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On the sensitivity of linear discriminant analysis to sampling variation and analytical errors.

The influence of analytical inaccuracy and imprecision on the linear discriminant function is considered. Analytical shifts occurring between the analysis of samples from each of two groups give spuriously low error rates if the function is evaluated on the training set, notably at high dimensions. Inaccuracy arising after the establishment of a discriminant function may change considerably the individual group error rates whereas the overall error rate is moderately affected. Imprecision decreases the group separation by an amount comparable to that in the univariate situation. In conclusion, evaluation of the error rates of a discriminant function on an independent test set is important to obtain realistic estimates of the performance and is preferable to using unbiased statistical methods or the split-sample principle based solely upon the training set.

Biometry↗

Estimation of pharmacokinetic parameters by orthogonal regression: comparison of four algorithms.

The contribution of non-linear orthogonal regression for estimation of individual pharmacokinetic parameters when drug concentrations and sampling times are subject to error was studied. The first objective was to introduce and compare four numerical approaches that involve different degrees of approximation for parameter estimation by orthogonal regression. The second objective was to compare orthogonal with non-orthogonal regression. These evaluations were based on simulated data sets from 300 'subjects', thereby enabling precision and accuracy of parameter estimates to be determined. The pharmacokinetic model was a one-compartment open model with first-order absorption and elimination rates. The inter-individual coefficients of variation (CV) of the pharmacokinetic parameters were in the range 33-100%. Eight measurement-error models for times and concentrations (homo- or heteroscedastic with constant CV) were considered. Accuracy of the four algorithms was very close in almost all instances (typical bias, 1-4%). Precision showed three expected trends: root mean squared error (RMSE) increased when the residual error was larger or the number of observations was smaller, and it was highest for the absorption rate constant and common error variance. Overall, RMSE ranged from 5 to 40%. It was found that the simplest algorithm for othogonal regression performed as well as the more complicated approaches. Errors in sampling time resulted in an increased bias and imprecision in individual parameter estimates (especially for k(a) in our example) and in common error variance when the estimation method did not take into account these errors. In this situation, use of orthogonal regression resulted in smaller bias and better precision.

Algorithms↗

Evaluating mixed samples as a source of error in non-invasive genetic studies using microsatellites.

The use of noninvasive genetic sampling (NGS) for surveying wild populations is increasing rapidly. Currently, only a limited number of studies have evaluated potential biases associated with NGS. This paper evaluates the potential errors associated with analysing mixed samples drawn from multiple animals. Most NGS studies assume that mixed samples will be identified and removed during the genotyping process. We evaluated this assumption by creating 128 mixed samples of extracted DNA from brown bear (Ursus arctos) hair samples. These mixed samples were genotyped and screened for errors at six microsatellite loci according to protocols consistent with those used in other NGS studies. Five mixed samples produced acceptable genotypes after the first screening. However, all mixed samples produced multiple alleles at one or more loci, amplified as only one of the source samples, or yielded inconsistent electropherograms by the final stage of the error-checking process. These processes could potentially reduce the number of individuals observed in NGS studies, but errors should be conservative within demographic estimates. Researchers should be aware of the potential for mixed samples and carefully design gel analysis criteria and error checking protocols to detect mixed samples.

Animals↗

Negative feedback control model of proximal convergence and accommodation.

