Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Sample Size”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18Linked to original sources
PubMed1995

Sample size: how many patients are necessary?

The need for sample size calculations is briefly reviewed: many of the arguments against small trials are already well known, and we only cursorily repeat them in passing. Problems that arise in the estimation of sample size are then discussed, with particular reference to survival studies. However, most of the issues which we discuss are equally applicable to other types of study. Finally, prognostic factor analysis designs are discussed, since this is another area in which experience shows that far too many studies are of an inadequate size and yield misleading results.

Clinical Trials as Topic↗
PubMed1992

Sample size determination for case-control studies and the comparison of stratified and unstratified analyses.

Woolson, Bean, and Rojas (1986, Biometrics 42, 927-932) present a simple approximation of sample size for Cochran's (1954, Biometrics 10, 417-451) test for detecting association between exposure and disease. It is useful in the design of case-control studies. We derive a sample size formula for Cochran's statistic with continuity correction which guarantees that the actual Type I error rate of the test does not exceed the nominal level. The corrected sample size is necessarily larger than the uncorrected one given by Woolson et al. and the relative difference between the two sample sizes is considerable. Allocation of equal number of cases and controls within each stratum is asymptotically optimal when the costs per case and control are the same. When any effect of stratification is absent, Cochran's stratified test, although valid, is less efficient than the unstratified one except for the important case of a balanced design.

Case-Control Studies↗
PubMed1994

Deviance estimates of sample size for equivalence tests in vaccine trials.

This paper proposes a sample size procedure for both equivalence and conventional tests for the comparison of two binomial proportions, based on the signed square root of the deviance. When the comparison is based on the odds ratio, I describe an alternate 'close' conditional exact method that gives results that support those given by the deviance method. I summarize the advantages of the deviance-based method and also show that in general equivalence situations the sample size estimate depends upon the measure of comparison selected, odds ratio, risk ratio or risk difference.

Binomial Distribution↗
PubMed2000

Re-calculating the sample size in internal pilot study designs with control of the type I error rate.

When designing a clinical trial, there is usually some uncertainty about the variability of the primary outcome variable. This may lead to an unnecessarily high or inadequately low sample size. The internal pilot study approach uses data from patients recruited up to an interim stage to re-estimate the variance and to re-calculate the final sample size accordingly. Previously, simulation studies have shown that this methodology may highly improve the chance to obtain a well-powered trial. However, it also turned out that the type I error rate may be inflated by this procedure. We quantify the maximum excess of the type I error rate for normally distributed outcomes. If strict control of the alpha-level is considered to be an important issue, a method is proposed to achieve this when re-calculating the sample size in internal pilot studies. The characteristics of the power distributions are investigated for various sample size adaptation rules and implications are discussed.

Data Interpretation, Statistical↗
PubMed1994

Statistical power, sample size, and their reporting in randomized controlled trials.

OBJECTIVE: To describe the pattern over time in the level of statistical power and the reporting of sample size calculations in published randomized controlled trials (RCTs) with negative results. DESIGN: Our study was a descriptive survey. Power to detect 25% and 50% relative differences was calculated for the subset of trials with negative results in which a simple two-group parallel design was used. Criteria were developed both to classify trial results as positive or negative and to identify the primary outcomes. Power calculations were based on results from the primary outcomes reported in the trials. POPULATION: We reviewed all 383 RCTs published in JAMA, Lancet, and the New England Journal of Medicine in 1975, 1980, 1985, and 1990. RESULTS: Twenty-seven percent of the 383 RCTs (n = 102) were classified as having negative results. The number of published RCTs more than doubled from 1975 to 1990, with the proportion of trials with negative results remaining fairly stable. Of the simple two-group parallel design trials having negative results with dichotomous or continuous primary outcomes (n = 70), only 16% and 36% had sufficient statistical power (80%) to detect a 25% or 50% relative difference, respectively. These percentages did not consistently increase over time. Overall, only 32% of the trials with negative results reported sample size calculations, but the percentage doing so has improved over time from 0% in 1975 to 43% in 1990. Only 20 of the 102 reports made any statement related to the clinical significance of the observed differences. CONCLUSIONS: Most trials with negative results did not have large enough sample sizes to detect a 25% or a 50% relative difference. This result has not changed over time. Few trials discussed whether the observed differences were clinically important. There are important reasons to change this practice. The reporting of statistical power and sample size also needs to be improved.

