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The genetic structure of admixed populations.

A method for simultaneously estimating the admixture proportions of a hybrid population and Wright's fixation index, FST, for that hybrid is presented. It is shown that the variance of admixture estimates can be partitioned into two components: (1) due to sample size, and (2) due to evolutionary variance (i.e., genetic drift). A chi-square test used to detect heterogeneity of admixture estimates from different alleles, or loci, can now be corrected for both sources of random errors. Hence, its value for the detection of natural selection from heterogeneous admixture estimates is improved. The estimation and testing procedures described above are independent of the dynamics of the admixture process. However, when the admixture dynamics can be specified, FST can be predicted from genetic principles. Two admixture models are considered here, gene flow and intermixture. These models are of value because they lead to very different predictions regarding the accumulation of genes from the parental populations and the accumulation of variance due to genetic drift. When there is not evidence for natural selection, and it is appropriate to apply these models to data, the variance effective size (Ne) of the hybrid population can be estimated. Applications are made to three human populations: two of these are Afro-American populations and one is a Yanomamö Indian village. Natural selection could not be detected using the chi-square test in any of these populations. However, estimates of effective population sizes do lead to a richer description of the genetic structure of these populations.

Black People↗

The precision of unbiased estimates of numerical density of endothelial cells in donor cornea.

The precision of estimates of central corneal endothelial density was studied in 16 human corneas stained by alizarine red and trypane blue. Estimates based on central counts and estimates based on peripheral counts were considered separately. The numerical density was estimated employing an unbiased sampling technique. From central counts estimates with an error of less than five per cent could be obtained. From peripheral counts a maximum precision of mean +/- 12.2 per cent could be obtained. The theoretical maximum precision was calculated by application of a variance component model. The precision of estimates was calculated for 1, 2 and 4 test areas of different sizes. Economy of sampling was evaluated by comparison of the actual precision to the theoretical maximum precision of estimates.

Cell Count↗

A detailed evaluation of adjustment methods for multiplicative measurement error in linear regression with applications in occupational epidemiology.

It is often appropriately assumed, based on both theoretical and empirical considerations, that airborne exposures in the workplace are lognormally distributed, and that a worker's mean exposure over a reference time period is a key predictor of subsequent adverse health effects for that worker. Unfortunately, it is generally impossible to accurately measure a worker's true mean exposure. We begin by introducing a familiar model for exposure that views this true mean, as well as logical surrogates for it, as lognormal random variables. In a more general context, we then consider the linear regression of a continuous health outcome on a lognormal predictor measured with multiplicative error. We discuss several candidate methods of adjusting for the measurement error to obtain consistent estimators of the true regression parameters. These methods include a simple correction of the ordinary least squares estimator based on the surrogate regression, the regression of the outcome on the covariates and on the conditional expectation of the true predictor given the observed surrogate, and a quasi-likelihood approach. By means of a simulation study, we compare the various methods for practical sample sizes and discuss important issues relevant to both estimation and inference. Finally, we illustrate promising adjustment strategies using actual lung function and dust exposure data on workers in the Dutch animal feed industry.

Analysis of Variance↗

The power of association studies to detect the contribution of candidate genetic loci to variation in complex traits.

The statistical power of five association study test statistics (two haplotype-based tests, two marker-based tests, and the Transmission Disequilibrium Test-Q5) to detect single nucleotide polymorphism (SNP)/phenotype associations in a linkage-disequilibrium-based candidate gene scan employing a number of SNPs is examined. Power is estimated as a function of realistic parameters expected to affect the likelihood of detecting a significant association: the number of SNPs examined, the scaled recombination size of the region examined, the proportion of variance in the trait attributable to a hidden causative polymorphism within the region, and the number of individuals or families examined. For the different combinations of parameter values, power is estimated from a large number of realizations of a simulated coalescent describing a single random mating population with mutation, random genetic drift, and recombination. This explicit population genetics model results in a distribution of DNA marker heterozygosities and linkage disequilibria that are likely to resemble those expected in actual population samples. The study concludes that (1) marker-based permutation tests are more powerful than simple haplotype-based tests, (2) there is sufficient power to detect the presence of causative polymorphisms of small effect if on the order of 500 individuals are sampled, (3) greater power is achieved by increasing the sample size than by increasing the number of polymorphisms, (4) association studies are generally more powerful than transmission disequilibrium-based tests, and (5) for the range of parameters considered association studies have a low repeatability unless sample sizes are on the order of 500 individuals. Estimates of 4Nc for a number of gene regions and human populations will be of use in determining the density of SNPs that are likely to be required for successful association studies.