A comprehensive model has been developed to illustrate the interactions between the observer and the surrounding environment in the control of oculomotor responses to distance or 3-D space. Accommodation and vergence respond to both spatiotopic (body reference) proximal percepts and retinotopic (eye referenced) physical stimuli of blur and disparity. Both spatiotopic and retinotopic stimuli are derived respectively from perceptual and physical correlates of negative feedback for eye position. The spatiotopic and retinotopic stimulus errors are combined in the feedforward path and drive a common oculomotor controller which has a phasic-tonic organization. Spatiotopic and retinotopic stimuli are shown to be effective over complementary operating ranges. Perceptual spatiotopic errors of gaze provide optimal stimuli for near responses to large depth intervals whereas physical-retinotopic cues of blur and disparity provide quantitative information about small binocular fixation errors. Small dynamic variations of target distance are sensed both spatiotopically and retinotopically. Coarse and fine spatiotopic errors of gaze are processed differently. Large spatiotopic errors are sampled intermittently at the beginning of the near response, whereas small retinotopic position errors and spatiotopic velocity errors are sampled continuously throughout the near response. Former reports of empirically observed higher velocity of vergence responses to very large depth intervals is explained in terms of stimulus sampling modes rather than in terms of separate oculomotor control mechanisms. The model demonstrates a complementary function of top-down spatiotopic cues, which are used to initiate the near response, and bottom-up retinotopic cues, which are used to refine and complete the near response. Cross-couplings by vergence-accommodation and accommodative-vergence serve to coordinate the components of the near response when feedback from sensed response of one motor system (i.e. vergence) is more accurate than that of the other motor system (i.e. accommodation). The model presented here is concerned primarily with the near response mediated by accommodation and disjunctive eye movements and not by the independent vergence mediated by non-conjugate or yoked saccades of unequal amplitude.

Accommodation, Ocular↗

World Health Organization quality assessment programme on HIV testing.

A serum panel comprising 19 samples of known (five positives and 14 negatives) but undisclosed HIV-1-antibody content was distributed to 30 national reference laboratories for HIV serology. In order to simulate normal circumstances of referral, participants were asked to test the panel for HIV-1-antibody status using their normal procedures. Results of testing were returned by 28 participants. There were great variations in the number and combinations of tests used. The number used ranged from one to five assays per laboratory and none of the 24 laboratories using two or more tests employed the same combination. A high average success rate of 99% was seen with the positive samples. More errors occurred with the negative samples, with an average of 87% correct negative reports. Only four of the 14 negative specimens were reported as negative by all participants.

Acquired Immunodeficiency Syndrome↗

Limitations of clearance determination using the single sample distribution volume method. An error analysis on the basis of compartment models.

To investigate the error possibly contained in the single sample distribution volume method for the determination of renal clearance, a mathematical model was applied to describe the effect of changes in distribution volume, clearance, intravascular space, intracompartmental exchange and the time point of blood sampling. The method was found to be valid only under well-defined circumstances (Topt = 45 +/- 5 min, Cl = 390 +/- 50 ml/min, Vd = 16.7 +/- 4 l, alpha = 0.05.V1 ml/min, V1/Vd = 0.5 +/- 0.05) as shown in sample calculations. Two-compartment model-based error calculations demonstrate that this technique implies at best an uncertainty of +/- 10% or more. Whilst it can be used preferably in healthy, normal-weight adults, it is not applicable, without error, under all other circumstances.

Humans↗

How good is the slope on the second exponential for estimating 51Cr-EDTA renal clearance? A Monte Carlo simulation.

It has been suggested that the slope of the second exponential of the plasma disappearance curve may be used to monitor changes in renal function instead of plasma clearance calculated using the slope-intercept method. The purpose of this study was to evaluate the magnitude of error in the slope induced by errors in sampling time and in activity measurement, and to compare it with the error observed in clearance. A model of mono-exponential curves based on two blood samples, taken at 120 and 240 min, was created. Normally distributed random errors were introduced into the sampling times and activity measurements. For each setting, the random errors were successively introduced 200 times and the coefficients of variation of the calculated slopes and clearances were determined. Variable errors in slope and clearance were induced by errors in sampling time and activity measurement. In general, the observed errors in the slope were high in the case of low slope values, decreasing progressively for increasing slope values. The errors in clearance followed a different pattern: highest errors were observed in the case of very low clearance, decreasing progressively for higher clearance values and attaining the minimal value at a lambda around 0.006 min-1, which corresponds to clearance of about 90 ml.min-1. The magnitude of the errors then started to increase again for higher clearance. For a large range of clearance values, the errors in the slope were higher than the errors in clearance. The only exceptions were cases with very high clearance rates. In conclusion, clearance calculation using the slope-intercept method should be preferred to that using the slope alone for monitoring changes in renal function.

