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PubMed1984

The bingo model of survivorship. II: statistical aspects of the bingo model of multiplicity 1 with application to hereditary polyposis of the colon.

Some Mendelian disorders (Huntington chorea, hereditary polyposis coli) are not manifest at birth but show a distribution in the age of onset. Patients at risk fall into three groups. In type I, they are affected when first examined. In type II, they are not affected at one visit, but are at a later visit. Those of type III (who comprise an indistinguishable mixture of those who have, and those who have not, inherited the gene) are never found to be affected. This paper posits a model that the age of onset is logistic. (It is a degenerate bingo model in which competing causes of death may be ignored.) The statistical properties of maximum likelihood estimation (MLE) are explored by Monte Carlo simulation of this logistic function with known arbitrary parameters. Two schemes are used: point-prevalence (or synchronic) data of types I and III, and piecewise longitudinal (diachronic) data; this allows all three types to be included. Samples of various sizes between 25 and 100 are used. While estimates of the parameters are positively biased (especially with small samples), the estimate of the mean appears to be consistent, almost unbiased, and fairly precise, though somewhat larger than the estimates from the lower bound (a fact that calls for some caution in interpreting actual data). The MLE was applied to 109 patients with the Gardner syndrome (GS); measures of variability found by applying MLE to four random subsets of 25 each were compared against the asymptotic estimates. The analysis was also applied to 36 persons with familial polyposis coli (FPC). The mean age of onset in GS and FPC was similar, and since they are rather earlier than is currently believed, it is recommended that regular supervision be started at not later than 10 years of age.

Adolescent↗
PubMed2004

Bayesian estimation of stimulus responses in Poisson spike trains.

A Bayesian method is developed for estimating neural responses to stimuli, using likelihood functions incorporating the assumption that spike trains follow either pure Poisson statistics or Poisson statistics with a refractory period. The Bayesian and standard estimates of the mean and variance of responses are similar and asymptotically converge as the size of the data sample increases. However, the Bayesian estimate of the variance of the variance is much lower. This allows the Bayesian method to provide more precise interval estimates of responses. Sensitivity of the Bayesian method to the Poisson assumption was tested by conducting simulations perturbing the Poisson spike trains with noise. This did not affect Bayesian estimates of mean and variance to a significant degree, indicating that the Bayesian method is robust. The Bayesian estimates were less affected by the presence of noise than estimates provided by the standard method.

Action Potentials↗
PubMed1999

Annual and seasonal variation of tick-borne encephalitis virus (TBEV) prevalence in ticks in selected hot spot areas in Germany using a nRT-PCR: results from 1997 and 1998.

