Regression of calculated variables in the presence of shared measurement error

To test hypotheses regarding relations between meaningful parameters, it is often necessary to calculate these parameters from other directly measured variables. For example, the relationship between O2 consumption and O2 delivery may be of interest, although these may be computed from measurements of cardiac output and blood O2 contents. If a measured variable is used in the calculation of two derived parameters, error in the measurement will couple the calculated parameters and introduce a bias, which can lead to incorrect conclusions. This paper presents a method of correcting for this bias in the linear regression coefficient and the Pearson correlation coefficient when calculations involve the nonlinear and linear combination of the measured variables. The general solution is obtained when the first two terms of a Taylor series expansion of the function can be used to represent the function, as in the case of multiplication. A significance test for the hypothesis that the regression coefficient is equal to zero is also presented. Physiological examples are provided demonstrating this technique, and the correction methods are also applied in simulations to verify the adequacy of the technique and to test for the magnitude of the coupling effect. In two previous studies of O2 consumption and delivery, the effect of coupled error is shown to be small when the range of O2 deliveries studied is large, and measurement errors are of reasonable size.     

The reliability of linear position transducer and force plate measurement of explosive force-time variables during a loaded jump squat in elite athletes

The best method of assessing muscular force qualities during isoinertial stretch shorten cycle lower body movements remains a subject of much debate. This study had 2 purposes: Firstly, to calculate the interday reliability of peak force (PF) measurement and a variety of force-time measures, and, secondly, to compare the reliability of the 2 most common technologies for measuring force during loaded jump squats, the linear position transducer (PT), and the force plate (FP). Twenty-five male elite level rugby union players performed 3 rebound jump squats with a 40-kg external load on 2 occasions 1 week apart. Vertical ground reaction forces (GRFs) were directly measured via an FP, and force was differentiated from position data collected using a PT. From these data, a number of force-time variables were calculated for both the FP and PT. Intraclass correlation coefficient (ICC), coefficient of variation (CV), and percent change in the mean were used as measures of between-session reliability. Additionally, Pearson's product moment correlation coefficients were used to investigate intercorrelations between variables and technologies. Both FP and PT were found to be a reliable means of measuring PF (ICC = 0.88-0.96, CV = 2.3-4.8%), and the relationship between the 2 technologies was very high and high for days 1 and 2, respectively (r = 0.67-0.88). Force-time variables calculated from FP data tended to have greater relative and absolute consistency (ICC = 0.70-0.96, CV = 5.1-51.8%) than those calculated from differentiated PT data (ICC = 0.18-0.95, CV = 7.7-93.6%). Intercorrelations between variables ranged from trivial to practically perfect (r = 0.00-1.00). It was concluded that PF can be measured reliably with both FP and PT technologies, and these measurements are related. A number of force-time values can also be reliably calculated via the use of GRF data. Although some of these force-time variables can be reliably calculated using position data, variation of measurement is generally greater when using position data to calculate force.     

EEG-activity patterns in visual information processing: characteristics, variance-analytical deliminiation, discriminance-analytical determination of undispensable variables and scale level

1. In order to determine the variable distributions of 5 activation dependent EEG activity patterns occurring during visual information processing, mean values and standard deviations of the percental quantities of the frequencies 4, 5, ..., 13 Hz, 14 to 20 Hz and 21 to 30 Hz, as well as the mean amplitudes in the frequency bands 3.5 ... 7.4 Hz, 7.5 ... 13.4 Hz and 13.5 to 30 Hz were determined on corresponding to 10 s samples. It could be demonstrated by regression analysis that an interval scale level can be assumed already on the basis of cethe percental quantities in the three last mentioned frequency bands. 2. On the basis of 18 relevant variables, all the adjacent activity patterns could be separated from each other by means of univariate variance analysis at pairwise mean value comparison by at least two variables. 3. After stepwise reduction of dispensable variables in the framework of a linear discriminance analysis an optimal set of variables was determined, comprising the percental quantities of the frequencies 4, 5, 6, 10, 12 Hz, and 14 to 20 Hz, as well as the mean value of the amplitudes in the frequency band 3.5 to 7.4 Hz. In 4 our of 5 elementary discriminance functions, the mean values calculated for each pattern were significantly distinguishable from each other (analysis of variance, Newman-Keuls test). 4. By linear regression analysis it could be shown that the classification system of the EEG activity patterns at visual information processing can be mapped on an interval scale after the reduction of variables, too. Finally, data about the reliability of the scoring procedure are presented.     

