although most have opted for simpler models which assume that differences in the studies do not appreciably affect the outcome under investigation. That is, he studies are taken to be homogeneous in that the underlying effect being investigated is the same in each study. This paper presents a random-effects linear regression technique which allows differences in the individual study features. The proposed methodology does not require iterative or other complicated procedures, making it more readily accessible to the applied researcher. We demonstrate this technique on a set of studies of the health effects of indoor NO2 exposure in children. It is seen that odds ratios from these studies vary considerably according to subject age, the study location, and the health endpoint considered. A simple synthesis which does not account for these differences may be misleading.

Air Pollutants, Occupational↗
PubMed2006

Ionic calcium determination in skim milk with molecular probes and front-face fluorescence spectroscopy: simple linear regression.

The purpose of this study was to determine if the ionic calcium content of skim milk could be determined using molecular probes and front-face fluorescence spectroscopy. Current methods for determining ionic calcium are not sensitive, overestimate ionic calcium, or require complex procedures. Molecular probes designed specifically for measuring ionic calcium could potentially be used to determine the ionic calcium content of skim milk. The goal of the current study was to develop foundation methods for future studies to determine ionic calcium directly in skim milk and other dairy products with molecular probes and fluorescence spectroscopy. In this study, the effect of pH on calcium-sensitive fluorescent probe (Rhod-5N and Fluo-5N) performance using various concentrations of skim milk was determined. The pH of diluted skim milk (1.9 to 8.9% skim milk), was adjusted to either 6.2 or 7.0, after which the samples were analyzed with fluorescent probes (1 microM) and front-face fluorescence spectroscopy. The ionic calcium content of each sample was also determined using a calcium ion-selective electrode. The results demonstrated that the ionic calcium content of each sample was highly correlated (R2 > 0.989) with the fluorescence intensities of the probe-calcium adduct using simple linear regression. Higher than suggested ionic calcium contents of 1,207 and 1,973 microM were determined with the probes (Fluo-5N and Rhod-5N) in diluted skim milk with pH 7.0 and 6.2, respectively. The fluorescence intensity of the probe-calcium adduct decreased with a decrease in pH for the same ionic calcium concentration. This study demonstrates that Fluo-5N and Rhod-5N can be used to determine the ionic-calcium content of diluted milk with front-face fluorescence spectroscopy. Furthermore, these probes may also have the potential to determine the ionic calcium content of undiluted skim milk.

Animals↗
PubMed1992

Linear regression analysis based on Buckley-James estimating equation.

In this note we consider the problem of drawing inference about the regression parameters in a linear model with survival data. A simple procedure based on the Buckley-James (1979, Biometrika 66, 429-436) estimating equation is proposed and illustrated with an example.

Heart Transplantation↗
PubMed1990

The role of hippocampal commissures in the interhemispheric transfer of epileptiform afterdischarges in the rat: a study using linear and non-linear regression analysis.

The role of the forebrain commissures and the septal area in the interhemispheric transfer of hippocampal afterdischarges (ADs) was investigated in the rat under halothane anesthesia. Electrical seizures were elicited from the dorsal hippocampus before and after commissurotomy. The degree of relatedness between EEG signals recorded from homologous sites of both hippocampi was quantified using two approaches: (i) a time domain analysis considering an AD as a succession of discrete bursts; the onset times of such bursts were measured and used to estimate interhemispheric onset delays; (ii) using signal analysis the linear (r2) and non-linear (h2) regression coefficients between pairs of EEG signals were computed as a function of time shift between the two signals. In this way the values of association (linear and non-linear) and the corresponding time delays were measured. In general a tetanus applied unilaterally to the dorsal CA3 field resulted in bilaterally synchronous ADs. The estimated interhemispheric time delay was in most cases zero. This bilateral synchrony disappeared after section of a specific part of the ventral hippocampal commissure (VHC), the dorso-caudal third, but was not affected by section of other commissural fibers or by a lesion of the septal area. This study also allowed evaluation of different methods of quantification of the association between EEG signals, namely the linear (r2) and the non-linear (h2) regression coefficients. The latter was shown to be a more robust measure than the former and to yield values of association even in cases in which r2 was at noise level. The experimental findings allow the conclusion that ADs elicited from an epileptogenic focus spread to homologous sites in the contralateral hemisphere following commissural systems that may be strong enough to ensure the forming of one bilateral oscillating system.

Animals↗
PubMed1988

Linear regression analysis of ultrasound follicular growth series: evidence for an abnormality of follicular growth in endometriosis patients.

Follicular diameter growth is a highly linear function of time. Recently, the potential utility of linear regression-derived parameters for describing and comparing cycles of follicular growth was described. The linearity of growth, growth rate constant (K), calculated date of growth onset (Do), total growth period (TGP), menstrual age at apparent ovulation (MAov), and peak follicular diameter (PFD) have been calculated from the follicular growth series of a group of patients with laparoscopically diagnosed endometriosis (n = 46). These parameters were compared with those of a group of normal volunteers (n = 18). The authors found significant differences between endometriosis patients and controls in follicular growth rate and total growth period. The effect of patients' clomiphene citrate usage on growth parameters in these patients was examined. Abnormalities in interrelationships between the growth parameters were detected, suggesting the possibility of subtle defects in the regulation of follicular growth in these patients.

Endometriosis↗
PubMed1989

A linear regression model for the analysis of life times.

A linear model is suggested for the influence of covariates on the intensity function. This approach is less vulnerable than the Cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed. A method of non-parametric estimation of regression functions is presented. This results in plots that may give information on the change over time in the influence of covariates. A test method and two goodness of fit plots are also given. The approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx.

Clinical Trials as Topic↗