The prevalence of tick-borne encephalitis virus (TBEV) in Ixodes ricinus tick populations in endemic areas of Germany with the highest TBE risk is unknown. Annual and seasonal differences in TBEV prevalence have also not been studied. Against this background, in May 1997 we started a systematic virus surveillance programme in ticks collected in locations known to have a high incidence of autochthonous TBE cases. These were 5 locations in Baden-Württemberg (Black Forest) and 8 locations in Bavaria (surrounding Passau). Field-collected ticks were randomly assigned to pools of 10 adults or 20 nymphs, respectively. The tick pools were tested for the presence of TBEV-RNA using a newly developed, sensitive nested reverse transcriptase polymerase chain reaction assay (nRT-PCR). The primer pairs were selected from the 5'-terminal noncoding region, a highly conserved part of the virus. The specificity was tested by computer homology searches of sequences, as well as by sequencing of the first and the second amplificates, by Southern blot hybridisation with a DIG-labelled oligonucleotide probe, and by restriction enzyme analysis. The method has proved to be very sensitive, with a detection limit of 20 fg of TBEV RNA per PCR run, or a single positive tick. Based on biostatistical considerations a sample size of at least 1000 ticks per estimation point was chosen. The estimated TBEV prevalence and confidence intervals (CI) were calculated from the nRT-PCR results of pooled samples (10 adults or 20 nymphs) using appropriate formulae for pooled testing. In order to identify the estimated TBEV prevalence as well as to assess the influence of annual and seasonal factors on TBEV prevalence, ticks were sampled twice a year (May and September) in 1997 and 1998 at exactly identical sites. These sites were selected because they were known to have had the highest incidence of autochthonous TBE cases during the previous 10 years. On sampling days, relevant local meteorological data were also noted. In total, 8500 I. ricinus ticks were investigated in this study, 4270 (3540 nymphs, 730 adults) from the Black Forest habitats, and 4230 (3680 nymphs, 550 adults) from the Bavarian locations. In the foci near Freiburg (Black Forest), the estimated virus prevalence was relatively high in the whole tick population, during 1997 with only slight seasonal differences [3.4% (confidence interval, CI, 2.3-4.8%) in May and 2.9% (CI 1.7-4.5%) in September]. In contrast, in 1998, in the same foci the estimated TBEV prevalence was considerably lower [1.1% (CI 0.5-2.0%) in May and 0.6% (CI 0.2-1.4%) in September]. Thus, while the seasonal differences again remained low, the annual variation was marked. In the Bavarian foci in 1997, the estimated virus prevalence of the whole tick population studied was lower than in the Black Forest foci and the seasonal fluctuations were low: in May 1997 0.9% (CI 0.4-1.8%) of the ticks were positive, in September 1.1% (CI 0.5-1.9%). In 1998, in May 2.0% (CI 1.1-3.3%) of the ticks were positive, and in September 1.1% (CI 0.5-2.1%). For the whole study period, every 50th to 100th I. ricinus nymph or adult in the Passau region was calculated to give a positive signal in the nRT-PCR. The TBEV prevalence data indicate that residents and visitors of areas in Germany known for high endemic activity take a significant risk of contracting TBEV infection, if bitten by ticks. In addition, the data suggest that annual fluctuations may exist in the whole tick population studied. Seasonal fluctuations of the virus prevalence in ticks were small.

Adult↗
PubMed1983

Robust estimation of population size in closed animal populations from capture-recapture experiments.

In this paper the problem of finding robust estimators of population size in closed K-sample capture-recapture experiments is considered. Particular attention is paid to models where heterogeneity of capture probabilities is allowed. First, a general estimation procedure is given which does not depend on any assumptions about the form of the distribution of capture probabilities. This is followed by a detailed discussion of the usefulness of the generalized jackknife technique to reduce bias. Numerical comparisons of the bias and variance of various estimators are given. Finally, a general discussion is given with several recommendations on estimators to be used in practice.

Animals↗
PubMed2006

Accuracy of hepatitis C virus core antigen testing in pools among seroconverters.

BACKGROUND: Screening blood units for hepatitis C virus (HCV) with nucleic acid testing (NAT) reduces the risk associated with the long "window period" (8-9 weeks) after HCV infection. The feasibility of adding the HCV core antigen assay in pools to the existing anti-HCV individual screening was examined as an alternative of NAT, for early detection of HCV. STUDY DESIGN AND METHODS: Eighteen HCV seroconversion panels were tested for HCV antibodies, HCV antigen, and HCV RNA. Each sample was tested for HCV antigen individually and in pools of 3, 6, and 12. Statistical analyses included estimation of time until detection of the first positive HCV antigen bleed in each pool size, with a locally weighted regression (LOWESS) model. Sensitivity was calculated compared to NAT. RESULTS: Detection of HCV antigen in individual samples and in pools of 3 and 6 significantly preceded the detection of antibodies by 63, 53, and 46 days, respectively. Although the sensitivity of the HCV antigen test decreased with the increase in pool size, the estimated overall sensitivity of the "two-stage" antigen and antibody screening (where NAT of individual samples was the gold standard) was not significantly different between individual and the different pool sizes. CONCLUSION: Screening for HCV antigen in pools of 6 can be considered an efficient and easier-to-implement alternative to the costly NAT for identifying blood donors in the seroconversion period. It may offer a cost-effective approach in resource utilization in poor countries, that, after the implementation of HCV antibody testing, want to further improve blood safety.

