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Seasonal outbreaks of influenza exert a considerable burden on health services, and are notorious for their variability from year to year. Making use of historical data from the Scottish sentinelle surveillance since 1972, a potential candidate model has been derived based on simple linear regression. It was applied with a measure of success in the 1999-2000 winter season.
BACKGROUND: Humphrey Statpac2 "glaucoma change probability analysis' is a widely available analysis technique to aid the clinician in the diagnosis of glaucomatous visual field deterioration. A comparison of this technique with the more recently described pointwise linear regression analysis (PROGRESSOR) is given. METHODS: Series of visual field data from a group of nine eyes of nine patients with normal-tension glaucoma were selected. Each series had 16 fields with mean follow-up of 5.7 years (SD 0.6 years). Statpac2 "glaucoma change probability analysis' was used to define test locations that had unequivocally deteriorated in the last three fields of each series. The accuracy of both Statpac2 and PROGRESSOR in providing early detection of these deteriorated locations was assessed. RESULTS: The sensitivity and specificity of the two techniques in predicting deteriorated locations were similar when a rate of luminance sensitivity loss of faster than 1 dB/year (2 dB/year for outer locations beyond 15 deg of eccentricity) with a slope significance of P < 0.10 was used as the regression definition of deterioration. The difficulties of comparing two techniques in the early diagnosis of field progression without a true external standard for field loss are illustrated. CONCLUSIONS: PROGRESSOR closely emulates the performance of Statpac2 in detecting sensitivity deterioration at individual test locations. This new technique, which uses all available data in a field series and gives the rate of sensitivity loss at each location, may provide a clinically useful method for detecting field progression in glaucoma.
The forward and reverse rate constants involved in carbamylation, activation, carboxylation, and inhibition of D-ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) have been estimated by a new technique of simultaneous non-linear regression of a differential equation kinetic model to multiple experimental data. Parameters predicted by the model fitted to data from purified spinach enzyme in vitro included binding affinity constants for non-substrate CO2 and Mg2+ of 200+/-80 microM and 700+/-200 microM, respectively, as well as a turnover number (k(cat)) of 3.3+/-0.5 s(-1), a Michaelis half-saturation constant for carboxylation (K(M,C)) of 10+/-4 microM and a Michaelis constant for RuBP binding (K(M,RuBP)) of 1.5+/-0.5 microM. These and other constants agree well with previously measured values where they exist. The model is then used to show that slow inactivation of RuBisCO (fallover) in oxygen-free conditions at low concentrations of CO2 and Mg2+ is due to decarbamylation and binding of RuBP to uncarbamylated enzyme. In spite of RuBP binding more tightly to uncarbamylated enzyme than to the activated form, RuBisCO is activated at high concentrations of CO2 and Mg2+. This apparent paradox is resolved by considering activation kinetics and the fact that while RuBP binds tightly but slowly to uncarbamylated enzyme, it binds fast and loosely to activated enzyme. This modelling technique is presented as a new method for determining multiple kinetic data simultaneously from a limited experimental data set. The method can be used to compare the properties of RuBisCO from different species quickly and easily.
A potentially useful method to monitor respiratory mechanics in artificially ventilated patients consists of analyzing the relationship between tracheal pressure (P), lung volume (V), and gas flow (V) by multiple linear regression (MLR) using a suitable model. Contrary to other methods, it does not require any particular flow waveform and, therefore, may be used with any ventilator. This approach was evaluated in three neonates and seven young children admitted into an intensive care unit for respiratory disorders of various etiologies. P and V were measured and digitized at a sampling rate of 40 Hz for periods of 20-48 s. After correction of P for the non-linear resistance of the endotracheal tube, the data were first analyzed with the usual linear monoalveolar model: P = PO + E.V + R.V where E and R are total respiratory elastance and resistance, and PO is the static recoil pressure at end-expiration. A good fit of the model to the data was seen in five of ten children. PO, E, and R were reproducible within cycles, and consistent with the patient's age and condition; the data obtained with two ventilatory modes were highly correlated. In the five instances in which the simple model did not fit the data well, they were reanalyzed with more sophisticated models allowing for mechanical non-homogeneity or for non-linearity of R or E. While several models substantially improved the fit, physiologically meaningful results were only obtained when R was allowed to change with lung volume. We conclude that the MLR method is adequate to monitor respiratory mechanics, even when the usual model is inadequate.