Chelating Agents↗

Detection of individual variation in enzyme activity in natural populations of Drosophila melanogaster.

The method allows the determination of the activity level of enzymes in a single fly and assessing the genetic composition of the given individual at these enzyme loci. Three isofemale lines were constructed which were monomorphic at several enzyme loci. Samples were prepared in two different ways: (i) individual samples--individuals were homogenised separately; (ii) collective samples--a common homogenate was prepared from several individuals. Oregon-R strain was also used to prepare a standard homogenate. The activities of alcohol dehydrogenase (ADH), alpha-glycerophosphate dehydrogenase (alpha GPDH), isocitrate dehydrogenase (IDH), and 6-phosphogluconate dehydrogenase (6PGDH), were measured in each sample on starch gel after the proteins were separated by electrophoresis. Enzyme activities were assessed by the optical density of the bands. Gel and position weights were estimated on the basis of the statistical analyses of the activities measured in the standard samples. Gel weights were then used to account for the activity differences among the gels while position weights were applied to correct for the general tendencies in the activities observed within the gels. The gel and position weighted activities of individual and collective samples were compared in the isofemale lines. The individual samples had approximately two times as much variation as the collective samples for all four enzymes. The electrophoretic method is sensitive enough to study the structure of the phenotypic variation in enzyme activity in the natural populations. The total variation among the standard samples was close to the within subline component of variation obtained for the collective samples (measurement error). This shows that the standard samples can be used to estimate the size of the measurement error.

Alcohol Dehydrogenase↗

The consistency of estimates obtained through central-location sampling: analysis of the Partnership for a Drug-Free America Attitude Tracking Study.

To evaluate the reliability and validity of estimates of drug use obtained through multiple-site central-location sampling, data from the Partnership Attitude Tracking Study (PATS), collected annually beginning in 1987, are tracked longitudinally and compared with data collected through traditional household interviews. Comparisons with demographic estimates from Current Population Surveys indicate that central-location sampling can provide a broadly representative sample of the adult population. However, there is some coverage bias in central-location sampling, most notably in the underrepresentation of adults who do not have high school diplomas. Sample estimates obtained from central-location sampling are consistent over time. Basic demographic characteristics of the samples--education, income, marital status, and area of residence--vary by less than 5% across the four waves of the tracking study. Prevalence estimates of self-reported drug use demonstrate an even higher degree of consistency over time. Comparisons of PATS and National Household Survey of Drug Abuse data and the Monitoring the Future data indicate a higher level of drug use and a lower level of perceived risk of occasional use among PATS respondents. While the trends in use and perceived risk reported in all studies are similar, we suggest that perceived threats to confidentiality and anonymity often result in significant underreporting of drug use, particularly in household surveys. Sample estimate differences are attributed to sampling and measurement error. Some discrepancy in prevalence estimates is associated with the fact that the PATS sample is not a true probability sample; as a result, the sampling error of the overall study cannot be estimated precisely. It is also likely that the difference in estimates between the studies is a product of the decreased measurement error of PATS methodology. In central-location sampling, respondents are completely anonymous and may feel more comfortable in providing honest answers about illicit activities such as drug use. The potential applications of this methodology are discussed.

Adolescent↗

Electrostatic effects in asbestos sampling. I: Experimental measurements.

