Choice Of Sample Size Research Articles

Evaluating the Risk in Sample Size Determination

This article considers experimental costs, besides power evaluation, in order to determine the sample size of an experiment. We focus on the use of standard tools of decision theory in the context of sample size determination. The loss function is defined, from the perspective of an experimenter which adopts the classical frequentist approach, and the risk function is computed. Then, we show the behavior of the risk function in the two-sample t-test, for a small sample experimental setting, with a medium-sized sample, and with large samples. Moreover, an objective criterion for a convenient sample size choice is introduced. Finally, a practical example of sample size determination, which also considers risk computation, is shown.

Bayesian sample size determination for binomial proportions

This paper presents several new results on Bayesian sample size deter- mination for estimating binomial proportions, and provides a comprehensive com- parative overview of the subject. We investigate the binomial sample size problem using generalized versions of the Average Length and Average Coverage Criteria, the Median Length and Median Coverage Criteria, as well as the Worst Outcome Criterion and its modied version. We compare sample sizes derived from highest posterior density and equal-tailed credible intervals. In some cases, we derive, for the rst time, closed form sample size formulae, and where this is not possible, we describe various numerical approaches. These range in complexity from Monte Carlo simulations to more sophisticated curve tting techniques, third order an- alytic approximations, and exact, but more computationally-intensive, methods. We compare the accuracy and eciency of the dieren t computational methods for each of the criteria and make recommendations about which methods are preferred. Finally, we consider, again for the rst time, issues surrounding prior robustness on the choice of sample size. Examples are given throughout the text.

Simple, Defensible Sample Sizes Based on Cost Efficiency

The conventional approach of choosing sample size to provide 80% or greater power ignores the cost implications of different sample size choices. Costs, however, are often impossible for investigators and funders to ignore in actual practice. Here, we propose and justify a new approach for choosing sample size based on cost efficiency, the ratio of a study's projected scientific and/or practical value to its total cost. By showing that a study's projected value exhibits diminishing marginal returns as a function of increasing sample size for a wide variety of definitions of study value, we are able to develop two simple choices that can be defended as more cost efficient than any larger sample size. The first is to choose the sample size that minimizes the average cost per subject. The second is to choose sample size to minimize total cost divided by the square root of sample size. This latter method is theoretically more justifiable for innovative studies, but also performs reasonably well and has some justification in other cases. For example, if projected study value is assumed to be proportional to power at a specific alternative and total cost is a linear function of sample size, then this approach is guaranteed either to produce more than 90% power or to be more cost efficient than any sample size that does. These methods are easy to implement, based on reliable inputs, and well justified, so they should be regarded as acceptable alternatives to current conventional approaches.

The choice of sample size: a mixed Bayesian / frequentist approach

Sample size computations are largely based on frequentist or classical methods. In the Bayesian approach the prior information on the unknown parameters is taken into account. In this work we consider a fully Bayesian approach to the sample size determination problem which was introduced by Grundy et al. and developed by Lindley. This approach treats the problem as a decision problem and employs a utility function to find the optimal sample size of a trial. Furthermore, we assume that a regulatory authority, which is deciding on whether or not to grant a licence to a new treatment, uses a frequentist approach. We then find the optimal sample size for the trial by maximising the expected net benefit, which is the expected benefit of subsequent use of the new treatment minus the cost of the trial.

SIZE REQUIREMENTS OF COMPACT SANDWICH SPECIMEN FOR TESTING OF BONE

It is well understood that bone quality deteriorates due to aging, disease, etc., and may be affected by factors at different length scales due to its hierarchical microstructure. Fracture toughness is one of the properties that assess bone quality. The compact sandwich (CS) specimen gives a better choice of bone sample size, and therefore suits a wide variety of fracture toughness testing needs and constraints. Reliable and statistically valid overall CS specimen size requirements are established in this paper; these serve as guidelines for choosing the CS specimen size. Finite element analysis (FEA) is used for simulating fracture toughness tests. Experimental fracture toughness tests are carried out to verify the FEA results. The experimental results are verified qualitatively by performing scanning electron microscopy (SEM) on the fractured specimen surfaces.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N . It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Power analysis for genome-wide association studies

