Higher order inference for the consensus mean in inter-laboratory studies

In inter-laboratory studies, a fundamental problem of interest is inference concerning the consensus mean, when the measurements are made by several laboratories which may exhibit different within-laboratory variances, apart from the between laboratory variability. A heteroscedastic one-way random model is very often used to model this scenario. Under such a model, a modified signed log-likelihood ratio procedure is developed for the interval estimation of the common mean. Furthermore, simulation results are presented to show the accuracy of the proposed confidence interval, especially for small samples. The results are illustrated using an example on the determination of selenium in non-fat milk powder by combining the results of four methods. Here, the sample size is small, and the confidence limits for the common mean obtained by different methods produce very different results. The confidence interval based on the modified signed log-likelihood ratio procedure appears to be quite satisfactory.     

A non-iterative confidence interval estimating procedure for the intraclass kappa statistic with multinomial outcomes

We obtain the asymptotic sample variance of the intraclass kappa statistic for multinomial outcome data. A modified Wald type procedure based on this theory is then used for confidence interval construction. The results of a simulation study show that the proposed non-iterative approach performs very well in terms of confidence interval coverage and width for samples as small as 50. The procedure is illustrated with two examples from previously published medical studies.     

Geometric models for calculating cell biovolume and surface area for phytoplankton

Phytoplankton biovolume can be measured or calculated throughthe calculation of similar geometric models. A set of geometricmodels is suggested for calculating cell biovolume and surfacearea for 284 phytoplankton genera in China Sea waters. Thirty-onegeometric shapes have been assigned to estimate the biovolumeand surface area of phytoplankton cells. Reductions of errorand microscopic effort are also discussed. The model has beenverified by its application in the China Seas regions. The softwareto make these calculations is available at http://www.ouc.edu.cn/csmxy/sunjun/biovolume.htm     

Statistical criteria for using short-term measurements as an index of 24-hour mean arterial pressure in unanesthetized unrestrained dogs

This study assessed the statistical validity of short time-interval measurements as estimators of true 24 hour mean arterial pressure in unanesthetized, unrestrained dogs. 24 hour intra-arterial pressure recordings were obtained using a stable FM telemetry system. The 24 hour pressure measurements approximated a normal distribution whose variance was inversely related to the selected averaging interval. Given the variance of a normal distribution one can calculate the 95% confidence interval for any single random measurement. Conversely the number of random samples necessary to be within a prescribed confidence interval can be determined. In this study, the 95% confidence interval for a single, random 30 minute arterial pressure average was calculated to be 11.2 mmHg. Only 4.8 +/- 1.4% of 480 individual 30 minute arterial pressure measurements fell beyond this confidence interval. These outlying values were distributed throughout the 24 hour period. The data suggest that randomly chosen short time-interval measurements may be a valid index of true 24 hour mean pressure if the average variance of a population is known and confidence intervals are defined.     

Calculation of narrower confidence intervals for tree mortality rates when we know nothing but the location of the death/survival events

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Confidence intervals for heritability for two-factor mating design single environment linear models

Summary Precision measurement is an essential part of heritability estimate interpretation. Approximate standard errors are commonly used as measures of precision for heritability on a progeny mean basis (H). Their derivation, however, is not inferred from the distribution theory for H. F-distribution based exact confidence intervals have been derived for some onefactor mating design H estimators. Extension of the confidence interval results from one-factor to twofactor mating designs is reported in this paper. Functions of heritability on a full-sib or half-sib progeny mean basis from nested or factorial mating design parameters were distributed according to the F-distribution. Exact confidence intervals were derived for heritability on a full-sib progeny mean basis. Exact confidence intervals for heritability on a half-sib progeny basis were adapted from previous results. Maize (Zea mays L.) data were used to estimate confidence intervals. Complete equations were given for interpolation in F-tables.Oregon Agricultural Experiment Station Technical Paper No. 7659     

Change in cyanobacterial biovolume due to preservation by Lugol's Iodine

Cyanobacterial biovolume is used as a guide to the public health risk from these organisms for users of potable and recreational waters. Most routine surveillance programs preserve phytoplankton samples before analysis. We tested the effect of Lugol's Iodine, a common preservative, on the cell biovolume of four common freshwater cyanobacteria, Microcystis aeruginosa, Anabaena circinalis, Cylindrospermopsis raciborskii and Aphanocapsa incerta. Linear dimensions and cell area were measured with an image analyser. All four species shrank after preservation. The magnitude of shrinkage varied with species and preservation time but was not affected by Lugol's concentration. The maximum shrinkage in each species was a 30–40% reduction compared to the live cell biovolume. These results suggest shrinkage can be a greater source of uncertainty in estimating the biovolume of toxigenic cyanobacteria in aquatic environments than natural variability in the cell dimensions, instrument precision or cell counting. Standardised cyanobacterial biovolume lists based on agreed geometric shapes and formulae would improve the value of this information for public health risk assessment.     