Blood Donors↗
PubMed1991

Sample size and dimensionality in multivariate classification: implications for body surface potential mapping.

This paper presents empirically determined guidelines for specifying the number of features appropriate for multivariate classification studies for given sample sizes. Sample size was considered adequate if the mean distance between two sample sets, taken from the same continuous multivariate distribution and projected onto the best separating direction, remained below a prescribed level. To quantitate the sample size requirement, homogeneity of sample set pairs of equal size. N, taken from the same continuous multivariate distribution was studied as a function of dimensionality. M. Homogeneity was characterized by the maximum absolute distances (Dmax) between the corresponding pairs of empirical cumulative probability distributions on the best separating projection. Computer generated data sets were used to estimate the cumulative probability distribution, P(D)M.N, for sample sizes, N, ranging from 5 to 100 and the dimensionality, M, ranging from 1 to 4. An empirical relationship between the estimated step-polygons and the Kolmogorov type one dimensional limiting distribution L(z) has been established. Based on the sample size data of 34 key papers on clinical body surface potential mapping (BSPM) it is noted that in 30% of the cases only one, and in 6% of the cases only two parameters could be used for statistical group representation to ensure a reasonable reliability (Dmax less than 0.2). In 56% of the published cases the sample sizes could not guarantee this reliability even for one feature or parameter.

Computer Simulation↗
PubMed2007

Confidence intervals for the amount of heterogeneity in meta-analysis.

Effect size estimates to be combined in a systematic review are often found to be more variable than one would expect based on sampling differences alone. This is usually interpreted as evidence that the effect sizes are heterogeneous. A random-effects model is then often used to account for the heterogeneity in the effect sizes. A novel method for constructing confidence intervals for the amount of heterogeneity in the effect sizes is proposed that guarantees nominal coverage probabilities even in small samples when model assumptions are satisfied. A variety of existing approaches for constructing such confidence intervals are summarized and the various methods are applied to an example to illustrate their use. A simulation study reveals that the newly proposed method yields the most accurate coverage probabilities under conditions more analogous to practice, where assumptions about normally distributed effect size estimates and known sampling variances only hold asymptotically.

Biometry↗
PubMed2001

Frequency-Dependent Streaming Potentials.

An experimental apparatus and data acquisition system was constructed to measure the streaming potential coupling coefficients as a function of frequency. The purpose of the experiments was to measure, for the first time, the real and imaginary portion of streaming potentials. In addition, the measured frequency range was extended beyond any previous measurements. Frequency-dependent streaming potential experiments were conducted on one glass capillary and two porous glass filters. The sample pore diameters ranged from 1 mm to 34 µm. Two frequency-dependent models (Packard and Pride) were compared to the data. Both Pride's and Packard's models have a good fit to the experimental data in the low- and intermediate-frequency regime. In the high-frequency regime, the data fit the theory after being corrected for capacitance effects of the experimental setup. Pride's generalized model appears to have the ability to more accurately estimate pore sizes in the porous medium samples. Packard's model has one unknown model parameter while Pride's model has four unknown model parameters, two of which can be independently determined experimentally. Pride's additional parameters may allow for a determination of permeability. Copyright 2001 Academic Press.

Journal Article↗
PubMedDate not supplied

Short metal capillary columns packed with polymer-coated fibrous materials in high-temperature gas chromatography.