This study examined records from the Navy Asbestos Medical Surveillance Program for 1984 through 1990 for Caucasian men (N = 129,598) using a population-based, cross-sectional, linear regression model. Continuous dependent variables were forced expiratory volume in 1 s and forced vital capacity (FVC), and continuous independent variables were age, height, weight, and tobacco use. A mid-period estimate of asbestos exposure was used because those values were reported as categorical variables. With asbestos exposure, forced expiratory volume in 1 s changed -3.2 cm3/year (t = -8.6, p = 0.000), and forced vital capacity changed -5.1 cm3/year (t = -11.8, p = 0.00). Those with more than 5 years of asbestos exposure demonstrated impairment over those with less exposure, and those with more than 15 years of exposure demonstrated even more impairment. These findings support the association of pulmonary function impairment with asbestos exposure for workers studied during this period.
This paper describes the influence of different populations on statistical multivariate classification rules and classification results where the word "population" refers only to the frequency of diagnoses to be expected, the so-called prior probabilities. Using linear regression as a multivariate classification technique and six groups consisting of five pathological conditions and normals as test data, it has been shown: (a) That the population influences to a great extent the selection of the best ECG-VCG measurements for the classification rule. (b) That a mismatch of the populations in the learning and test sets can considerably decrease the number of correct classifications. (c) That a certain correction of the mismatch can be achieved when the prior probabilities in the learning and test sets are known, Further, the paper discusses the change of prior probabilities over the years at the Variety Club Heart Hospital in the University of Minnesota and its effect on the performance of the classification algorithm which has been used.
In comparing running median, tolerance, cusum, and regression methods for trend detection over a small number of visits, Yang et al. found that application of multiple Z-tests on the basis of a simple linear regression for each site separately was the most efficient for detection of trends at several sites simultaneously. Because the use of multiple Z-tests completely ignores the covariance among measurements taken from different sites, to improve the power we propose a global chi 2-test. Assuming the covariance matrix known, we have found that the proposed chi 2-test procedure is more powerful than multiple Z-tests for two-sided alternatives when both the correlation among measurements and the number of sites are small. We also have found that the former procedure can have power uniformly larger than the latter when ratios of slopes to standard deviations of measurements at different sites vary and the number of sites is large. In fact, in the latter situation, the proposed global chi 2-test procedure, usually used only for two-sided alternatives, can even have power larger than that of multiple Z-tests for one-sided alternatives. In the situation where the ratios of slopes to standard deviations of measurements are all equal, however, the proposed multivariate approach based on the chi 2-test distribution is the least efficient, especially when the number of sites and the correlation are moderate or large. Finally, to account for the effect of multiple tests over a series of visits on the overall alpha-level, on the basis of Monte Carlo simulations, we compute critical values for sequential use of the proposed multivariate test procedure.
EEG correlates of a range of psycholinguistic word properties were used to investigate the time course of access to psycholinguistic information during visual word recognition. Neurophysiological responses recorded in a visual lexical decision task were submitted to linear regression analysis. First, 10 psycholinguistic features of each of 300 stimulus words were submitted to a principal component analysis, which yielded four orthogonal variables likely to reflect separable processes in visual word recognition: Word length, Letter n-gram frequency, Lexical frequency and Semantic coherence of a word's morphological family. Since the lexical decision task required subjects to distinguish between words and pseudowords, the binary variable Lexicality was also investigated using a factorial design. Word-pseudoword differences in the event-related potential first appeared at 160 ms after word onset. However, regression analysis of EEG data documented a much earlier effect of both Word length and Letter n-gram frequency around 90 ms. Lexical frequency showed its earliest effect slightly later, at 110 ms, and Semantic coherence significantly correlated with neurophysiological measures around 160 ms, simultaneously with the lexicality effect. Source estimates indicated parieto-temporo-occipital generators for the factors Length, Letter n-gram frequency and Word frequency, but widespread activation with foci in left anterior temporal lobe and inferior frontal cortex related to Semantic coherence. At later stages (>200 ms), all variables exhibited simultaneous EEG correlates. These results indicate that information about surface form and meaning of a lexical item is first accessed at different times in different brain systems and then processed simultaneously, thus supporting cascaded interactive processing models.
The dual dosimeter technique for determining both the absorbed dose of neutrons and photons in a mixed field has been applied to multiple dosimeter use. The data were analyzed by a linear regression method which yields the neutron dose from the slope and the photon dose from the intercept and an estimation of the uncertainty of the photon dose can also be obtained. Measurements were made on a high energy neutron beam and the photon dose obtained both as a function of field size and depth in a tissue equivalent phantom.