Computational Biology↗

Measuring and estimating diagnostic accuracy when there are three ordinal diagnostic groups.

This article studies the problem of measuring and estimating the diagnostic accuracy when there are three ordinal diagnostic groups. We use a receiver operating characteristic (ROC) surface to describe the probabilities of correct classifications into three diagnostic groups based on various sets of diagnostic thresholds of a test and propose to use the entire and the partial volume under the surface to measure the diagnostic accuracy. Mathematical properties and probabilistic interpretations of the proposed measure of diagnostic accuracy are discussed. Under the assumption of normal distributions of the diagnostic test from three diagnostic groups, we present the maximum likelihood estimate to the volume under the ROC surface and give the asymptotic variance to the estimate. We further propose several asymptotic confidence interval estimates to the volume under the ROC surface. The performance of these confidence interval estimates is evaluated in terms of attaining the nominal coverage probability based on a simulation study. In addition, we develop a method of sample size determination to achieve an adequate accuracy of the confidence interval estimate. Finally, we demonstrate the proposed methodology by applying it to the clinical diagnosis of early stage Alzheimer's disease based on the neuropsychological database of the Washington University Alzheimer's Disease Research Center.

Alzheimer Disease↗

Power estimation for the Dorfman-Berbaum-Metz method.

RATIONALE AND OBJECTIVES: The authors describe how to perform power and sample size computations for the Dorfman-Berbaum-Metz method for analyzing multireader receiver operating characteristic (ROC) studies when data from a pilot study or from a previous study similar to the planned study are available. MATERIALS AND METHODS: Power and sample size computations are described in a step-by-step procedure. RESULTS: To illustrate the power computation method we treat 2 studies that did not show a significant difference between modalities as pilot studies for planning future studies. For the future studies we plan to compare the modalities with respect to the mean of the treatment-reader area under the curve (AUC) estimates. We show how to estimate the reader and case sample sizes for each future study to have 80% power to detect a specified difference in modality AUCs. CONCLUSIONS: Application of the power and sample size computation procedure for the Dorfman-Berbaum-Metz method is straightforward. For a given effect size there will be several different reader and case sample size combinations that yield the desired power. It is important that the pilot study or previous study used for the computations be comparable to the planned study with respect to the modalities, reader expertise, case selection, and ratio of normal to abnormal cases.

Analysis of Variance↗

A preliminary evaluation of causal models of male and female acquisition of pilot skills.

Based on a previous study, a causal model of acquisition of pilot job knowledge and flying skills was tested on separate samples of male and female students. Causal model parameters were estimated separately for each sample and, due to the small sample size for women, no between-groups statistical tests were conducted. The results are viewed as tentative because of the small sample of female students; however, the path coefficient parameter estimates are still useful. The model showed a direct influence of general cognitive ability (g) on the acquisition of job knowledge and an indirect influence on the acquisition of flying skills. The direct and indirect influence of cognitive ability on flying skills was a little stronger for women than for men. Additionally, the path between prior job knowledge (JKp) and flying performance was somewhat stronger for women than for men. Consistent with previous findings, the influence of early flying skills on later flying skills was very strong. No argument for a sex-separated training syllabus is supported.