Covariate-adjusted varying coefficient models

Covariate-adjusted regression was recently proposed for situations where both predictors and response in a regression model are not directly observed, but are observed after being contaminated by unknown functions of a common observable covariate. The method has been appealing because of its flexibility in targeting the regression coefficients under different forms of distortion. We extend this methodology proposed for regression into the framework of varying coefficient models, where the goal is to target the covariate-adjusted relationship between longitudinal variables. The proposed method of covariate-adjusted varying coefficient model (CAVCM) is illustrated with an analysis of a longitudinal data set containing calcium absorbtion and intake measurements on 188 subjects. We estimate the age-dependent relationship between these two variables adjusted for the covariate body surface area. Simulation studies demonstrate the flexibility of CAVCM in handling different forms of distortion in the longitudinal setting.     

Absolute quantification of proteins by LCMSE: a virtue of parallel MS acquisition

Relative quantification methods have dominated the quantitative proteomics field. There is a need, however, to conduct absolute quantification studies to accurately model and understand the complex molecular biology that results in proteome variability among biological samples. A new method of absolute quantification of proteins is described. This method is based on the discovery of an unexpected relationship between MS signal response and protein concentration: the average MS signal response for the three most intense tryptic peptides per mole of protein is constant within a coefficient of variation of less than +/-10%. Given an internal standard, this relationship is used to calculate a universal signal response factor. The universal signal response factor (counts/mol) was shown to be the same for all proteins tested in this study. A controlled set of six exogenous proteins of varying concentrations was studied in the absence and presence of human serum. The absolute quantity of the standard proteins was determined with a relative error of less than +/-15%. The average MS signal responses of the three most intense peptides from each protein were plotted against their calculated protein concentrations, and this plot resulted in a linear relationship with an R(2) value of 0.9939. The analyses were applied to determine the absolute concentration of 11 common serum proteins, and these concentrations were then compared with known values available in the literature. Additionally within an unfractionated Escherichia coli lysate, a subset of identified proteins known to exist as functional complexes was studied. The calculated absolute quantities were used to accurately determine their stoichiometry.     

Kinetics of the processes of desorption from fatty acid monolayers

The surface area, A, of contracting fatty acid monolayers was measured as a function of time, t, at constant surface pressure. In the initial temporal phase, ln A was linear with radical t. In a subsequent steady-state phase, ln A was linear with t. The initial desorption coefficient for sodium palmitate, K(i), and the steady-state desorption coefficient, K(s), varied directly with surface pressure and subphase pH, and these desorption coefficients also varied with the composition of the subphase buffer. However, the K(s)/K(i) ratio was independent of these variables. The diffusion coefficient, D(25), for sodium palmitate calculated from desorption coefficient ratios was 4.8 +/- 0.6 x 10(-6) cm(2)/sec. This value was in reasonable agreement with D(25) for sodium palmitate measured by time-lag diffusion, 3.7 +/- 0.6 x 10(-6) cm(2)/sec. D(25) values obtained for a series of fatty acids suggested that higher members of the series diffused as small aggregates averaging two to four molecules in size. Kinetic and diffusion data both supported a model for the desorption process described by Ter Minassian-Saraga.     

A metric space approach to the information channel capacity of spike trains

A novel method is presented for calculating the information channel capacity of spike trains. This method works by fitting a χ-distribution to the distribution of distances between responses to the same stimulus: the χ-distribution is the length distribution for a vector of Gaussian variables. The dimension of this vector defines an effective dimension for the noise and by rephrasing the problem in terms of distance based quantities, this allows the channel capacity to be calculated. As an example, the capacity is calculated for a data set recorded from auditory neurons in zebra finch.     