An interval estimation of expected response to selection

Summary A method is presented here for obtaining an interval estimate of expected response to selection based on results of a progeny test experiment. The structure of the constructed confidence limits is then examined for the influence of the numbers of lines and replicates on the precision of predicting the expected response to selection.     

Statistics of divergence times.

Given the number of nucleotide substitutions between two species (K) and the substitution rate nu, the expectation of the corresponding divergence time is usually calculated as K/(2 nu). This is strictly true only if nu is regarded as a constant because the ratio of two random variables, such as K/(2 nu), has distributional properties different from those of the distribution of K. Therefore, both the mean and any confidence interval for divergence times are unknown in this situation. We model the distribution of K and nu using the Gamma distribution and calculate the mean and 95% confidence interval for the corresponding divergence time. These calculations are compared with results obtained by bootstrapping sequence data from the model plant Arabidopsis thaliana and its relatives. We show that for nonoverlapping pairs of phylogenetic distances, our method approaches the bootstrap results very closely. In contrast, regarding the mutation rate as a constant leads to strong underestimation of the confidence interval. An implementation of our method of computing divergence times is accessible through a web interface at http://www.soft.ice.mpg.de/cite.     

Accuracy of Biovolume Formulas for CMEIAS Computer-Assisted Microscopy and Body Size Analysis of Morphologically Diverse Microbial Populations and Communities

Cell biovolume is a commonly used metric of microbial abundance analyzed by computer-assisted microscopy, but the accuracies of most biovolume formulas have not been validated by ground truth data. We examined the accuracy of 17 biovolume formulas by comparing the computed volumes of 3D models representing 11 microbial morphotypes (cocci, spirals, curved rods, U-shaped rods, regular straight rods, unbranched filaments, ellipsoids, clubs, prosthecates, rudimentary branched rods, and branched filaments) to the volume displacement of the same objects as ground truth. As anticipated, formula accuracy was significantly influenced by the morphotype examined. A few formulas performed very accurately (> 95 %), especially those that adapted to the cell’s shape, whereas others were consistently inaccurate or only accurate for one or two morphotypes. As an example of application, indices of morphological diversity in a freshwater biofilm assemblage were shown to be significantly different when microbial abundance among morphotype classes was measured as biovolume body mass rather than cell counts. Spatial analysis of biovolume body mass can also provide insights on the in situ ecophysiological attributes among individuals in microbial populations and communities, including their spatially autocorrelated allometric scaling interrelationships between body size, metabolic activity, resource apportionment and use, food web dynamics, and various cell-cell interactions affecting their growth and colonization behavior within spatially structured biofilm landscapes. This improved computing technology of biovolume algorithms with proven accuracy identifies which formula(s) should be used to compute microbial biovolumes in 2D images of morphologically diverse communities acquired by conventional phase-contrast light microscopy at single-cell resolution.     

A new method for choosing sample size for confidence interval-based inferences

Scientists often need to test hypotheses and construct corresponding confidence intervals. In designing a study to test a particular null hypothesis, traditional methods lead to a sample size large enough to provide sufficient statistical power. In contrast, traditional methods based on constructing a confidence interval lead to a sample size likely to control the width of the interval. With either approach, a sample size so large as to waste resources or introduce ethical concerns is undesirable. This work was motivated by the concern that existing sample size methods often make it difficult for scientists to achieve their actual goals. We focus on situations which involve a fixed, unknown scalar parameter representing the true state of nature. The width of the confidence interval is defined as the difference between the (random) upper and lower bounds. An event width is said to occur if the observed confidence interval width is less than a fixed constant chosen a priori. An event validity is said to occur if the parameter of interest is contained between the observed upper and lower confidence interval bounds. An event rejection is said to occur if the confidence interval excludes the null value of the parameter. In our opinion, scientists often implicitly seek to have all three occur: width, validity, and rejection. New results illustrate that neglecting rejection or width (and less so validity) often provides a sample size with a low probability of the simultaneous occurrence of all three events. We recommend considering all three events simultaneously when choosing a criterion for determining a sample size. We provide new theoretical results for any scalar (mean) parameter in a general linear model with Gaussian errors and fixed predictors. Convenient computational forms are included, as well as numerical examples to illustrate our methods.     

Defining absolute confidence limits in the identification of Caulobacter proteins by peptide mass mapping

A derivatization reaction, guanidination, was recently reported that increases MALDI-TOF MS sensitivity toward lysine-terminated peptides. Its application conveys sequence information that can be used as a parameter in peptide mass mapping database searches. This paper presents a systematic study of the impact of guanidination on proteomic analysis of an entire bacterial organelle. Sixty-two 2-D gel isolated proteins from Caulobacter crescentus stalks were studied. A novel computer algorithm, Prodigies, was developed to analyze the data. Absolute confidence limits associated with protein assignments were established using Monte Carlo simulations of database searches. The advantages of guanidination are illustrated using both experimental and theoretical data.     