Adult↗

Markov chain Monte Carlo analysis of human Y-chromosome microsatellites provides evidence of biased mutation.

We describe a Markov Chain Monte Carlo analysis of five human Y- chromosome microsatellite polymorphisms based on samples from five diverse populations. Our analysis provides strong evidence for mutational bias favoring increase in length at all loci. Estimates of population coalescent times and population size from our two largest samples, one African and one European, suggest that the African population is older but smaller and that the English East Anglian population has undergone significant expansion, being larger but younger. We conclude that Markov Chain Monte Carlo analysis of microsatellite haplotypes can uncover information not apparent when the microsatellites are considered independently. Incorporation of population size as a variable should allow us to estimate the timing and magnitude of major historical population trends.

Algorithms↗

Design and analysis of phase I clinical trials.

The Phase I clinical trial is a study intended to estimate the so-called maximum tolerable dose (MTD) of a new drug. Although there exists more or less a standard type of design for such trials, its development has been largely ad hoc. As usually implemented, the trial design has no intrinsic property that provides a generally satisfactory basis for estimation of the MTD. In this paper, the standard design and several simple alternatives are compared with regard to the conservativeness of the design and with regard to point and interval estimation of an MTD (33rd percentile) with small sample sizes. Using a Markov chain representation, we found several designs to be nearly as conservative as the standard design in terms of the proportion of patients entered at higher dose levels. In Monte Carlo simulations, two two-stage designs are found to provide reduced bias in maximum likelihood estimation of the MTD in less than ideal dose-response settings. Of the three methods considered for determining confidence intervals--the delta method, a method based on Fieller's theorem, and a likelihood ratio method--none was able to provide both usefully narrow intervals and coverage probabilities close to nominal.

Dose-Response Relationship, Drug↗

Synthesis of pharmacokinetic parameters of vancomycin via bootstrap methods.

OBJECTIVE: For the adjustment of individual vancomycin dosages, we estimate the important pharmacokinetic quantities half-life, clearance, and volume of distribution. MATERIAL: To obtain reliable information 293 observations from 244 patients were extracted from 23 published studies on vancomycin. Information about vancomycin's pharmacokinetics out of different sources represents an increase in sample size and, therefore, interpretive power. METHODS: Once the whole of the data had been stratified into a small number of homogeneous clusters based on cofactors, different (robust) estimators (mean, median, Winsorized, and trimmed mean) were calculated for the expected value of the pharmacokinetic parameters of vancomycin within the clusters. Measures of the statistical accuracy such as standard error, bias, mean square error, and confidence interval were estimated via bootstrap methods from large bootstrap sample sizes to compare the quality of the estimators. RESULTS: Due to the homogenization of the data all individual estimator functions yield very similar results and the empirical mean works fairly well as an estimate. The most frequently used estimator with the smallest estimated mean square error was the Winsorized mean.

Adult↗

Modeling exposures for DNA methylation profiles.

We extend the finite mixture model to estimate the association between exposure and latent disease subtype measured by DNA methylation profiles. Estimates from this model are compared with those obtained from the simpler two-phase approach of first clustering the DNA methylation data followed by associating exposure with disease subtype using logistic regression. The two models are fit to data from a study of colorectal adenomas and are compared in a simulation study. Depending on the analytic approach, we obtain different estimates of the odds ratio (OR) and its 95% confidence interval (95% CI) for the association of RBC folate and DNA methylation subtype in colorectal adenomas (OR, 0.31; 95% CI, 0.08-1.26 from the extended finite mixture model; OR, 0.44; 95% CI, 0.15-1.28 from the two-phase approach; n = 58 case subjects). Although our results could be a chance occurrence due to fluctuations from small sample size, we did a simulation study using larger samples and found that differences between the two approaches emerge when there is noise in the cluster analysis. In the naive two-phase approach, the estimate of the OR is biased towards the null, and its SE is underestimated when there is error in the cluster assignment. Estimates from the extended mixture model are unbiased and have the correct SE estimate but may require larger sample sizes for convergence. Thus, when the clusters are not identified with certainty, the extended mixture model is preferred for valid estimation of the OR and CI.