BackgroundGenome-wide association studies are a promising new tool for deciphering the genetics of complex diseases. To choose the proper sample size and genotyping platform for such studies, power calculations that take into account genetic model, tag SNP selection, and the population of interest are required.ResultsThe power of genome-wide association studies can be computed using a set of tag SNPs and a large number of genotyped SNPs in a representative population, such as available through the HapMap project. As expected, power increases with increasing sample size and effect size. Power also depends on the tag SNPs selected. In some cases, more power is obtained by genotyping more individuals at fewer SNPs than fewer individuals at more SNPs.ConclusionGenome-wide association studies should be designed thoughtfully, with the choice of genotyping platform and sample size being determined from careful power calculations.

A Bayesian approach for incorporating economic factors in sample size design for clinical trials of individual drugs and portfolios of drugs

Classical approaches to clinical trial design ignore economic factors that determine economic viability of a new drug. We address the choice of sample size in Phase III trials as a decision theory problem using a hybrid approach that takes a Bayesian view from the perspective of a drug company and a classical Neyman-Pearson view from the perspective of regulatory authorities. We incorporate relevant economic factors in the analysis to determine the optimal sample size to maximize the expected profit for the company. We extend the analysis to account for risk by using a 'satisficing' objective function that maximizes the chance of meeting a management-specified target level of profit. We extend the models for single drugs to a portfolio of clinical trials and optimize the sample sizes to maximize the expected profit subject to budget constraints. Further, we address the portfolio risk and optimize the sample sizes to maximize the probability of achieving a given target of expected profit.

Sample Size and Replication in 2D Gel Electrophoresis Studies

Two-dimensional gel electrophoresis can be an expensive technology, and many studies are based on a modest number of replicates. It is important that the statistical power is sufficient to detect protein expression differences of interest. This paper reviews the application of power calculations and considers how other issues affect the choice of sample size. The important distinction between biological and technical replication is made, and the superiority of the former is emphasized.

Alternative Bayes factors: Sample size determination and discriminatory power assessment

Alternative Bayes factors are families of methods used for hypothesis testing and model selection when sensitivity to priors is a concern and also when prior information is weak or lacking. This paper deals with two related problems that arise in the practical use of these model choice criteria: sample size determination and evaluation of discriminatory power. We propose a pre-experimental approach to cope with both these issues. Specifically, extending the evidential approach of Royall (J Am Stat Assoc 95(451):760–780, 2000) and following De Santis (J Stat Plan Inference 124(1):121–144, 2004), we propose a criterion for sample size choice based on the predictive probability of observing decisive and correct evidence. The basic idea is to select the minimal sample size that guarantees a sufficiently high pre-experimental probability that an alternative Bayes factor provides strong evidence in favor of the true hypothesis. It is also argued that a predictive analysis is a natural approach to the measurement of discriminatory power of alternative Bayes factors. The necessity of measuring discrimination ability depends on the fact that alternative Bayes factors are, in general, less sensitive to prior specifications than ordinary Bayes factors and that this gain in robustness corresponds to a reduced discriminative power. Finally, implementation of the predictive approach with improper priors is discussed and possible strategies are proposed.