Mathematical model for the estimation of hemodynamic and oxygenation variables by tissue spectroscopy

This article presents a quasistatic, compartmental model of tissue-level hemodynamics and oxygenation that leads to a set of formulas, which is suitable to calculate important physiological variables from the mean tissue concentration and saturation of hemoglobin, measured by tissue spectroscopy. Dimensioned quantities are represented relative to their baseline value in the equations (relative value = perturbed/baseline). All model parameters are non-dimensional. The model is based and extends on a number of previous works: previous models of similar aim and scope are consolidated, and every critical assumptions and approximations are treated explicitly; extensions include for example the incorporation of the Fahraeus-effect and the separate estimation of the volume changes of the arterial and the venous compartments. The information content of spectroscopic data alone is shown to be valuable, but limited: the relative venous volume, the oxygen extraction fraction and the relative cellulovascular coupling (defined as the ratio of blood flow and oxygen consumption) can be calculated from these data, if the alterations in arterial blood volume are negligible. The number of variables estimated by the derived formulas can be increased if local blood flow is measured simultaneously: in this case, the relative arterial and venous volume and resistance, the oxygen extraction fraction, and the relative oxygen consumption can be determined. Given that this model considers arterial blood pressure, saturation and hematocrit as its inputs, when measured, the model becomes applicable in such conditions as hyper- or hypotension, hypoxic hypoxia, hemodilution and hemorrhage, where these variables do change. The estimation of the changes in arterial resistance can be applied to estimate the extent of an autoregulatory response.     

A stochastic dynamical model for the characterization of the geometrical structure of dendritic processes

Under certain basic assumptions the branching pattern of dendrites can be modeled as a Galton-Watson process in varying environment. Using results from graph theory we compute the probability distributions, expectations and variances for biologically significant variables such as the number of (intermediate and terminal) branches, the maximum number of orders, etc., together with the limit behavior of these quantities. Furthermore, the probability measure induced by the Galton-Watson process on the set of all trees is calculated. The measure assigns to any set of branching patterns the probability that it is realized by a certain process, which is completely described through the bifurcation probabilities.     

Use of the correlation of liability in twins and siblings in the study of birth defects

The epidemiologic approach to determining the etiology of disease involves identification of potential risk factors and then comparison of disease incidence among people with varying levels of exposure to the potential risk factors. This paper defines risk factors which correspond to different levels of genetic and environmental proximity to index cases of birth defects. Genetic proximity is estimated by the coefficient of relationship (R): 0.5 for siblings and dizygotic twins and 1.0 for monozygotic twins. Environmental proximity is measured by a combination of two variables: one variable for those potentially preventable risk factors common to siblings (S) and another for those common only to twins (T). Discordance in identical twins is attributed to a third type of environmental factors (U) that are unshared by twins and include random (stochastic) factors. The association between these risk factors and birth defects is estimated by using a linear model of the correlation of liability for different relatives. The coefficients derived from the model reflect the relative importance of genetic and different types of environmental risk factors as causes for the defects and can be used to identify birth defects most likely to be caused by measurable and possibly preventable risk factors. These defects could then be assigned high priority for future studies and preventive efforts.     

Predicting rates of inbreeding in populations undergoing selection

Tractable forms of predicting rates of inbreeding (DeltaF) in selected populations with general indices, nonrandom mating, and overlapping generations were developed, with the principal results assuming a period of equilibrium in the selection process. An existing theorem concerning the relationship between squared long-term genetic contributions and rates of inbreeding was extended to nonrandom mating and to overlapping generations. DeltaF was shown to be approximately (1)/(4)(1 - omega) times the expected sum of squared lifetime contributions, where omega is the deviation from Hardy-Weinberg proportions. This relationship cannot be used for prediction since it is based upon observed quantities. Therefore, the relationship was further developed to express DeltaF in terms of expected long-term contributions that are conditional on a set of selective advantages that relate the selection processes in two consecutive generations and are predictable quantities. With random mating, if selected family sizes are assumed to be independent Poisson variables then the expected long-term contribution could be substituted for the observed, providing (1)/(4) (since omega = 0) was increased to (1)/(2). Established theory was used to provide a correction term to account for deviations from the Poisson assumptions. The equations were successfully applied, using simple linear models, to the problem of predicting DeltaF with sib indices in discrete generations since previously published solutions had proved complex.     

