Viktor Witkovský

Breath isoprene - aspects of normal physiology related to age, gender and cholesterol profile as determined in a proton transfer reaction mass spectrometry study

Abstract Background: This study was performed to clarify variations in breath isoprene concentrations with age, gender, body mass index (BMI) and total serum cholesterol. Our cohort consisted of 205 adult volunteers of different smoking background without health complaints. Total cholesterol in blood serum was measured in 79 of these volunteers. Methods: Mixed expiratory exhaled breath was sampled using Tedlar bags. Concentrations of isoprene were then determined using proton transfer reaction-mass spectrometry. Results: Isoprene concentrations ranged from 5.8 to 274.9 ppb, with an overall geometric mean (GM) of 99.3 ppb. There was no statistically significant difference in mean isoprene in breath between males and females (GM 105.4 and 95.5 ppb, respectively). Ageing led to a decrease in concentration in men, with an estimated slope of the regression line for log-transformed isoprene concentrations of –0.0049, but did not influence isoprene levels in women. We did not observe any significant correlation between isoprene breath content and cholesterol level in blood, even after adjusting for the possible influence of age. Similarly, no correlation was found between isoprene levels and BMI. Conclusions: Isoprene concentrations in exhaled breath showed gender-specific correlations with respect to age. Further investigations are necessary to clarify the relation between isoprene concentrations in exhaled breath and cholesterol levels and synthesis rates in blood. Clin Chem Lab Med 2008;46:1011–8.

On the exact computation of the density and of the quantiles of linear combinations of t and F random variables

The inversion formula for evaluation of the distribution of a linear combination of independent t and F random variables, respectively, is suggested. The method is applied to computing the exact confidence intervals for the common mean of several normal populations. This method is compared with the known approximate methods.

Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model

The studied topic is motivated by the problem of interlaboratory comparisons. This paper focuses on the confidence interval estimation of the between group variance in the unbalanced heteroscedastic one-way random effects model. Several interval estimators are proposed and compared by means of the simulation study. The most recommended (safest) is the confidence interval based on Bonferronis inequality.

Modification of probability distributions. Applied to word length research

In linguistic modelling, a number of probability distributions must be modified because of different individual influences on the data and gradual shifts to new attractors. Several kinds of modifications, estimations and tests of already published models are presented for fitting purposes.

Exact distribution of positive linear combinations of inverted chi-square random variables with odd degrees of freedom

The exact distribution of a linear combination with positive coefficients of inverted chi-square variables with odd degrees of freedom is derived. This distribution function could be expressed as another linear combination of distribution functions of chi-square random variables.

Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase

Optical interferometers are widely used in dimensional metrology applications. Among them are many quadrature homodyne interferometers. These exhibit two sinusoidal interference signals shifted, in the ideal case, by 90° to allow a direction sensitive detection of the motion responsible for the actual phase change. But practically encountered signals exhibit additional offsets, unequal amplitudes and a phase shift that differs from 90°. In order to demodulate the interference signals the so called Heydemann correction is used in almost all cases, i.e. an ellipse is fitted to both signals simultaneously to obtain the offsets, amplitude and the phase lag. Such methods are typically based on a simplified least squares fit that leads to a system of linear equations, which can be solved directly in one step. Although many papers related to this subject have been published already only a few of them consider the uncertainties related to this demodulation scheme. In this paper we propose a new method for fitting the ellipse, based on minimization of the geometric distance between the measured and fitted signal values, which provides locally best linear unbiased estimators (BLUEs) of the unknown model parameters, and simultaneously also estimates of the related statistical uncertainties, including the uncertainties of estimated phases and/or displacements.