Statistical tests with accurate size and power for balanced linear mixed models

The convenience of linear mixed models for Gaussian data has led to their widespread use. Unfortunately, standard mixed model tests often have greatly inflated test size in small samples. Many applications with correlated outcomes in medical imaging and other fields have simple properties which do not require the generality of a mixed model. Alternately, stating the special cases as a general linear multivariate model allows analysing them with either the univariate or multivariate approach to repeated measures (UNIREP, MULTIREP). Even in small samples, an appropriate UNIREP or MULTIREP test always controls test size and has a good power approximation, in sharp contrast to mixed model tests. Hence, mixed model tests should never be used when one of the UNIREP tests (uncorrected, Huynh-Feldt, Geisser-Greenhouse, Box conservative) or MULTIREP tests (Wilks, Hotelling-Lawley, Roy's, Pillai-Bartlett) apply. Convenient methods give exact power for the uncorrected and Box conservative tests. Simulations demonstrate that new power approximations for all four UNIREP tests eliminate most inaccuracy in existing methods. In turn, free software implements the approximations to give a better choice of sample size. Two repeated measures power analyses illustrate the methods. The examples highlight the advantages of examining the entire response surface of power as a function of sample size, mean differences, and variability.

Influence of cocoa components on the PCR detection of soy lecithin DNA

The labelling of genetically modified organisms (GMOs) is mandatory in the EU. To comply with this regulation, the International Standardisation Organisation recently published standards for the extraction of DNA and PCR detection of GMOs. The PCR detection of (GM) soy lecithin in chocolate however is not an easy assignment. For the most part this is due to inhibitors such as polyphenols resulting from the cocoa mass and the low level of soy lecithin present. Many factors however, such as the choice of extraction method, sample size and PCR protocol influence the PCR end result. Therefore, preconditions regarding the quality, quantity and purity of the extracted DNA should be carefully determined to guarantee a successful GMO analysis.

Covariation Assessments with Costly Information Collection in Audit Planning: An Experimental Study

SUMMARY: In this paper we report the results of two experiments that investigate auditing covariation-estimate revisions when there are countervailing incentives for effectiveness and efficiency. Covariation estimates assess the degree of association between a “Clue” that auditors might observe, and its potentially associated “Condition.” We find that when participants choose which information to obtain from a contingency table (i.e., Cell Choice), they obtain too few cells of information in predictable patterns. Second, we find that when covariation estimation biases occur, they do so more due to this insufficient information collection rather than improper processing of collected information. Third, when participants collect information randomly and cannot choose particular cells (i.e., Sample-Size Choice), covariation estimation biases are significantly reduced. Finally, when participants are sensitized to the importance of all four cells of information, they collect more cells in subsequent Cell Choice, resulting in covariation estimate revisions that are more normative than those of non-sensitized participants. Overall, this evidence implies that when auditors estimate the association between an unfamiliar Clue-Condition pair, their estimates are more biased when they choose specific cells of information than when they choose sample size. Sensitization can reduce this bias and, therefore, could be important to auditor training and the design of decision aids.

A measure of the performance of biomarkers for disease

The statistical properties required for effective biomarkers for disease are examined. It is shown that an "effectiveness parameter" D can be calculated that summarises the performance of a given biomarker and can distinguish between effective and ineffective biomarkers. D can be readily calculated from published summaries of biomarker levels and provides a simpler alternative to the commonly used "Area under the Curve" statistic. The impact of within-individual and between-individual variation in biomarker levels is also evaluated. An approach to the choice of sample size for experiments to estimate D is described.

False discovery rate, sensitivity and sample size for microarray studies

In microarray data studies most researchers are keenly aware of the potentially high rate of false positives and the need to control it. One key statistical shift is the move away from the well-known P-value to false discovery rate (FDR). Less discussion perhaps has been spent on the sensitivity or the associated false negative rate (FNR). The purpose of this paper is to explain in simple ways why the shift from P-value to FDR for statistical assessment of microarray data is necessary, to elucidate the determining factors of FDR and, for a two-sample comparative study, to discuss its control via sample size at the design stage. We use a mixture model, involving differentially expressed (DE) and non-DE genes, that captures the most common problem of finding DE genes. Factors determining FDR are (1) the proportion of truly differentially expressed genes, (2) the distribution of the true differences, (3) measurement variability and (4) sample size. Many current small microarray studies are plagued with large FDR, but controlling FDR alone can lead to unacceptably large FNR. In evaluating a design of a microarray study, sensitivity or FNR curves should be computed routinely together with FDR curves. Under certain assumptions, the FDR and FNR curves coincide, thus simplifying the choice of sample size for controlling the FDR and FNR jointly.