Publishing↗
PubMed1996

Study design and sample size considerations for half-life studies.

Most studies on the half-lives of environmental contaminants have been based on small sample sizes and a limited number of repeated measurements. In this paper, we address issues of study design and sample size for half-life studies. Useful guidelines are provided for choosing the number of repeats and the optimal time interval between repeats for estimating an individual's half-life with a given level of precision, while minimizing the cost of the study. In addition, sample size and power considerations for studies comparing two population half-lives are investigated. An example is presented using data from a study on polychlorinated biphenyls and breast cancer.

Breast Neoplasms↗
PubMed2003

Effect of sample size and P-value filtering techniques on the detection of transcriptional changes induced in rat neuroblastoma (NG108) cells by mefloquine.

BACKGROUND: There is no known biochemical basis for the adverse neurological events attributed to mefloquine. Identification of genes modulated by toxic agents using microarrays may provide sufficient information to generate hypotheses regarding their mode of action. However, this utility may be compromised if sample sizes are too low or the filtering methods used to identify differentially expressed genes are inappropriate. METHODS: The transcriptional changes induced in rat neuroblastoma cells by a physiological dose of mefloquine (10 micro-molar) were investigated using Affymetrix arrays. A large sample size was used (total of 16 arrays). Genes were ranked by P-value (t-test). RT-PCR was used to confirm (or reject) the expression changes of several of the genes with the lowest P-values. Different P-value filtering methods were compared in terms of their ability to detect these differentially expressed genes. A retrospective power analysis was then performed to determine whether the use of lower sample sizes might also have detected those genes with altered transcription. RESULTS: Based on RT-PCR, mefloquine upregulated cJun, IkappaB and GADD153. Reverse Holm-Bonferroni P-value filtering was superior to other methods in terms of maximizing detection of differentially expressed genes but not those with unaltered expression. Reduction of total microarray sample size (< 10) impaired the capacity to detect differentially expressed genes. CONCLUSIONS: Adequate sample sizes and appropriate selection of P-value filtering methods are essential for the reliable detection of differentially expressed genes. The changes in gene expression induced by mefloquine suggest that the ER might be a neuronal target of the drug.

Animals↗
PubMed2003

Effect of sample preparation, length of time, and sample size on quantification of total lipids from bovine liver.

The objective was to evaluate the effect of sample preparation (pulverization under liquid nitrogen, homogenization, or sonication), time length of sonication (0-60 s), shaking in chloroform/methanol solvent (0, 2, 4, or 12 h), incubation in chloroform (0 or 12 h), and drying of extracted lipids at 50 degrees C (2, 4, 6, or 24 h), and sample size (50-250 mg) on quantification of total lipids from bovine liver. Pulverization under liquid nitrogen yielded the lowest recovery. Sonication was least time-consuming for sample preparation. Precise estimates and the greatest recovery were obtained with 30 s of sonication, at least 2 h of shaking in chloroform/methanol solvent, 12 h of incubation in chloroform, and at least 6 h of drying. Sample sizes of at least 150 mg gave precise estimates. The results demonstrate that sample preparation, time length of different steps of the extraction procedure, and sample size affect quantification of total lipid from bovine liver.

Animals↗
PubMed2002

Sample size determination for establishing equivalence/noninferiority via ratio of two proportions in matched-pair design.

In this article, we propose approximate sample size formulas for establishing equivalence or noninferiority of two treatments in match-pairs design. Using the ratio of two proportions as the equivalence measure, we derive sample size formulas based on a score statistic for two types of analyses: hypothesis testing and confidence interval estimation. Depending on the purpose of a study, these formulas can be used to provide a sample size estimate that guarantees a prespecified power of a hypothesis test at a certain significance level or controls the width of a confidence interval with a certain confidence level. Our empirical results confirm that these score methods are reliable in terms of true size, coverage probability, and skewness. A liver scan detection study is used to illustrate the proposed methods.

Biopsy↗
PubMed1989

Sample size and power for comparing two or more treatment groups in clinical trials.

Methods for determining sample size and power when comparing two groups in clinical trials are widely available. Studies comparing three or more treatments are not uncommon but are more difficult to analyse. A linear nomogram was devised to help calculate the sample size required when comparing up to five parallel groups. It may also be used retrospectively to determine the power of a study of given sample size. In two worked examples the nomogram was efficient. Although the nomogram offers only 5% and 1% significance levels and can be used only for up to five treatment groups, this is sufficient for most researchers.