Electrostatic charge can cause errors during sampling of airborne asbestos fibers and other particles. The change in particle trajectories caused by charge effects during sampling can result in nonuniform deposits on the collecting filter surface and net loss of sample. The degree of these electrostatic effects depends on particle charge, sampler charge, sampler conductivity, and sampling flow rate and direction. The purpose of this research was to evaluate the dependence of sampling efficiency and sample uniformity on these variables. Humidity has been postulated as a primary determinant of particle charge during aerosol generation. Measurements of particle charge and concentration were made as a function of relative humidity with chrysotile fibers generated from a fluidized bed. A strong increase in charge and a decrease in concentration of fibers was noted as the relative humidity was decreased below 15%. The effects of conductive versus nonconductive samplers and sampling flow rate were measured as a function of particle and sampler charge levels. Nonconductive samplers can carry a large and variable charge distribution on their surfaces. This can result in a biased and highly variable particle deposit on the filter when sampling charged particles. Conductive cowls spread any acquired charge over the entire surface and produce a more symmetrical and less biased charged particle deposit. Increasing the sampling flow rate will improve sampling efficiency and decrease deposit variability because the charged particle has less time to interact with the field produced by the sampler. These results suggest that sampling problems caused by electrostatic charge interactions are most likely to occur under low humidity conditions of dust generation, that sampling should be done at as high a flow rate as possible to reduce these effects, and that analysts should select fields toward the center of the filter to minimize bias and variability.

Aerosols↗

Comparative analysis of population age-sex distribution from sample and complete enumeration: 1970 and 1980 census data.

"This paper will attempt to analyze the degree of distortion introduced by sampling, if any, on the age and sex distribution of the population based on the information taken [in the 1970 census] from the sample households. Specifically, the 1970 age and sex distribution of the Philippine population based on the 5-percent sample households will be compared with that obtained from the information supplied by all households, i.e., the actual age and sex distribution of the Philippines....Findings...suggest a failure of the estimation procedures used in past censuses to correct errors attributable to sampling. In particular, the type of sampling error highlighted in this paper is the distortion introduced by sampling in age-sex distribution."

Age Distribution↗

Lesion type misidentification: EEG potential sampling and source reconstruction errors.

Accurate EEG source reconstruction needs an appropriate volume conductor head model including, in the presence of a morphological brain lesion, a lesion compartment. Lesion electrical properties (conductivity) can not be measured in vivo and need to be retrieved from literature on the base of lesion type identification, performed by means of diagnostic imaging. However, different pathologies can appear similar at bioimages inspection, leading to uncertain diagnosis and in turn to wrong lesion conductivity assumption. Besides many factors, source reconstruction accuracy depends on lesion conductivity value and on electrodes placing (scalp potential sampling). We investigated the relation between electrodes sampling of the EEG and source reconstruction accuracy in case of uncertain lesion type identification. We adopted an eccentric-spheres head model (including the lesion) and a dipole source. We simulated several pathological conditions considering different electrode montages on the scalp: a "clinical like" sampling with 64 electrodes and an extended sampling with 128 electrodes. Source reconstruction was performed assuming wrong lesion type identification (i.e. introducing an error in the model parametrical setting). We found large errors for both source localization (LE) and source intensity estimations. Maximum LE could be reduced (from 30 to 27 mm) by the extended sampling. Conversely, the mean values of LE mostly increased using more electrodes. The benefit of enlarging the sampling was clear for the intensity estimation. In conclusion, only the most inaccurate source reconstruction could be improved changing electrodes placing; the inherent source reconstruction error due to model parameter setting could not be avoided.

Brain Diseases↗

Implications of measurement error in exposure for the sample sizes of case-control studies.

In this paper, recent results describing the effects of measurement error on estimation of the association between an exposure and a disease are applied to sample size calculation in case-control studies. Models of the relation between true exposure and a surrogate exposure measure assessed with error are used to derive equations for sample size determination. The results show that the sample size of a study based on an exposure variable which is measured with error must be larger by a factor of 1/rho 2 than if exposure were measured without error, where rho is the correlation between the true exposure and the surrogate exposure measure. Review of the magnitude of measurement error in dietary assessments suggests that failure to account for measurement error in sample size determination for case-control studies of diet and disease could lead to marked underestimation of the required sample size.