Adenoma↗

A Monte-Carlo estimation of effect size distortion due to significance testing.

A Monte-Carlo study was done with true effect sizes in deviation units ranging from 0 to 2 and a variety of sample sizes. The purpose was to assess the amount of bias created by considering only effect sizes that passed a statistical cut-off criterion of alpha = .05. The deviation values obtained at the .05 level jointly determined by the set effect sizes and sample sizes are presented. This table is useful when summarizing sets of studies to judge whether published results reflect an accurate appraisal of an underlying effect or a distorted estimate expected because significant studies are published and nonsignificant results are not. The table shows that the magnitudes of error are substantial with small sample sizes and inherently small effect sizes. Thus, reviews based on published literature could be misleading and especially so if true effect sizes were close to zero. A researcher should be particularly cautious of small sample sizes showing large effect sizes when larger samples indicate diminishing smaller effects.

Humans↗

Contribution of sampling to the variability of pesticide residue data.

The uneven distribution of pesticide residues among the treated objects leads to an inevitable variability of pesticide residue levels measured in the samples, which may significantly contribute to the combined uncertainty of the analytical results. A total of 8844 unit-crop residue data derived from 57 lots and 19 field trials were evaluated to determine the characteristic features of residue distribution in unit crops and composite samples. The average residue levels and the corresponding coefficient of variation (CV) values obtained for individual units taken from a given lot showed wide variation from lot to lot. There was no significant difference between the CVs of residue levels in sample sets of various unit crops or composite sample populations of different sizes taken from various crops. The CV values for levels of residues taken from individual lots followed normal distribution. Very good correlation was found between the CVs of the parent and sample populations. The experimentally obtained values were very close to those expected on the basis of the central limit theorem. The estimated typical relative standard uncertainties of sampling medium-size crops for pesticide residue analysis in the cases of sample sizes of 5, 10, and 25 were 37, 25, and 16%, respectively.

Algorithms↗

Inferring modes of colonization for pest species using heterozygosity comparisons and a shared-allele test.

Long-range dispersal of a species may involve either a single long-distance movement from a core population or spreading via unobserved intermediate populations. Where the new populations originate as small propagules, genetic drift may be extreme and gene frequency or assignment methods may not prove useful in determining the relation between the core population and outbreak samples. We describe computationally simple resampling methods for use in this situation to distinguish between the different modes of dispersal. First, estimates of heterozygosity can be used to test for direct sampling from the core population and to estimate the effective size of intermediate populations. Second, a test of sharing of alleles, particularly rare alleles, can show whether outbreaks are related to each other rather than arriving as independent samples from the core population. The shared-allele statistic also serves as a genetic distance measure that is appropriate for small samples. These methods were applied to data on a fruit fly pest species, Bactrocera tryoni, which is quarantined from some horticultural areas in Australia. We concluded that the outbreaks in the quarantine zone came from a heterogeneous set of genetically differentiated populations, possibly ones that overwinter in the vicinity of the quarantine zone.

Animals↗

Sizing clinical trials with variable endpoint event rates.

Although many researchers in cardiovascular clinical trials have disciplined themselves to execute sample size calculations in the design of their studies, these computations become difficult in the presence of control group endpoint event rate uncertainty. Recent experience in cardiovascular clinical trials suggests that, although one may know the control group event rate during the design phase of the trial, it can decrease during the trial's execution. Its resultant overestimation can lead to a power reduction with serious consequences for the trial's interpretation. Although the investigators may acknowledge the likelihood that the control group event rate will decrease during the time course of the trial, there is no formal means to adjust the design phase estimate. In this paper, I first formulate the sample size as a function of the control group event rate theta and then I place a proper probability distribution on theta, allowing for the uncertainty in this parameter's value during the course of the study. From this assumption, the sample size itself becomes a random variable, whose expectation and variance are computed. I explore the implications for sample size for various reasonable proper probability distributions on the control group event rate.