Gene–environment interactions in human diseases

Studies of gene-environment interactions aim to describe how genetic and environmental factors jointly influence the risk of developing a human disease. Gene-environment interactions can be described by using several models, which take into account the various ways in which genetic effects can be modified by environmental exposures, the number of levels of these exposures and the model on which the genetic effects are based. Choice of study design, sample size and genotyping technology influence the analysis and interpretation of observed gene-environment interactions. Current systems for reporting epidemiological studies make it difficult to assess whether the observed interactions are reproducible, so suggestions are made for improvements in this area.

SAMPLING STRATEGIES FOR DETECTING RARE IMPURITIES: AN APPLICATION IN GENE THERAPY PRODUCTS

ABSTRACT Detection of rare impurities in drug products presents special challenges. Replication competent adenovirus (RCA) is a rare impurity found in adenovirus–based gene therapy products. Various methods are used for detection of RCAs. We primarily focus on qualitative assays. Acceptance sampling plans for detecting RCAs in batches of gene therapy products are discussed. Assuming that the number of RCA units per patient dose follows a Poisson distribution, operating characteristics (OC) of these sampling plans can be studied. The OC curves display the acceptance probabilities for batches with specific true but unknown level of RCA and can be used to assess the specificity and sensitivity of the test strategies. Application of Bayesian methodologies in the assessment of RCA levels in drug batches is also discussed. Using observed data and prior belief, a 95% credible region for the number of RCA units per patient dose can be constructed. Both classical and Bayesian calculations display the impact of sample size, sampling fraction, and assay quality on the detection of RCA. For better sensitivity, the largest possible sampling fraction that does not interfere with the logistics and the performance of the assay should be used. The choice of sample size will depend on the upper limit of the biologically safe level of RCA, the testing strategy, the desired level of sensitivity and specificity, and also on practical issues.

The use of GARCH models in VaR estimation

We evaluate the performance of an extensive family of ARCH models in modeling the daily Value-at-Risk (VaR) of perfectly diversified portfolios in five stock indices, using a number of distributional assumptions and sample sizes. We find, first, that leptokurtic distributions are able to produce better one-step-ahead VaR forecasts; second, the choice of sample size is important for the accuracy of the forecast, whereas the specification of the conditional mean is indifferent. Finally, the ARCH structure producing the most accurate forecasts is different for every portfolio and specific to each equity index.

Comparação do uso de rastreabilidade para suínos em grupo e individual

With the increasing demand of traced products to supply national and international market, it is urgent the development of knowledge about the processes of animal's identification and the tracing of information related to production. This research aimed to compare two kinds of swine traceability: individual and in group, using the electronic identification and data recording system. It was used 50 piglets identified at birth, and the control variables of weight gain and feed conversion were used for comparing both systems. A sample was considered from the feasible error established by a specialist. A function was developed and validated from the sample size choice. It was found that for faster data recording an identified piglet sample can be used for tracing information, and the final error will be inversely proportional to the size of the sample.

Analysis of Means Tables Using Mathematical Processors

Introduced by Ellis Ott in the 1960s, the analysis of means (abbreviated ANOM) procedure provides a simple graphical technique for testing for differences between the means of several populations. The ANOM charts are easy to use, similar in appearance and interpretation to control charts, and usually give the same results as the more familiar analysis of variance technique. Unfortunately, the ANOM decision limits depend upon tables of constants that are usually only available in printed form or from specialized software programs. In this article we present new formulas for the ANOM constants and then illustrate how commonly available mathematical processors can be used to calculate the ANOM constants. This approach makes the ANOM constants easily accessible, portable, and unrestricted with regard to the choice of significance level, sample size, and number of populations.