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Results for “Sample size estimation”

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At least 631 records · Page 35Linked to original sources
PubMed1994

Determining the size of a cross-sectional sample to estimate the age-specific incidence of an irreversible disease.

The design of a cross-sectional survey to estimate the age-specific incidence of an irreversible disease is considered, where the incidence rate is not changing over time and the risk of mortality is not affected by the onset of disease. The sample is assumed to give information on the current age and disease status of individuals, but not on age at onset of the disease. We consider the problem of determining overall sample size in this context, as well as how best to choose the distribution of sampling across various age groups. These issues are considered with the aim of obtaining incidence estimates achieving acceptable levels of precision. The proposed methods are illustrated by measles incidence estimation.

Adolescent↗
PubMed1992

Correlated binomial variates: properties of estimator of intraclass correlation and its effect on sample size calculation.

In group randomized studies, the sample size calculations are complicated by within group (worksite, community, etc.) correlation. We compare by simulation the moment method and the more standard ANOVA method of estimating the intraclass correlation. We find the former is less biased for a small to moderate number of clusters but the difference disappears when the appropriate degree of freedom is used for the ANOVA estimator. We propose a simulation approach for sample size determination and illustrate it with an example.

Analysis of Variance↗
PubMedDate not supplied

Effectiveness research and implications for study design: sample size and statistical power.

Most clinical trials have started to incorporate more broadly defined outcome measures, such as health-related quality of life, to complement clinical status measures as well as direct costs and cost-effectiveness analyses. Contrasting a broad range of outcome and cost measures, we analyze the implications for sample sizes and study design using data from prior mental health and primary care studies that span a wide range of practice settings, patient populations, and geographic areas. While meaningful clinical symptomatic differences are often detectable with sample sizes of well under 100 per cell, detecting even large changes in health-related quality of life generally requires several hundred observations per cell. Reasonable precision in cost estimates usually requires sample sizes in the thousands. Very few clinical trials or observational effectiveness studies that incorporate quality of life or cost measures have such sample sizes, resulting in many (unreported) null findings and, due to publication biases favoring significant results, scientific publications that exaggerate true effects. It raises issues for the general direction of clinical trials and effectiveness studies, as well as for how cost and health-related quality of life results based on small studies should be dealt with in publications.

Clinical Trials as Topic↗
PubMed1999

Classifier design for computer-aided diagnosis: effects of finite sample size on the mean performance of classical and neural network classifiers.

Classifier design is one of the key steps in the development of computer-aided diagnosis (CAD) algorithms. A classifier is designed with case samples drawn from the patient population. Generally, the sample size available for classifier design is limited, which introduces variance and bias into the performance of the trained classifier, relative to that obtained with an infinite sample size. For CAD applications, a commonly used performance index for a classifier is the area, Az, under the receiver operating characteristic (ROC) curve. We have conducted a computer simulation study to investigate the dependence of the mean performance, in terms of Az, on design sample size for a linear discriminant and two nonlinear classifiers, the quadratic discriminant and the backpropagation neural network (ANN). The performances of the classifiers were compared for four types of class distributions that have specific properties: multivariate normal distributions with equal covariance matrices and unequal means, unequal covariance matrices and unequal means, and unequal covariance matrices and equal means, and a feature space where the two classes were uniformly distributed in disjoint checkerboard regions. We evaluated the performances of the classifiers in feature spaces of dimensionality ranging from 3 to 15, and design sample sizes from 20 to 800 per class. The dependence of the resubstitution and hold-out performance on design (training) sample size (Nt) was investigated. For multivariate normal class distributions with equal covariance matrices, the linear discriminant is the optimal classifier. It was found that its Az-versus-1/Nt curves can be closely approximated by linear dependences over the range of sample sizes studied. In the feature spaces with unequal covariance matrices where the quadratic discriminant is optimal, the linear discriminant is inferior to the quadratic discriminant or the ANN when the design sample size is large. However, when the design sample is small, a relatively simple classifier, such as the linear discriminant or an ANN with very few hidden nodes, may be preferred because performance bias increases with the complexity of the classifier. In the regime where the classifier performance is dominated by the 1/Nt term, the performance in the limit of infinite sample size can be estimated as the intercept (1/Nt= 0) of a linear regression of Az versus 1/Nt. The understanding of the performance of the classifiers under the constraint of a finite design sample size is expected to facilitate the selection of a proper classifier for a given classification task and the design of an efficient resampling scheme.