Bayes Theorem↗

Stereological methods for quantifying cell surface specializations in epithelia, including a concept for counting desmosomes and hemidesmosomes.

We present stereological procedures for morphometric evaluation of intercellular junctions appearing in ultrathin sections of epithelia. A model representing desmosomes and hemidesmosomes as flat, circular discs differentiated within the plasma membrane of epithelial cells forms a basis for estimating number per unit volume of tissue or per unit area of cell surface. Methods for estimating relative surfaces are also provided. Consideration is given to problems of tissue sampling, varying feature size and finite section thickness. The procedures are improvements over earlier estimates of number per unit area of section or per unit length of membrane. Worked examples of calculations are included and methods are illustrated further by reference to quantitative studies of hamster cheek pouch epithelium during experimental carcinogenesis.

9,10-Dimethyl-1,2-benzanthracene↗

Variability of airborne microflora in a hospital ward within a period of one year.

The aim of the study was to determine the seasonal variability of the airborne microflora in a hospital ward of the pneumonological department, with regard to potential impact on respiratory status of asthmatic patients hospitalized in the ward. Microbiological air sampling was carried out for a period of 1 year from June-May, during work-days, 16-21 days per month. Each day, the air samples were collected twice: in the morning at 09:00 and in the afternoon at 13:00. Air samples were taken with a custom-designed particle-sizing slit sampler enabling estimations of both total and respirable fractions of the microbial aerosol. Air samples for determination of bacteria were taken on blood agar and air samples for determination of fungi were taken on Sabouraud agar. Mean monthly concentrations of total microorganisms (bacteria + fungi) in the air of the examined hospital ward were between 296.1-529.9 cfu/m3. Mean monthly concentrations of airborne bacteria ranged from 257.1-436.3 cfu/m3, with peak values in November and May and the lowest values from December to February. Mean monthly concentrations of airborne fungi showed much greater variation than bacteria and ranged from 9.9-96.1 cfu/m3 with the very distinct peak in November and the lowest value in May. The variations in monthly concentrations of total microorganisms, bacteria and fungi in the air of hospital ward were statistically significant (p < 0.001). The concentrations of total airborne microorganisms, bacteria and fungi recorded in the hospital in the morning were significantly greater compared to those recorded in the afternoon (p < 0.01). The mean monthly values of respirable fraction for total microorganisms were within a range of 17.3-44.4%, for bacteria within a range of 17.2-44.8%, and for fungi within a range of 2.2-39.1%. The most common microorganisms in the air of the examined ward were Gram-positive cocci which accounted for 31.4-46.4% of the total count. Gram-negative bacteria and corynebacteria were less numerous, forming respectively 11.8-27.5% and 9.6-20.0% of the total count. Endospore-forming bacilli and actinomycetes occurred in small proportions, respectively 0.3-3.2% and 0-2.0% of the total count. Fungi formed 7.6-42.5% of the total count. The prevailing species was Aspergillus fumigatus which constituted on average 77.0% of total fungal strains isolated from the air of the hospital ward. A significant decrease of spirographic indices (VC, FEV1) in asthmatic patients hospitalized in the ward, at increase of the concentration of airborne bacteria and/or fungi, was found in 9 out of 24 examined patients (37.5%) and in 19 out of 192 analysed single relationships (9.9%). In conclusion, although bacteria and fungi occurred in the air of the examined hospital ward in relatively low numbers (of the order 10(2) cfu/m3 and 10(1) cfu/m3 respectively), they should be considered as a possible cause of asthma exacerbations in some patients because of the presence of Aspergillus fumigatus and other potentially pathogenic species.

Adult↗

Inferring linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations.

Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.

Alleles↗