Automatic Determination of Bacterioplankton Biomass by Image Analysis

Image analysis was applied to epifluorescense microscopy of acridine orange-stained plankton samples. A program was developed for discrimination and binary segmentation of digitized video images, taken by an ultrasensitive video camera mounted on the microscope. Cell volumes were estimated from area and perimeter of the objects in the binary image. The program was tested on fluorescent latex beads of known diameters. Biovolumes measured by image analysis were compared with directly determined carbon biomasses in batch cultures of estuarine and freshwater bacterioplankton. This calibration revealed an empirical conversion factor from biovolume to biomass of 0.35 pg of C μm⁻³ (± 0.03 95% confidence limit). The deviation of this value from the normally used conversion factors of 0.086 to 0.121 pg of C μm⁻³ is discussed. The described system was capable of measuring 250 cells within 10 min, providing estimates of cell number, mean cell volume, and biovolume with a precision of 5%.     

Automated computation of relative flow resistance using a pulsed Doppler flowmeter

Use of a pulsed Doppler flowmeter to assess changes in blood flow resistance often requires a laborious series of calculations, and full characterization of resistance changes frequently necessitates replotting of calculated data. To facilitate the interpretation of pulsed Doppler flowmetry data, a simple, inexpensive device was constructed that computes the signal ratio of mean arterial pressure (MAP) to directional pulsed Doppler outputs. With this device, relative flow resistance can be recorded and quantitatively assessed at a glance in three vascular beds in real time. This computer-like device was designed around the Burr-Brown DIV100HP integrated circuit. C741G OpAmps provide input buffering, zeroing, and ranging adjustments enabling the user to accurately follow resistance over a very broad range of changes without exceeding the device's operating limits. A LM339 quad comparator monitors the input of each DIV100 and indicates when operating limits are exceeded via a channel-specific LED indicator and an audible alarm. No significant attenuation of the input signals occurs over the range of direct current to 50 kHz, and the output is without significant phase shift. Comparisons with calculated changes in resistance derived from the MAP and pulsed Doppler flowmetry in unanesthetized, unrestrained rats confirmed that resistance changes can be measured with precision and accuracy.     

Confidence Intervals in Qtl Mapping by Bootstrapping

The determination of empirical confidence intervals for the location of quantitative trait loci (QTLs) was investigated using simulation. Empirical confidence intervals were calculated using a bootstrap resampling method for a backcross population derived from inbred lines. Sample sizes were either 200 or 500 individuals, and the QTL explained 1, 5, or 10% of the phenotypic variance. The method worked well in that the proportion of empirical confidence intervals that contained the simulated QTL was close to expectation. In general, the confidence intervals were slightly conservatively biased. Correlations between the test statistic and the width of the confidence interval were strongly negative, so that the stronger the evidence for a QTL segregating, the smaller the empirical confidence interval for its location. The size of the average confidence interval depended heavily on the population size and the effect of the QTL. Marker spacing had only a small effect on the average empirical confidence interval. The LOD drop-off method to calculate empirical support intervals gave confidence intervals that generally were too small, in particular if confidence intervals were calculated only for samples above a certain significance threshold. The bootstrap method is easy to implement and is useful in the analysis of experimental data.     

Confidence intervals for the mean of diagnostic test charge data containing zeros

In this paper, we consider the problem of interval estimation for the mean of diagnostic test charges. Diagnostic test charge data may contain zero values, and the nonzero values can often be modeled by a log-normal distribution. Under such a model, we propose three different interval estimation procedures: a percentile-t bootstrap interval based on sufficient statistics and two likelihood-based confidence intervals. For theoretical properties, we show that the two likelihood-based one-sided confidence intervals are only first-order accurate and that the bootstrap-based one-sided confidence interval is second-order accurate. For two-sided confidence intervals, all three proposed methods are second-order accurate. A simulation study in finite-sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator (MVUE)-based interval except for the case of one-sided lower end-point intervals when the skewness is very small. Among the proposed one-sided intervals, the bootstrap interval has the best coverage accuracy. For the two-sided intervals, when the sample size is small, the bootstrap method still yields the best coverage accuracy unless the skewness is very small, in which case the bias-corrected ML method has the best accuracy. When the sample size is large, all three proposed intervals have similar coverage accuracy. Finally, we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression.     