Computer Simulation↗
PubMed2000

A Simple Colloidal Synthesis for Gram-Quantity Production of Water-Soluble ZnS Nanocrystal Powders.

A simple, inexpensive, and reproducible procedure is described for large-scale synthesis of highly stable nanocrystalline ZnS powders. Cysteine-capped ZnS nanocrystals (NCs) were produced by a colloidal aqueous synthesis, employing a ligand-competition mechanism in which sulfide was introduced into a preformed zinc-cysteine solution. The synthesis procedure resulted in highly concentrated ZnS NC solutions ( approximately 100 mM) which could be ethanol-precipitated, redissolved, and dried to produce fine powders stable for more than 30 months at 4 degrees C. The NC powders were readily dissolved in aqueous solvents to concentrations as high as 300 mM. ZnS NCs could be prepared without cysteine capping, but only at extremely dilute concentrations ( approximately 0.2 mM ZnSO(4)) as per Sooklal et al. J. Phys. Chem. 100, 4551 (1996). The 30-month-old ZnS NC powders retained their original optical and photocatalytic properties and could be handled much like routine shelf chemicals, unaffected by ambient air or moderate moisture and temperature. UV/vis absorption spectroscopy showed band gap energies (E(g)) ranging from 4.82 eV (257 nm lambda(max)) to 4.47 eV (277 nm lambda(max)) for ZnS samples prepared with 0.25-2.0 initial sulfide ratios (as compared to zinc). Samples stored at 4 degrees C for 30 months showed equivalent band gap energies and spectral profiles. The average NC particle size was estimated to be 6.08+/-0.76 nm by high-resolution transmission electron microscopy. Selected-area electron diffraction and X-ray diffraction analyses concurred in suggesting a hexagonal crystal structure, with diffractions near d=3.1, 1.9, and 1.6 Å. The average NC composition of size-fractionated samples was estimated to be Cys(1)Zn(7)S(6). p-Nitrophenol, a model organic, was photocatalytically degraded using 30-month-old ZnS NC powders dissolved in an aqueous buffer. Rates of degradation (first-order rate constant k=0.261 min(-1); t(1/2)=2.66 min) were comparable to those of experiments using freshly prepared ZnS NCs (first-order rate constant k=0.247 min(-1); t(1/2)=2.80 min), further demonstrating the long-term stability of thus-produced NC powders. Copyright 2000 Academic Press.

Journal Article↗
PubMed2000

Sample size tables for receiver operating characteristic studies.

OBJECTIVE: I provide researchers with tables of sample size for multiobserver receiver operating characteristic (ROC) studies that compare the diagnostic accuracies of two imaging techniques. MATERIALS AND METHODS: I computed the number of patients and observers needed as a function of five parameters: the measure of diagnostic accuracy (area under the ROC curve, sensitivity at a false-positive rate </= 0.10, or specificity at a false-negative rate </= 0.10), conjectured level of accuracy, suspected difference in accuracy between the two imaging techniques, observer variability, and ratio of patients without to patients with the condition. RESULTS: The numbers of patients and observers required vary dramatically with these five parameters, increasing with more refined measures of accuracy, with lower accuracy levels, with smaller suspected differences, with greater observer variability, and with less balanced designs. The number of patients required for a study can be reduced by increasing the number of observers, and vice versa. When the intra- and interobserver variability is large, a study design with just four observers is usually inadequate. CONCLUSION: Many factors must be considered when determining the appropriate sample sizes for multiobserver ROC studies. My tables serve only as initial ballpark estimates. Investigators should compute sample size using parameters that reflect their clinical application.