Analysis of Variance↗
PubMed1995

Estimating sample sizes for binary, ordered categorical, and continuous outcomes in two group comparisons.

Sample size calculations are now mandatory for many research protocols, but the ones useful in common situations are not all easily accessible. This paper outlines the ways of calculating sample sizes in two group studies for binary, ordered categorical, and continuous outcomes. Formulas and worked examples are given. Maximum power is usually achieved by having equal numbers in the two groups. However, this is not always possible and calculations for unequal group sizes are given.

Data Interpretation, Statistical↗
PubMed2006

Lowering sample size in comparative analyses can indicate a correlation where there is none: example from Rensch's rule in primates.

The fact that characters may co-vary in organism groups because of shared ancestry and not always because of functional correlations was the initial rationale for developing phylogenetic comparative methods. Here we point out a case where similarity due to shared ancestry can produce an undesired effect when conducting an independent contrasts analysis. Under special circumstances, using a low sample size will produce results indicating an evolutionary correlation between characters where an analysis of the same pattern utilizing a larger sample size will show that this correlation does not exist. This is the opposite effect of increased sample size to that expected; normally an increased sample size increases the chance of finding a correlation. The situation where the problem occurs is when co-variation between the two continuous characters analysed is clumped in clades; e.g. when some phylogenetically conservative factors affect both characters simultaneously. In such a case, the correlation between the two characters becomes contingent on the number of clades sharing this conservative factor that are included in the analysis, in relation to the number of species contained within these clades. Removing species scattered evenly over the phylogeny will in this case remove the exact variation that diffuses the evolutionary correlation between the two characters - the variation contained within the clades sharing the conservative factor. We exemplify this problem by discussing a parallel in nature where the described problem may be of importance. This concerns the question of the presence or absence of Rensch's rule in primates.

Animals↗
PubMed1988

Sample size and power for case-control studies when exposures are continuous.

In estimating the sample size for a case-control study, epidemiologic texts present formulae that require a binary exposure of interest. Frequently, however, important exposures are continuous and dichotomization may result in a 'not exposed' category that has little practical meaning. In addition, if risks vary monotonically with exposure, then dichotomization will obscure risk effects and require a greater number of subjects to detect differences in the exposure distributions among cases and controls. Starting from the usual score statistic to detect differences in exposure, this paper develops sample size formulae for case-control studies with arbitrary exposure distributions; this includes both continuous and dichotomous exposure measurements as special cases. The score statistic is appropriate for general differentiable models for the relative odds, and, in particular, for the two forms commonly used in prospective disease occurrence models: (1) the odds of disease increase linearly with exposure; or (2) the odds increase exponentially with exposure. Under these two models we illustrate calculation of sample sizes for a hypothetical case-control study of lung cancer among non-smokers who are exposed to radon decay products at home.

Environmental Exposure↗
PubMed2002

Sample size, confidence, and contingency judgement.

According to statistical models, the acquisition function of contingency judgement is due to confidence increasing with sample size. According to associative models, the function reflects the accumulation of associative strength on which the judgement is based. Which view is right? Thirty university students assessed the relation between a fictitious medication and a symptom of skin discoloration in conditions that varied sample size (4, 6, 8 or 40 trials) and contingency (delta P = .20, .40, .60 or .80). Confidence was also collected. Contingency judgement was lower for smaller samples, while confidence level correlated inversely with sample size. This dissociation between contingency judgement and confidence contradicts the statistical perspective.

Adult↗
PubMed2005

Power and sample size calculations in the presence of phenotype errors for case/control genetic association studies.

BACKGROUND: Phenotype error causes reduction in power to detect genetic association. We present a quantification of phenotype error, also known as diagnostic error, on power and sample size calculations for case-control genetic association studies between a marker locus and a disease phenotype. We consider the classic Pearson chi-square test for independence as our test of genetic association. To determine asymptotic power analytically, we compute the distribution's non-centrality parameter, which is a function of the case and control sample sizes, genotype frequencies, disease prevalence, and phenotype misclassification probabilities. We derive the non-centrality parameter in the presence of phenotype errors and equivalent formulas for misclassification cost (the percentage increase in minimum sample size needed to maintain constant asymptotic power at a fixed significance level for each percentage increase in a given misclassification parameter). We use a linear Taylor Series approximation for the cost of phenotype misclassification to determine lower bounds for the relative costs of misclassifying a true affected (respectively, unaffected) as a control (respectively, case). Power is verified by computer simulation. RESULTS: Our major findings are that: (i) the median absolute difference between analytic power with our method and simulation power was 0.001 and the absolute difference was no larger than 0.011; (ii) as the disease prevalence approaches 0, the cost of misclassifying a unaffected as a case becomes infinitely large while the cost of misclassifying an affected as a control approaches 0. CONCLUSION: Our work enables researchers to specifically quantify power loss and minimum sample size requirements in the presence of phenotype errors, thereby allowing for more realistic study design. For most diseases of current interest, verifying that cases are correctly classified is of paramount importance.