The high-temperature gas chromatographic (GC) separation of several semivolatile compounds is studied with a short metal capillary column packed with fibrous material, having a polydimethylsiloxane coating thereon. Taking advantage of the excellent heat-resistance of the fiber and also the combination of the surface-deactivated metal capillary, a temperature-programmed separation up to 450 degrees C is successfully demonstrated for the separation of polymer standard samples. The average molecular weight of the commercially-available polymer standard samples for size exclusion chromatography (SEC) is estimated by high-temperature GC analysis and compared with the nominal value determined by a conventional SEC method. Although a slight deviation for the number-average molecular weight is observed between the GC and SEC analysis, the data for the weight-average molecular weight shows a good agreement in these methods. The results also suggest the future possibility of the fiber-packed metal capillary as a miniaturized GC column with an increased sample loading capacity.

Journal Article↗
PubMed2005

How effective for fold recognition is a potential of mean force that includes relative orientations between contacting residues in proteins?

We estimate the statistical distribution of relative orientations between contacting residues from a database of protein structures and evaluate the potential of mean force for relative orientations between contacting residues. Polar angles and Euler angles are used to specify two degrees of directional freedom and three degrees of rotational freedom for the orientation of one residue relative to another in contacting residues, respectively. A local coordinate system affixed to each residue based only on main chain atoms is defined for fold recognition. The number of contacting residue pairs in the database will severely limit the resolution of the statistical distribution of relative orientations, if it is estimated by dividing space into cells and counting samples observed in each cell. To overcome such problems and to evaluate the fully anisotropic distributions of relative orientations as a function of polar and Euler angles, we choose a method in which the observed distribution is represented as a sum of delta functions each of which represents the observed orientation of a contacting residue, and is evaluated as a series expansion of spherical harmonics functions. The sample size limits the frequencies of modes whose expansion coefficients can be reliably estimated. High frequency modes are statistically less reliable than low frequency modes. Each expansion coefficient is separately corrected for the sample size according to suggestions from a Bayesian statistical analysis. As a result, many expansion terms can be utilized to evaluate orientational distributions. Also, unlike other orientational potentials, the uniform distribution is used for a reference distribution in evaluating a potential of mean force for each type of contacting residue pair from its orientational distribution, so that residue-residue orientations can be fully evaluated. It is shown by using decoy sets that the discrimination power of the orientational potential in fold recognition increases by taking account of the Euler angle dependencies and becomes comparable to that of a simple contact potential, and that the total energy potential taken as a simple sum of contact, orientation, and (phi,psi) potentials performs well to identify the native folds.

Journal Article↗
PubMed1998

Application of GEE procedures for sample size calculations in repeated measures experiments.

Derivation of the minimum sample size is an important consideration in an applied research effort. When the outcome is measured at a single time point, sample size procedures are well known and widely applied. The corresponding situation for longitudinal designs, however, is less well developed. In this paper, we adapt the generalized estimating equation (GEE) approach of Liang and Zeger to sample size calculations for discrete and continuous outcome variables. The non-central version of the Wald Chi 2 test is considered. We use the damped exponential family of correlation structures described in Muñoz et al. for the 'working' correlation matrix among the repeated measures. We present a table of minimum sample sizes for binary outcomes, and discuss extensions that account for unequal allocation, staggered entry and loss to follow-up.

Bias↗
PubMed1991

Sampling strategies for toxic air contaminants.

Annual concentrations of toxic air contaminants are of primary concern from the perspective of chronic human exposure assessment and risk analysis. Despite recent advances in air quality monitoring technology, resource and technical constraints often impose limitations on the availability of a sufficient number of ambient concentration measurements for performing environmental risk analysis. Therefore, sample size limitations, representativeness of data, and uncertainties in the estimated annual mean concentration must be examined before performing quantitative risk analysis. In this paper, we discuss several factors that need to be considered in designing field-sampling programs for toxic air contaminants and in verifying compliance with environmental regulations. Specifically, we examine the behavior of SO2, TSP, and CO data as surrogates for toxic air contaminants and as examples of point source, area source, and line source-dominated pollutants, respectively, from the standpoint of sampling design. We demonstrate the use of bootstrap resampling method and normal theory in estimating the annual mean concentration and its 95% confidence bounds from limited sampling data, and illustrate the application of operating characteristic (OC) curves to determine optimum sample size and other sampling strategies. We also outline a statistical procedure, based on a one-sided t-test, that utilizes the sampled concentration data for evaluating whether a sampling site is compliance with relevant ambient guideline concentrations for toxic air contaminants.