Line-segment confidence bands for repeated measures

For the case of repeated measures on Y with mean values linear in a concomitant variable Z in [a, b], a straight-line confidence band over [a, b] is given with width linear in Z. Graphical presentation of such line-segment confidence bands can help emphasize that appropriate inferences are limited to the range of the data. Because the line-segment bands are designed to cover a finite interval, they are usually more efficient than the widely used hyperbolic bands. Conditions for favorable relative efficiency of area bounded are given. This easily computed trapezoidal confidence region is formulated in terms of a growth-curve model.     

The empirical coverage of confidence intervals: Point estimates and confidence intervals for confidence levels

Many confidence intervals calculated in practice are potentially not exact, either because the requirements for the interval estimator to be exact are known to be violated, or because the (exact) distribution of the data is unknown. If a confidence interval is approximate, the crucial question is how well its true coverage probability approximates its intended coverage probability. In this paper we propose to use the bootstrap to calculate an empirical estimate for the (true) coverage probability of a confidence interval. In the first instance, the empirical coverage can be used to assess whether a given type of confidence interval is adequate for the data at hand. More generally, when planning the statistical analysis of future trials based on existing data pools, the empirical coverage can be used to study the coverage properties of confidence intervals as a function of type of data, sample size, and analysis scale, and thus inform the statistical analysis plan for the future trial. In this sense, the paper proposes an alternative to the problematic pretest of the data for normality, followed by selection of the analysis method based on the results of the pretest. We apply the methodology to a data pool of bioequivalence studies, and in the selection of covariance patterns for repeated measures data.     

Modeling a fibula transplant in mandibular reconstructions: evaluation of the effects of a minimal number of osteotomies on the contour of the jaw.

The fibula osteocutaneous free flap has become the preferred method for most cases of mandibular reconstruction after oncologic surgical ablation. To recreate the parabolic form of the mandible, the fibula has to be divided up into segments using a closed wedge osteotomy technique. The number of osteotomies is preferably kept to a minimum so that segmental periosteal circulation is not compromised and also to keep operating time to a minimum. The limited number of osteotomies creates an angular contour. The aim of this study was to establish the degree to which overcorrection or undercorrection would occur when a subtotal reconstruction from ramus to ramus was simulated using five bony segments and four osteotomies. The study was carried out using 30 preserved jaws; the contour lines of the jaws were transferred onto tracing paper using a cardboard template. The contour of the mandible was divided into five sections (ramus, body, symphysis, body, and ramus). Because of the cutting off of the curvature in the original jaw outline, the lateral side of the body will become narrower and the chin broader. This also results in an underprojection (displacement) of the chin. To follow the original contour of the jaw as accurately as possible, all these anomalies must be minimized. The amount of under- and overprojection is calculated for a displacement of 1.0, 1.5, 2.5, 5.0, 7.5, and 10 mm of the chin. The most accurate reconstruction of the mandibular contour is achieved with a displacement of 1.5 or 2.5 mm. To preserve sufficient periosteal circulation, the minimum width of bone segments must be 15 mm or more. This concerns especially the symphysis section. On the basis of a fibula thickness of 14 mm, the internal bone width of the symphysis section is calculated. With a displacement of 1.5 mm, the average internal width of the bone segment is 14.8 mm, with a range of 9.9 to 23.0 mm (95 percent confidence interval, 12.8 to 16.7 mm). Therefore, a displacement of 2.5 mm with an internal bone width of 16.4 mm is preferred (range, 11.9 to 24.8 mm; 95 percent confidence interval, 15.5 to 18.2 mm). The loss of lateral projection is minimal (5.8 mm) and the resulting chin width is acceptable (average, 35.0 mm). In conclusion, we propose that in a subtotal procedure, an acceptable jaw reconstruction can be achieved with a limited number of osteotomies. The bone length of the symphysis section remains within safe limits. If the defect is of limited dimensions, then the resulting jaw contour is even more accurate.     

Estimation of amoeba cell volume from nuclear diameter and its application to studies in protozoan ecology

To facilitate the estimation of cell volume in uninucleate, naked amoebae (gymnamoebae) the relationship, log cell volume (µm³) = 0.882 + 3.117log nuclear diameter (µm³), is presented. This links mean cell volume to mean nuclear diameter and provides a useful tool for protozoan ecologists interested in estimating the biovolume of amoebae in laboratory or field samples. While it is virtually impossible to measure rigid axes from which volume can be calculated in these amorphous cells, it is relatively easy to measure the diameter of the nucleus in living or fixed material. This relationship has shown that most uninucleate amoebae surveyed have volumes ranging between only 188 µm³ and 2860 µm³; this range reflects the volumes of the majority of amoebae in the field. These small volumes are unexpected since many amoebae have locomotive forms greater than 20 µm in length giving the impression that their cell volumes should be correspondingly large. This is not the case, however, because most amoebae are extremely flat when viewed in profile. The small cell volume of most amoeba species has ecological implications when numerical data is transformed to biovolume and biomass units.