Alzheimer Disease↗
PubMed2004

Optimal number of features as a function of sample size for various classification rules.

MOTIVATION: Given the joint feature-label distribution, increasing the number of features always results in decreased classification error; however, this is not the case when a classifier is designed via a classification rule from sample data. Typically (but not always), for fixed sample size, the error of a designed classifier decreases and then increases as the number of features grows. The potential downside of using too many features is most critical for small samples, which are commonplace for gene-expression-based classifiers for phenotype discrimination. For fixed sample size and feature-label distribution, the issue is to find an optimal number of features. RESULTS: Since only in rare cases is there a known distribution of the error as a function of the number of features and sample size, this study employs simulation for various feature-label distributions and classification rules, and across a wide range of sample and feature-set sizes. To achieve the desired end, finding the optimal number of features as a function of sample size, it employs massively parallel computation. Seven classifiers are treated: 3-nearest-neighbor, Gaussian kernel, linear support vector machine, polynomial support vector machine, perceptron, regular histogram and linear discriminant analysis. Three Gaussian-based models are considered: linear, nonlinear and bimodal. In addition, real patient data from a large breast-cancer study is considered. To mitigate the combinatorial search for finding optimal feature sets, and to model the situation in which subsets of genes are co-regulated and correlation is internal to these subsets, we assume that the covariance matrix of the features is blocked, with each block corresponding to a group of correlated features. Altogether there are a large number of error surfaces for the many cases. These are provided in full on a companion website, which is meant to serve as resource for those working with small-sample classification. AVAILABILITY: For the companion website, please visit http://public.tgen.org/tamu/ofs/ CONTACT: e-dougherty@ee.tamu.edu.

Algorithms↗
PubMed2000

Sample size considerations for the evaluation of prognostic factors in survival analysis.

When the role of a new prognostic factor is investigated, careful planning of an appropriate study is required. This includes an assessment of the power of the study in terms of sample sizes. An adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors. With survival time as endpoint this will usually be done with the Cox proportional hazards model. Sample size and power formulae in survival analysis have been developed by Schoenfeld for randomized treatment comparisons. In the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest. In this situation, the existing sample size and power formulae are not valid and may not be applied. In this paper, Schoenfeld's formula is first extended to the situation where a correlated factor is included in the analysis. The validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation. Second, an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor. This extends the formula for independent effects. Finally, the approach is illustrated by an example on the prognostic impact of DNA ploidy and other factors in advanced ovarian cancer.

Computer Simulation↗
PubMed1981

Population studies on Oncomelania quadrasi, the snail intermediate host of Schistosoma japonicum, in the Philippines. 2. Necessary sample size for snail density survey.

In order to save time and manpower for the density surveys of Oncomelania quadrasi, the snail host of Schistosoma japonicum in the Philippines, the minimal necessary sample size (q) was determined using a formula, q greater than t2/E2(1d - 1 + 1/-x). This formula is based on the Id dispersion index [2, 3] which varies with the degree of clumping of unevenly distributed animals. A nomograph was prepared for the ready determination of the necessary sample size for various degrees of clumping (Id) and mean density (-x) to be encountered in the field. The reliability of the sampling procedure with an interval of 5 m distance, which has been adopted to the routine snail survey in the Philippines, was examined using the relative error (E). The relative errors calculated ranged below or around 20% (E = 0.2). Therefore, the existing sampling method was proven to be highly reliable as the field survey. Comparison was made between the sample size actually taken and the minimum needed theoretically determined by this method, by adopting the Student's t = 1 and relative error E = 0.3 as a permissible reliability level in the field. The actual sample size was more than twice the minimum needed for 21 out of 30 populations surveyed and less than the needed in 5 of the 30 surveys.

Animals↗