ROC Curve↗
PubMed1985

On pooling across strata when frequency matching has been followed in a cohort study.

In a study designed to assess the relationship between a dichotomous exposure and the eventual occurrence of a dichotomous outcome, frequency matching has been proposed as a way to balance the exposure cohorts with respect to the sampling distribution of potential confounding factors. This paper discusses the pooled estimator for the log relative risk, and provides an estimator for its variance which takes into account the dependency in the pooled outcomes induced by frequency matching. The pooled estimator has asymptotic relative efficiency less than but close to 1, relative to the usual, inverse variance weighted, stratified estimator. Simulations suggest, however, that the pooled estimator is likely to outperform the stratified estimator when samples are of moderate size. This estimator carries the added advantage that it consistently estimates a meaningful population parameter under heterogeneity of the relative risk across strata.

Analysis of Variance↗
PubMed1994

Population screening for carrier status: effects of test limitations on precision of carrier prevalence rates.

Because of genetic heterogeneity and ambiguity of test results, only rarely will carrier screening identify all carriers of a given autosomal recessive disorder. However, the fraction of carriers identified by the test can be estimated in a case frequency study. The population carrier rate then is the rate observed in a population screening study divided by the fraction of all defective alleles detected by the screening test, estimated in the case frequency study. For example, suppose 3% of a population are found to carry the delta F508 mutation for cystic fibrosis (CF) during population screening. If a case frequency study in this same population finds that 75% of the alleles of CF cases represent the delta F508 mutation, then the estimated population carrier rate is 4% (= .03/.75). The precision of this estimate involves the precision of both the fraction of carriers detected in the case frequency study and the proportion of carriers observed in the population screening study. Standard formulae for estimating the confidence interval and sample size consider only the variability in the population screening study. Since these formulae underestimate the true variability of the estimate of the population carrier rate, the sample size calculated for a population screening study is also underestimated. We present formulae which incorporate the variability in both factors, and illustrate the effect of this additional variability on confidence limits for estimates and sample size when planning a study.

Biometry↗
PubMed1999

A random coefficient degradation model with random sample size.

In testing product reliability, there is often a critical cutoff level that determines whether a specimen is classified as "failed." One consequence is that the number of degradation data collected varies from specimen to specimen. The information of random sample size should be included in the model, and our study shows that it can be influential in estimating model parameters. Two-stage least squares (LS) and maximum modified likelihood (MML) estimation, which both assume fixed sample sizes, are commonly used for estimating parameters in the repeated measurements models typically applied to degradation data. However, the LS estimate is not consistent in the case of random sample sizes. This article derives the likelihood for the random sample size model and suggests using maximum likelihood (ML) for parameter estimation. Our simulation studies show that ML estimates have smaller biases and variances compared to the LS and MML estimates. All estimation methods can be greatly improved if the number of specimens increases from 5 to 10. A data set from a semiconductor application is used to illustrate our methods.

Computer Simulation↗
PubMed1983

Regional differences in the distribution of dividing cells in hamster cheek pouch epithelium.

Examination of vinblastine-arrested metaphase figures in sections from the medial wall of 15 hamster cheek pouches showed that: (1) the distribution of dividing cells was non-random and (2) mitotic activity declined in an anteroposterior direction. Although there was some variation between different pouches these features were statistically significant (P less than 0.05) in individual pouches from half the animals and highly significant (P less than 0.005) when the data from all pouches were pooled. The average sample size required to determine a mitotic index representative of the whole length of the pouch was equivalent to approximately 32 mm of surface length of epithelium or 4562 basal cells. This estimate exceeds the sample size generally examined and it is suggested that inadequate sampling could account for some of the inconsistencies in the literature on hamster cheek pouch cell kinetic data.

Animals↗
PubMed2001

Estimation of admixture proportions: a likelihood-based approach using Markov chain Monte Carlo.