Permeability-surface area product and reflection coefficient of the parietal pleura in dogs.

The parameters describing the permeability of the parietal pleura to liquid and total plasma proteins were measured in five anesthetized adult dogs. Small areas of parietal pleura (approximately 1 cm2) and the underlying endothoracic fascia were exposed through resection of the skin and the intercostal muscles. The portion of the thorax containing the pleural windows was removed from the chest and fixed over a bath of whole autologous plasma, the inner parietal pleural surface facing the bath. Small hemispheric Perspex capsules (surface area 0.28 cm2) connected to a pressure manometer were glued to the pleural windows; a subatmospheric pressure was set into the capsule chamber to create step hydraulic transpleural pressure gradients (delta P) ranging from 5 to 60 cmH2O. Transpleural liquid flows (Jv) and protein concentration of the capsular filtrate (Cfilt) and of the plasma bath were measured at each delta P. The transpleural protein flux (Js) at each delta P was calculated by multiplying Jv by the corresponding Cfilt. The hydraulic conductivity (Lp) of the parietal pleura was obtained from the slope of the Jv vs. delta P linear regression. The average Lp from 14 capsules was 9.06 +/- 4.06 (SD) microliters.h-1.cmH2O-1.cm-2. The mathematical treatment of the Js vs. Jv relationship allowed calculation of the unique Peclet number at the maximal diffusional protein flux and a corresponding osmotic permeability coefficient for plasma protein of 1 x 10(-5) +/- 0.97 x 10(-5) cm/s. The reflection coefficient calculated from the slope of the linear phase of the Js vs. Jv relationship was 0.11 +/- 0.05.(ABSTRACT TRUNCATED AT 250 WORDS)     

Derivation of the Formula to Calculate the Chemical Potential Difference for the Components Involved in Identity Exchange Moves in Gibbs Ensemble Simulation of Mixtures

Since temperature and pressure are specified at the beginning of a simulation run in the Gibbs ensemble Monte Carlo (GEMC) method for mixtures, the condition of equilibrium is fulfilled through two sets of equalities in each phase: one set for the chemical potentials of the components of smaller molecules (calculated from transfer trial moves), and the other set for the differences between the chemical potentials of the components of larger molecules and the components of smaller molecules (calculated from identity exchange trial moves). The formula to calculate the former quantities is known since the time the GEMC method was proposed. However, the formula to calculate the latter quantities has recently been given in the literature without a formal derivation. In this work, a statistical-mechanical derivation of that formula is presented, within the framework of the canonical ensemble, and some justification is given for its extension to the Gibbs ensemble.     

Kinetic study of the linear stage of thermocurrent instability in the framework of the Boltzmann equation for a model gas

The linear stage of thermocurrent instability is investigated for a model gas in which the integral of inelastic collisions of electrons with gas particles has a divergent form and the frequencies of elastic and inelastic collisions are independent of the electron velocity. The proposed approach consists in the reduction of the Boltzmann equation for electrons in an inhomogeneous plasma to a set of equations for the moments of the electron velocity distribution function. The instability growth rate and the wave phase velocity as functions of the perturbation wavenumber are calculated, the maximum growth rate and the corresponding wavenumber are determined, and the dependence of these quantities on the degree of plasma quasineutrality is examined. It is demonstrated that the model satisfactorily (both qualitatively and quantitatively) describes the linear stage of thermocurrent instability in helium.     