For the purpose of examining the association between blood lead levels and household-specific soil lead levels, we used a multivariate linear regression model to find a slope factor relating soil lead levels to blood lead levels. We used previously collected data from the Agency for Toxic Substances and Disease Registry's (ATSDR's) multisite lead and cadmium study. The data included the blood lead measurements (0.5 to 40.2 microg/dL) of 1015 children aged 6-71 months, and corresponding household-specific environmental samples. The environmental samples included lead in soil (18.1-9980 mg/kg), house dust (5.2-71,000 mg/kg), interior paint (0-16.5 mg/cm2), and tap water (0.3-103 microg/L). After adjusting for income, education of the parents, presence of a smoker in the household, sex, and dust lead, and using a double log transformation, we found a slope factor of 0.1388 with a 95% confidence interval of 0.09-0.19 for the dose-response relationship between the natural log of the soil lead level and the natural log of the blood lead level. The predicted blood lead level corresponding to a soil lead level of 500 mg/kg was 5.99 microg/kg with a 95% prediction interval of 2. 08-17.29. Predicted values and their corresponding prediction intervals varied by covariate level. The model shows that increased soil lead level is associated with elevated blood leads in children, but that predictions based on this regression model are subject to high levels of uncertainty and variability.
A patient treated for infectious syphilis is cured when serologic tests become non-reactive, which may take years to achieve. Our objective is to develop a method to determine, within months, whether the patient has responded adequately to treatment. Previous research and our exploratory graphical analysis suggested that treatment response is linear when we applied logarithmic transformations of the axes. If the response to treatment is linear, titres recorded within the first few months of treatment will determine the slope of the line and one can develop an action line in future research. We used a non-parametric method to assess whether the logarithmic transformation improved the linearity and then we applied three different methods of testing lack of fit in linear regression. Based upon a sample size that reflects a clinically reasonable number of data points, the results of these tests provided no evidence against linearity.
Regression analysis has been used to characterize the relationship between an exposure dose and the incidence of an adverse health effect such as cancer. However, the regression rarely describes the true relationship due to uncertainties in dose-response data and relationships. Therefore, a method is developed to perform dose-response assessments by a fuzzy linear regression which explicitly exhibit these uncertainties. This method is applied to define the relationship between a particular nitrate dose to humans and its corresponding cancer risk.
PURPOSE: We planned to optimize the effect of formulation variables on the percent drug entrapment (PDE) of the liposomes encapsulating leuprolide acetate by reverse phase evaporation method using Artificial neural network (ANN) and Multiple linear regression (MLR). METHOD: Twenty seven formulations were prepared based on 3x3 factorial design. The volume of aqueous phase (X(1)), HSPC/DSPG [negative charge] (X(2)), and HSPC/Cholesterol (X(3)) were selected as the causal factors. Potential variables such as concentration of lipid: drug and hydration medium were kept constant in experimental design. The PDE (dependent variable) and the transformed values of independent variables were subjected to multiple regression analysis to establish a second order polynomial equation (full model). A set of PDE and causal factors was used as tutorial data for the ANN and fed into a computer. The feed forward back propagation (bp) method was optimized. The ANN model and MLR were validated for accurate prediction of PDE. RESULTS: To simplify the polynomial equation, F-statistic was applied to reduce polynomial equation (reduced model) by neglecting non-significant (P<0.05) terms. The reduced polynomial equation was used to plot three two-dimensional contour plots at fixed levels of -1, 0 and 1 of the variable X(3) to obtain various combination values of the two other independent variables (X(1) and X(2)) at predetermined PDE. The root mean square value of the trained ANN model by feed forward bp method was 0.0000354, which indicated that the optimal model was reached. The optimization methods developed by both ANN and MLR were validated by preparing another six liposomal formulations. The predetermined PDE (from ANN and MLR) and the experimental data were compared with predicted data by paired "t" test, no statistically significant difference was observed. ANN showed less error compared to MLR. CONCLUSIONS: These findings demonstrate that the ANN model provides more accurate prediction and is quite useful in the optimization of pharmaceutical formulations when compared to multiple regression analysis method. The normalized error (NE) value observed with the optimal ANN model was 0.0211 while it was 0.0658 for the full model in the case of second-order polynomial equation composed of the combination of causal factors (X(1), X(2) and X(3)). Thus the derived equation, contour plots and ANN helps in predicting the values of the independent variables for maximum PDE in the preparation of leuprolide acetate liposomes by reverse phase evaporation technique.