Air Pollutants↗
PubMed2001

On estimating the proportion of variance in a phenotypic trait attributable to a measured locus.

The measured genotype approach can be used to estimate the variance contributions of specific candidate loci to quantitative traits of interest. We show here that both the naive estimate of measured-locus heritability, obtained by invoking infinite-sample theory, and an estimate obtained from a bias-corrected variance estimate based on finite-sample theory, produce biased estimates of heritability. We identify the sources of bias, and quantify their effects. The two sources of bias are: (1) the estimation of heritability from population samples as the ratio of two variances, and (2) the existence of sampling error. We show that neither heritability estimator is less biased (in absolute value) than the other in all situations, and the choice of an ideal estimator is therefore a function of the sample size and magnitude of the locus-specific contribution to the overall phenotypic variance. In most cases the bias is small, so that the practical implications of using either estimator are expected to be minimal.

Bias↗
PubMed2005

Effect of item redundancy on Rasch item and person estimates.

One of the assumptions of many latent trait models is local independence. This assumption specifies that, after controlling for the underlying trait, item responses are independent. Given the lack of studies of model robustness against such violations, it appears that this assumption is frequently taken for granted. Therefore, this study investigated the robustness of Rasch item and person estimates with simulated data under varying number of items, sample sizes, and levels of item redundancy. Item and person reliabilities, the standard deviations of the person and item estimates, the root mean squared differences and mean signed differences among person and item estimates, the correlations between person estimates, and the percentage of person estimates shifting by more than .50 logits were used to evaluate the impact of item redundancy. Both norm and criterion-reference interpretations may be influenced by the imputation of redundancy into the data. However, it appears that the amount of redundancy needs to be considerable before such interpretations would be adversely impacted. Suggestions for further simulation research are provided.

Humans↗
PubMed1996

Estimating gene flow in island populations.

A new method is presented for estimating the rate of gene flow into island populations using the distribution of alleles in samples from a number of islands. The pseudo maximum likelihood estimator (PMLE) that we derive may be applied to species with either discrete or continuous generation times. For Wright's discrete-generation island model, the method provides an estimate of theta = 2Nm where N is the (haploid) population size on each island and m is the fraction of individuals replaced by immigrants in each generation. For a continuous-generation island model, the corresponding parameter theta is the ratio of the immigration rate phi to the individual birth rate lambda. Monte Carlo simulations are used to compare the statistical properties of the PMLE with those of two alternative estimators of theta derived from Wright's F-statistics. The PMLE is shown to have greatest efficiency (least mean square error) in most cases for a wide range of sample sizes and parameter values. The PMLE is applied to estimate theta using mtDNA haplotypes and allozymes for subdivided populations of African elephants and Channel Island foxes.

Alleles↗
PubMed2005

Errors in the estimation of the variance: implications for multiple-probability fluctuation analysis.

Synapses play a crucial role in information processing in the brain. Amplitude fluctuations of synaptic responses can be used to extract information about the mechanisms underlying synaptic transmission and its modulation. In particular, multiple-probability fluctuation analysis can be used to estimate the number of functional release sites, the mean probability of release and the amplitude of the mean quantal response from fits of the relationship between the variance and mean amplitude of postsynaptic responses, recorded at different probabilities. To determine these quantal parameters, calculate their uncertainties and the goodness-of-fit of the model, it is important to weight the contribution of each data point in the fitting procedure. We therefore investigated the errors associated with measuring the variance by determining the best estimators of the variance of the variance and have used simulations of synaptic transmission to test their accuracy and reliability under different experimental conditions. For central synapses, which generally have a low number of release sites, the amplitude distribution of synaptic responses is not normal, thus the use of a theoretical variance of the variance based on the normal assumption is not a good approximation. However, appropriate estimators can be derived for the population and for limited sample sizes using a more general expression that involves higher moments and introducing unbiased estimators based on the h-statistics. Our results are likely to be relevant for various applications of fluctuation analysis when few channels or release sites are present.