When populations are separated for long periods and then brought into contact for a brief episode in part of their range, this can result in genetic admixture. To analyze this type of event we considered a simple model under which two parental populations (P1 and P2) mix and create a hybrid population (H). After that event, the three populations evolve under pure drift without exchange during T generations. We developed a new method, which allows the simultaneous estimation of the time since the admixture event (scaled by the population size t(i) = T/N(i), where N(i) is the effective population size of population i) and the contribution of one of two parental populations (which we call p1). This method takes into account drift since the admixture event, variation caused by sampling, and uncertainty in the estimation of the ancestral allele frequencies. The method is tested on simulated data sets and then applied to a human data set. We find that (i) for single-locus data, point estimates are poor indicators of the real admixture proportions even when there are many alleles; (ii) biallelic loci provide little information about the admixture proportion and the time since admixture, even for very small amounts of drift, but can be powerful when many loci are used; (iii) the precision of the parameters' estimates increases with sample size n = 50 vs. n = 200 but this effect is larger for the t(i)'s than for p1; and (iv) the increase in precision provided by multiple loci is quite large, even when there is substantial drift (we found, for instance, that it is preferable to use five loci than one locus, even when drift is 100 times larger for the five loci). Our analysis of a previously studied human data set illustrates that the joint estimation of drift and p1 can provide additional insights into the data.

Bayes Theorem↗
PubMed2005

A Bayesian approach on sample size calculation for comparing means.

In clinical research, parameters required for sample size calculation are usually unknown. A typical approach is to use estimates from some pilot studies as the true parameters in the calculation. This approach, however, does not take into consideration sampling error. Thus, the resulting sample size could be misleading if the sampling error is substantial. As an alternative, we suggest a Bayesian approach with noninformative prior to reflect the uncertainty of the parameters induced by the sampling error. Based on the informative prior and data from pilot samples, the Bayesian estimators based on appropriate loss functions can be obtained. Then, the traditional sample size calculation procedure can be carried out using the Bayesian estimates instead of the frequentist estimates. The results indicate that the sample size obtained using the Bayesian approach differs from the traditional sample size obtained by a constant inflation factor, which is purely determined by the size of the pilot study. An example is given for illustration purposes.

Aged↗
PubMed1995

Microbiologic evaluation of carcasses before and after washing in a beef slaughter plant.

The effect of washing on the bacterial contamination of beef carcasses in a modern abattoir was evaluated. Twenty-six carcasses were evaluated at the end of the slaughter process before and after washing, and 13 other carcasses were evaluated only after being washed. An excision sample (5 x 5 x 0.5 cm) was collected from 10 sites on each carcass immediately before washing and at an adjacent site immediately after washing. Aerobic bacterial colonies were enumerated, using hydrophobic grid membrane filter technology. After washing, the log10 of the most probable number of growth units/cm2 decreased (P < 0.01) at the lateral rump site, increased (P < 0.01) at the thorax and neck sites, but was unchanged at the other 7 sites, compared with before washing. The sample size required to estimate, within 0.5 log10 units, the mean log10 most probable number of growth units/cm2 at a site for use in future group-carcass evaluations was determined and compared with a previously used sample size definition. It was concluded that the washing process described did not result in a major change in the bacterial contamination of carcasses.

Abattoirs↗
PubMed2006

A brief update on lung stereology.

Lung stereology has a long and successful tradition. From mice to men, the application of new stereological methods at several levels (alveoli, parenchymal cells, organelles, proteins) has led to new insights into normal lung architecture, parenchymal remodelling in emphysema-like pathology, alveolar type II cell hyperplasia and hypertrophy and intracellular surfactant alterations as well as distribution of surfactant proteins. The Euler number of the network of alveolar openings, estimated using physical disectors at the light microscopic level, is an unbiased and direct estimate of alveolar number. Surfactant-producing alveolar type II cells can be counted and sampled for local size estimation with physical disectors at a high magnification light microscopic level. The number of their surfactant storage organelles, lamellar bodies, can be estimated using physical disectors at the EM level. By immunoelectron microscopy, surfactant protein distribution can be analysed with the relative labelling index. Together with the well-established classical stereological methods, these design-based methods now allow for a complete quantitative phenotype analysis in lung development and disease, including the structural characterization of gene-manipulated mice, at the light and electron microscopic level.