An iterative approach was achieved for fitting piecewise linear functions to nonrectilinear responses of biological variables. This algorithm is used to estimate the parameters of the two (or more) regression functions and the separation point(s) (thresholds, sensitivities) by statistical approximation. Although it is often unknown whether the response of a biological variable is adequately described by one rectilinear regression function or by piecewise linear regression function(s) with separation point(s), an F test is proposed to determine whether one regression line is the optimal fitted function. A FORTRAN-77 program has been developed for estimating the optimal parameters and the coordinates of the separation point(s). A few sets of data illustrating this kind of problem in the analysis of thermoregulation, osmoregulation, and the neuronal responses are discussed.
The Scatchard plot is an essential tool for the estimation of binding parameters in biochemistry. In certain situations the fitting of a hyperbolic line is required in this context. It is proposed to solve this non-linear regression problem by robust methods. A method according to Huber and Dutter (1974) is outlined and its good applicability is demonstrated.
Minimal latencies of F waves were determined for the ulnar and sciatic-tibial nerves in 17 dogs of various breeds, weighing between 8 to 25 kg. A linear regression model was fitted to the data (r = 0.78 and 0.87, respectively), so that latencies could be predicted despite the large variation in limb lengths among different breeds of dogs.
The relative solvent accessibility (RSA) of an amino acid residue in a protein structure is a real number that represents the solvent exposed surface area of this residue in relative terms. The problem of predicting the RSA from the primary amino acid sequence can therefore be cast as a regression problem. Nevertheless, RSA prediction has so far typically been cast as a classification problem. Consequently, various machine learning techniques have been used within the classification framework to predict whether a given amino acid exceeds some (arbitrary) RSA threshold and would thus be predicted to be "exposed," as opposed to "buried." We have recently developed novel methods for RSA prediction using nonlinear regression techniques which provide accurate estimates of the real-valued RSA and outperform classification-based approaches with respect to commonly used two-class projections. However, while their performance seems to provide a significant improvement over previously published approaches, these Neural Network (NN) based methods are computationally expensive to train and involve several thousand parameters. In this work, we develop alternative regression models for RSA prediction which are computationally much less expensive, involve orders-of-magnitude fewer parameters, and are still competitive in terms of prediction quality. In particular, we investigate several regression models for RSA prediction using linear L1-support vector regression (SVR) approaches as well as standard linear least squares (LS) regression. Using rigorously derived validation sets of protein structures and extensive cross-validation analysis, we compare the performance of the SVR with that of LS regression and NN-based methods. In particular, we show that the flexibility of the SVR (as encoded by metaparameters such as the error insensitivity and the error penalization terms) can be very beneficial to optimize the prediction accuracy for buried residues. We conclude that the simple and computationally much more efficient linear SVR performs comparably to nonlinear models and thus can be used in order to facilitate further attempts to design more accurate RSA prediction methods, with applications to fold recognition and de novo protein structure prediction methods.
This research is focused on prenatal and early postnatal mercury (Hg) exposure among the riverside people along the Upper Madeira river in the Amazon. Linear regression models were developed to predict the hair Hg concentration in infants. The independent variables included in the model of Group 1 (87 pairs of mothers and their infants) were the average maternal hair Hg concentration and maternal age. Group 2 (31 pairs) included maternal segmental hair Hg concentrations. For the segmental hair Hg analysis over time, it was assumed that hair grows at a rate of 11 cm per month. Thus, information on the timing of the dates of pregnancy and breast feeding from the birth history was used to cut the hair strands into segments, making them correspond to the mother's reproductive stage of life (31 pairs of mothers and their infants). Breast milk Hg concentration results were included with segmental and average maternal hair Hg concentration values (22 and 44 pairs of mothers and their infants, respectively). The models including the breast milk Hg concentration indicated that 61 and 55% of the variability of the infant hair Hg concentrations were due to the independent variables: segmental maternal hair Hg with breast milk Hg and average maternal hair Hg with breast milk Hg, respectively. The regression coefficients were in the range of 0.19 to 0.90, and P values were in the range of 0.0001 to 0.1490. Further recommendations include fish advisories to prevent critical Hg exposures during reproductive life and investigation of neurobehavioral performance of this study population.