Animals↗
PubMed1997

An examination of methods for sample size recalculation during an experiment.

In designing experiments, investigators frequently can specify an important effect that they wish to detect with high power, without the ability to provide an equally certain assessment of the variance of the response. If the experiment is designed based on a guess of the variance, an under-powered study may result. To remedy this problem, there have been several procedures proposed that obtain estimates of the variance from the data as they accrue and then recalculate the sample size accordingly. One class of procedures is fully sequential in that it assesses after each response whether the current sample size yields the desired power based on the current estimate of the variance. This approach is efficient, but it is not practical or advisable in many situations. Another class of procedures involves only two or three stages of sampling and recalculates the sample size based on the observed variance at designated times, perhaps coinciding with interim efficacy analyses. The two-stage approach can result in substantial oversampling, but it is feasible in many situations, whereas the three-stage approach corrects the problem of oversampling, but is less feasible. We propose a procedure that aims to combine the advantages of both the fully sequential and the two-stage approaches. This quasi-sequential procedure involves only two stages of sampling and it applies to the stopping rule from the fully sequential procedure to data beyond the initial sample which we obtain via multiple imputation. We show through simulations that when the initial sample size is substantially less than the correct sample size, the mean squared error of the final sample size calculated from the quasi-sequential procedure can be considerably less than that from the two-stage procedure. We compare the distributions of these recalculated sample sizes and discuss our findings for alternative procedures, as well.

Anti-HIV Agents↗
PubMed2006

Minimum sample size requirements for bone density precision assessment produce inconsistency in clinical monitoring.

INTRODUCTION: Detection of change during bone mineral density (BMD) monitoring is affected by test precision. The International Society of Clinical Densitometry (ISCD) recommends that each center determine precision error using repeat measurements in 30 subjects (or an equivalent method providing 30 degrees of freedom). METHODS: We hypothesized that this sample size may be too small for a robust precision estimate, which could affect the performance of BMD monitoring in clinical practice. Replicate measurements of the spine and total hip (198 spine and 193 hip scan pairs) were obtained (interval 6+/-5 days). The sample was randomly divided into six groups of 30 patients each. Root mean square standard deviation (RMS-SD in g/cm(2)) and coefficient of variation (RMS-CV in %) precision errors and corresponding 95% least significant change (LSC) were calculated for each group and the pooled sample. LSC cutoffs were applied to 1,420 individuals from the Manitoba Bone Density Program who had follow-up measurements on the same instrument (interval 21+/-9 months). While the pooled spine RMS-SD was 0.017 and pooled hip RMS-SD was 0.009 g/cm(2), sample sizes of 30 gave a range of RMS-SD point estimates from 0.012 to 0.021 for the spine and from 0.008 to 0.012 for the hip. RESULTS: When the respective LSC cutoffs were applied to the 1,420 follow-up scan pairs, the fraction of patients categorized with significant change in the spine varied from 20.7% to 46.0%; four of the six LSCs based upon 30 subjects gave fractions significantly different from the pooled LSC of 30.7%. Significant change fractions for the hip varied from 31.1% to 51.1%; two of the six LSCs based upon 30 subjects gave fractions significantly different from the pooled LSC of 40.1%. Similar results were obtained using relative precision errors. CONCLUSION: BMD precision studies using a sample size of 30 are insufficient to reliably characterize precision error or change during clinical monitoring.

Absorptiometry, Photon↗