Cell Count↗
PubMed1998

The coefficient of error of optical fractionator population size estimates: a computer simulation comparing three estimators.

The optical fractionator is a design-based two-stage systematic sampling method that is used to estimate the number of cells in a specified region of an organ when the population is too large to count exhaustively. The fractionator counts the cells found in optical disectors that have been systematically sampled in serial sections. Heretofore, evaluations of optical fractionator performance have been made by performing tests on actual tissue sections, but it is difficult to evaluate the coefficient of error (CE), i.e. the precision of a population size estimate, by using biological tissue samples because they do not permit a comparison of an estimated CE with the true CE. However, computer simulation does permit making such comparisons while avoiding the observational biases inherent in working with biological tissue. This study is the first instance in which computer simulation has been applied to population size estimation by the optical fractionator. We used computer simulation to evaluate the performance of three CE estimators. The estimated CEs were evaluated in tests of three types of non-random cell population distribution and one random cell population distribution. The non-random population distributions varied by differences in 'intensity', i.e. the expected cell counts per disector, according to both section and disector location within the section. Two distributions were sinusoidal and one was linearly increasing; in all three there was a six-fold difference between the high and low intensities. The sinusoidal distributions produced either a peak or a depression of cell intensity at the centre of the simulated region. The linear cell intensity gradually increased from the beginning to the end of the region that contained the cells. The random population distribution had a constant intensity over the region. A 'test condition' was defined by its population distribution, the period between consecutive sampled sections and the spacing between consecutive sampled disectors. There were 1000 independently simulated cell populations for each test condition, and a 'trial' was conducted for each of these cell populations. In each trial we calculated the (unique) true CE of the population size estimate and the three CE estimates obtained by applying the Scheaffer-Mendenhall-Ott (SMO) and both Gundersen-Jensen (GJ) estimators. We compared the estimated CEs with the true CEs for each population distribution. We found that the CE estimates obtained by the SMO estimator were closer to the true CEs and had less scatter than those of the nugget-modified GJ estimator. Both had small positive bias. The CE estimates obtained by the unmodified GJ estimator exhibited widely varying bias and large scatter. In all the population distributions we tested, the average true CE was very nearly proportional to 1/square root of QT, where QT is the average number of cells counted in the two-stage systematic sample.

Cell Count↗
PubMed2005

FDR-controlling testing procedures and sample size determination for microarrays.

Microarrays are used increasingly to identify genes that are truly differentially expressed in tissues under different conditions. Planning such studies requires establishing a sample size that will ensure adequate statistical power. For microarray analyses, false discovery rate (FDR) is considered to be an appropriate error measure. Several FDR-controlling procedures have been developed. How these procedures perform for such analyses has not been evaluated thoroughly under realistic assumptions. In order to develop a method of determining sample sizes for these procedures, it needs to be established whether these procedures really control the FDR below the pre-specified level so that the determined sample size indeed provides adequate power. To answer this question, we first conducted simulation studies. Our simulation results showed that these procedures do control the FDR at most situations but under-control the FDR when the proportion of positive genes is small, the most likely scenarios. Thus, these existing procedures can overestimate the power and underestimate the sample size. Accordingly, we developed a simulation-based method to provide more accurate estimates for power and sample size.

Algorithms↗
PubMed1996

Risch's lambda values for human obesity.

OBJECTIVE: Risch's lambda statistic (lambda R) is related to the heritability of traits and can be useful in several contexts, including the conduct of power analyses to determine sample size for gene mapping studies. However, values of lambda R have not been presented for human obesity. DESIGN AND RESULTS: Using both analytic and empirical approaches, the present study calculates estimates of lambda R. Examples are provided to illustrate the use of these estimates for determining sample size for genetic mapping studies.

Adolescent↗