Exact Likelihood Ratio Test for the Parameters of the Linear Regression Model with Normal Errors

Exact Likelihood Ratio Test for the Parameters of the Linear Regression Model with Normal Errors In this paper we present an exact likelihood ratio test (LRT) for testing the simple null hypothesis on all parameters of the linear regression model with normally distributed errors. In particular, we consider the simultaneous test for the regression parameters, β, and the error standard deviation, σ. The critical values of the LRT are presented for small sample sizes and a small number of explanatory variables for usual significance levels, α = 0.1, 0.05, and 0.01. The test is directly applicable for construction of the (1 - α)-confidence region for the parameters (β,σ) and the simultaneous tolerance intervals for future observations in linear regression models. For comparison, the suggested method for construction of the tolerance factors of the symmetric (1 - γ)-content simultaneous (1 - α)-tolerance intervals is illustrated by a simple numerical example.

Univariate linear calibration via replicated errors-in-variables model

In this paper, we deal with the comparative calibration problem, i.e. with the situation when one instrument or measurement technique is calibrated against another, each of which is subject to the measurement error. We propose an approximate, small sample, calibration confidence interval of the unknown true value of the measured substance in units of the more precise instrument, given measurement in units of the less precise instrument. Here we deal with the simplest case—single-use linear univariate calibration, i.e. the case in which we assume linear relationship between the two measurement techniques (instruments), and, further, that the calibration procedure is conducted in order to obtain one value for an unknown, reported together with an interval estimate. The method for deriving the approximate confidence interval is based on estimation of the calibration line via the replicated errors-in-variables model. The model is locally linearized and the Wald-type F-statistic is constructed. An essential point in this approach is the use of the F-approximation of the distribution of the F-statistic suggested by Kenward and Roger [Kenward, M.G. and Roger, J.H., 1997, Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 53, 983–997]. The statistical properties of the proposed interval estimator are verified by simulations for wide spectrum of experimental designs and compared with two standard univariate interval estimates—the classical approach for deriving the calibration interval was proposed by Eisenhart [Eisenhart, C., 1939, The interpretation of certain methods and their use in biological and industrial research. Annals of Mathematical Statistics, 10, 162–186] and the inverse method was proposed by Krutchkoff [Krutchkoff, R.G., 1967, Classical and inverse methods of calibration. Technometrics, 9, 425–439].

Variability issues in determining the concentration of isoprene in human breath by PTR-MS

This paper deals with variability issues connected with the proton transfer reaction-mass spectrometry (PTR-MS) measurements of isoprene concentration. We focus on isoprene as an abundant and widely studied compound in human breath. The variability caused by the measurement process is described by the within-sample distribution. Thus, based on the formula for computing isoprene concentration that reflects the principle of the PTR-MS, a theoretical model for the within-sample distribution of isoprene concentration is suggested. This model, which assumes that the distribution is proportional to a quotient of two independent Poisson-distributed random variables, is then confronted with empirical distributions obtained from 17 breath samples collected from a healthy individual within a month. (In each sample, isoprene concentration was determined 97 times.) The empirical within-sample distributions are also compared to normal and log-normal distributions. While those seem to be satisfactory approximations, the theoretical model is found suitable only in 10 out of 17 breath samples. We also comment on the stability of samples during the measurement process in the PTR-MS instrument and, for the sake of comparison, determine the within-sample and the within-subject variability of isoprene concentrations in our data. The respective geometric standard deviations are 1.01 and 1.29.

Neuronal Oscillations in Various Frequency Bands Differ between Pain and Touch

Although humans are generally capable of distinguishing single events of pain or touch, recent research suggested that both modalities activate a network of similar brain regions. By contrast, less attention has been paid to which processes uniquely contribute to each modality. The present study investigated the neuronal oscillations that enable a subject to process pain and touch as well as to evaluate the intensity of both modalities by means of Electroencephalography. Nineteen healthy subjects were asked to rate the intensity of each stimulus at single trial level. By computing Linear mixed effects models (LME) encoding of both modalities was explored by relating stimulus intensities to brain responses. While the intensity of single touch trials is encoded only by theta activity, pain perception is encoded by theta, alpha and gamma activity. Beta activity in the tactile domain shows an on/off like characteristic in response to touch which was not observed in the pain domain. Our results enhance recent findings pointing to the contribution of different neuronal oscillations to the processing of nociceptive and tactile stimuli.