Bias↗

Absolute free energy calculations by thermodynamic integration in four spatial dimensions.

An optimized technique for calculating the excess chemical potential of small molecules in dense liquids and the binding affinity of molecular ligands to biomolecules is reported. In this method, a molecular species is coupled to the system of interest via a nonphysical fourth spatial dimension w through which insertion or extraction can be carried out [R. Pomes, E. Eisenmesser, C. B. Post et al., J. Chem. Phys. 111, 3387 (1999)]. Molecular simulations are used to compute the potential of mean force (PMF) acting on the solute molecule in the fourth dimension. The excess chemical potential of that molecule is obtained as the difference in the PMF between fully coupled and fully decoupled systems. The simplicity, efficiency, and generality of the method are demonstrated for the calculation of the hydration free energies of water and methanol as well as sodium, cesium, and chloride ions. A significant advantage over other methods is that the 4D-PMF approach provides a single effective and general route for decoupling all nonbonded interactions (i.e., both Lennard-Jones and Coulombic) at once for both neutral and charged solutes. Direct calculation of the mean force from thermodynamic integration is shown to be more computationally efficient than calculating the PMF from umbrella sampling. Statistical error analysis suggests a simple strategy for optimizing sampling. The detailed analysis of systematic errors arising from the truncation of Coulombic interactions in a solvent droplet of finite size leads to straightforward corrections to ionic hydration free energies.

Journal Article↗

Nucleotide analogs and new buffers improve a generalized method to enrich for low abundance mutations.

A high sensitivity method for detecting low level mutations is under development. A PCR reaction is performed in which a restriction site is introduced in wild-type DNA by alteration of specific bases. Digestion of wild-type DNA by the cognate restriction endonuclease (RE) enriches for products with mutations within the recognition site. After reamplification, mutations are identified by a ligation detection reaction (LDR). This PCR/RE/LDR assay was initially used to detect PCR error in known wild-type samples. PCR error was measured in low |Deltap K a| buffers containing tricine, EPPS and citrate, as well as otherwise identical buffers containing Tris. PCR conditions were optimized to minimize PCR error using perfect match primers at the Msp I site in the p53 tumor suppressor gene at codon 248. However, since mutations do not always occur within pre-existing restriction sites, a generalized PCR/RE/LDR method requires the introduction of a new restriction site. In principle, PCR with mismatch primers can alter specific bases in a sequence and generate a new restriction site. However, extension from 3' mismatch primers may generate misextension products. We tested conversion of the Msp I (CCGG) site to a Taq I site (TCGA). Conversion was unsuccessful using a natural base T mismatch primer set. Conversion was successful when modified primers containing the 6 H,8 H -3, 4-dihydropyrimido[4,5- c ][1,2]oxazine-7-one (Q6) base at 3'-ends were used in three cycles of preconversion PCR prior to conversion PCR using the 3' natural base T primers. The ability of the pyrimidine analog Q6 to access both a T-like and C-like tautomer appears to greatly facilitate the conversion.

Base Sequence↗

Quantitative proteomics for two-dimensional gels using difference gel electrophoresis.

Difference gel electrophoresis (DIGE) technology provides a powerful quantitative component to proteomics experiments involving two-dimensional (2D) gel electrophoresis. DIGE allows for the detection of subtle changes in protein abundance with statistical confidence while controlling for gel-to-gel variation, as well as additional variation that is non-biological in origin (e.g., sample preparation error, normal variation in a system). Samples are differentially labeled with spectrally resolvable fluorescent dyes (Cy2, Cy3, and Cy5) and co-resolved for direct quantification within the same 2D gel. Increased statistical confidence is obtained when combining experimental repetition with internal standards such that independent replicate measurements from single- and multivariable analyses can be intercompared with a relatively small number of coordinated DIGE gels.

Electrophoresis, Gel, Two-Dimensional↗