Maximum likelihood estimation of two-level latent variable models with mixed continuous and polytomous data

Two-level data with hierarchical structure and mixed continuous and polytomous data are very common in biomedical research. In this article, we propose a maximum likelihood approach for analyzing a latent variable model with these data. The maximum likelihood estimates are obtained by a Monte Carlo EM algorithm that involves the Gibbs sampler for approximating the E-step and the M-step and the bridge sampling for monitoring the convergence. The approach is illustrated by a two-level data set concerning the development and preliminary findings from an AIDS preventative intervention for Filipina commercial sex workers where the relationship between some latent quantities is investigated.     

Relating species density to environmental variables in presence of spatial autocorrelation: a study case on soil nematodes distribution

The relationships between soil nematodes and soil texture, carbon content and depth were assessed in both a cultivated and uncultivated plots. Simple correlation coefficient analyses indicated a negative linear correlation between the plant-parasitic species Helicotylenchus retnsus Siddiqui and Brown and soil clay content in the uncultivated site. However, Mantel Lests showed this correlation to be spurious and only due to the presence of a common spatial pattern in the variables distribution. Both H. retusus density and soil clay content appeared to be independently driven by a common, unknown cause. The use of suitable statistical methods to analyse spatially dependent variables proved to be particularly fruitful in that they prevent spurious correlations and allow us to test different causal models involving the set of variables at hand.     

Non linear relationships between anthropometric and motor-endurance variables

Nonlinear regressions are rare in anthropology. In this paper we have tried to identify the significance and the character of the linear and non-linear relations between some anthropometric measures and the motor-endurance status. All subjects (300 moderately physically active males, mean aged 24 +/- 3.4 years) were measured for body weight, body height, body mass index, push-ups, sit ups, standing high jump, 50 meters swimming, and 1500 meters running. Linear (general model: y = a+bx) and nonlinear regression (general model: y = a+bx+cx2) was calculated simultaneously. According to the presented results the non-linear-square relation between variables can be expected: a) if there is evident cause why two absolutely different sub-groups of subjects should reach equal results in the criterion, b) if a non-linear-square basis for the established relationship can be found. In conclusion, simple linear and non linear regression procedures are to be used for the identification of linear and nonlinear predictors in nonlinear multiple regressions.     

The appropriate use of regression equations for the estimation of segmental inertia parameters

Linear regression equations are commonly used in conjunction with experimental data to provide linear relationships between quantities which are dimensionally distinct. In many cases theoretical relationships between such quantities are known and can be used as a basis for non-linear regression equations. This study compares linear and non-linear approaches for estimating the segmental moments of inertia from anthropometric measurements using the data of Chandler et al. [Chandler et al. (1975) Investigation of inertial properties of the human body. AMRL Technical Report 74-137, Wright Patterson Air Force Base. OH.] Right limb data were used to derive the equations while left limb data were used as a cross-validation sample to evaluate the inertia estimates calculated from the equations. For the limb segments the standard error estimates had average values of 21% for the linear equations and 13% for the non-linear equations. Data on a 10 yr-old boy was used to compare the two approaches outside the sample range. The mean percentage residuals were 286% for the linear equations and 20% for the non-linear equations. A set of non-linear equations is provided.     

Multilocus heterozygosity and inbreeding in the Siberian jay

Because of its common negative association with fitness, inbreeding is a major concern in conservation biology. Traditionally it has been measured as individual inbreeding coefficient calculated from the pedigree, but recently multilocus heterozygosity estimates have become commonly used as proxies. However, theoretical and simulation studies have cast doubt on the validity of these surrogates especially when they are based on only a few molecular markers. Yet, empirical studies reporting the correlation between multilocus heterozygosity and inbreeding coefficient are rare. We studied this relationship in a wild Siberian jay (Perisoreus infaustus) population subject to a long-term field study over 30 years. The correlations between inbreeding coefficient and the employed heterozygosity measures—standardized heterozygosity and internal relatedness—based on 21 microsatellite loci were weak. These results together with results from theoretical and simulation studies caution against use of multilocus heterozygosity estimates to study inbreeding in natural populations.