Size Calculation Methods Research Articles

Sample size calculation for the Wilcoxon–Mann–Whitney test adjusting for ties

In this paper we study sample size calculation methods for the asymptotic Wilcoxon-Mann-Whitney test for data with or without ties. The existing methods are applicable either to data with ties or to data without ties but not to both cases. While the existing methods developed for data without ties perform well, the methods developed for data with ties have limitations in that they are either applicable to proportional odds alternatives or have computational difficulties. We propose a new method which has a closed-form formula and therefore is very easy to calculate. In addition, the new method can be applied to both data with or without ties. Simulations have demonstrated that the new sample size formula performs very well as the corresponding actual powers are close to the nominal powers.

Sample Size Calculations Based on Generalized Estimating Equations for Population Pharmacokinetic Experiments

ABSTRACT We present a method for calculating the sample size of a pharmacokinetic study analyzed using a mixed effects model within a hypothesis testing framework. A sample size calculation method for repeated measurement data analyzed using generalized estimating equations has been modified for nonlinear models. The Wald test is used for hypothesis testing of pharmacokinetic parameters. A marginal model for the population pharmacokinetic is obtained by linearizing the structural model around the subject specific random effects. The proposed method is general in that it allows unequal allocation of subjects to the groups and accounts for situations where different blood sampling schedules are required in different groups of patients. The proposed method has been assessed using Monte Carlo simulations under a range of scenarios. NONMEM was used for simulations and data analysis and the results showed good agreement.

A Note on Comparing Exposure Data to a Regulatory Limit in the Presence of Unexposed and a Limit of Detection

In some occupational health studies, observations occur in both exposed and unexposed individuals. If the levels of all exposed individuals have been detected, a two-part zero-inflated log-normal model is usually recommended, which assumes that the data has a probability mass at zero for unexposed individuals and a continuous response for values greater than zero for exposed individuals. However, many quantitative exposure measurements are subject to left censoring due to values falling below assay detection limits. A zero-inflated log-normal mixture model is suggested in this situation since unexposed zeros are not distinguishable from those exposed with values below detection limits. In the context of this mixture distribution, the information contributed by values falling below a fixed detection limit is used only to estimate the probability of unexposed. We consider sample size and statistical power calculation when comparing the median of exposed measurements to a regulatory limit. We calculate the required sample size for the data presented in a recent paper comparing the benzene TWA exposure data to a regulatory occupational exposure limit. A simulation study is conducted to investigate the performance of the proposed sample size calculation methods.

Sample size for FDR-control in microarray data analysis

We consider identifying differentially expressing genes between two patient groups using microarray experiment. We propose a sample size calculation method for a specified number of true rejections while controlling the false discovery rate at a desired level. Input parameters for the sample size calculation include the allocation proportion in each group, the number of genes in each array, the number of differentially expressing genes and the effect sizes among the differentially expressing genes. We have a closed-form sample size formula if the projected effect sizes are equal among differentially expressing genes. Otherwise, our method requires a numerical method to solve an equation. Simulation studies are conducted to show that the calculated sample sizes are accurate in practical settings. The proposed method is demonstrated with a real study.

Sample size calculation for multiple testing in microarray data analysis

Microarray technology is rapidly emerging for genome-wide screening of differentially expressed genes between clinical subtypes or different conditions of human diseases. Traditional statistical testing approaches, such as the two-sample t-test or Wilcoxon test, are frequently used for evaluating statistical significance of informative expressions but require adjustment for large-scale multiplicity. Due to its simplicity, Bonferroni adjustment has been widely used to circumvent this problem. It is well known, however, that the standard Bonferroni test is often very conservative. In the present paper, we compare three multiple testing procedures in the microarray context: the original Bonferroni method, a Bonferroni-type improved single-step method and a step-down method. The latter two methods are based on nonparametric resampling, by which the null distribution can be derived with the dependency structure among gene expressions preserved and the family-wise error rate accurately controlled at the desired level. We also present a sample size calculation method for designing microarray studies. Through simulations and data analyses, we find that the proposed methods for testing and sample size calculation are computationally fast and control error and power precisely.

Efficient Bayesian Sample Size Calculation for Designing a Clinical Trial with Multi‐Cluster Outcome Data

AbstractHealth care utilization and outcome studies call for hierarchical approaches. The objectives were to predict major complications following percutaneous coronary interventions by health providers, and to compare Bayesian and non‐Bayesian sample size calculation methods. The hierarchical data structure consisted of: (1) Strata: PGY4, PGY7, and physician assistant as providers with varied experiences; (2) Clusters: ks providers per stratum; (3) Individuals: ns patients reviewed by each provider. The main outcome event illustrated was mortality modeled by a Bayesian beta‐binomial model. Pilot information and assumptions were utilized to elicit beta prior distributions. Sample size calculations were based on the approximated average length, fixed at 1%, of 95% posterior intervals of the mean event rate parameter. Necessary sample sizes by both non‐Bayesian and Bayesian methods were compared. We demonstrated that the developed Bayesian methods can be efficient and may require fewer subjects to satisfy the same length criterion.

Sample size calculations for clustered binary data

In this paper we propose a sample size calculation method for testing on a binomial proportion when binary observations are dependent within clusters. In estimating the binomial proportion in clustered binary data, two weighting systems have been popular: equal weights to clusters and equal weights to units within clusters. When the number of units varies cluster by cluster, performance of these two weighting systems depends on the extent of correlation among units within each cluster. In addition to them, we will also use an optimal weighting method that minimizes the variance of the estimator. A sample size formula is derived for each of the estimators with different weighting schemes. We apply these methods to the sample size calculation for the sensitivity of a periodontal diagnostic test. Simulation studies are conducted to evaluate a finite sample performance of the three estimators. We also assess the influence of misspecified input parameter values on the calculated sample size. The optimal estimator requires equal or smaller sample sizes and is more robust to the misspecification of an input parameter than those assigning equal weights to units or clusters.

Adapting sample size calculations to repeated measurements in clinical trials

Many of the repeated-measures sample size calculation methods presented in the literature are not suitable when: ” the different treatments are assumed to be equal on average at baseline time due to randomization, ” and the experimenters are interested in a pre-specified difference to be detected after a specific time period. The method presented here has been developed for those cases where a multivariate normal distribution can reasonably be assumed. It is likelihood-based and has been designed to be flexible enough to handle repeated-measures models, including a non-linear change in time, and an arbitrary correlation structure.

A proposal of a bedroom size calculation method based on bedroom selections according to family growth

A proposal of a bedroom size calculation method based on bedroom selections according to family growth

A Free-Flooding Acoustical Resonator for Measurement of Bubble Size Distributions

Abstract An instrument for the measurement of bubble size distributions is described. The sensing element exploits the free-flooding resonator design of Medwin with modifications to overcome the limitations in the original implementation, especially those due to a sensitivity to ambient pressure fluctuations in the surrounding medium. A mathematical model of the resonator provides insight into the factors affecting its performance and motivates application of appropriate signal processing algorithms. Comparison of different bubble size calculation methods shows the direct approach of Commander and MacDonald to be most successful. The stability of this new implementation of the resonator facilitates accurate measurement of the complex dispersion relation. Comparison of the real and imaginary components then leads to the definition of a measurement quality factor that may be calculated for each sample. Practical considerations are discussed for implementation of autonomous battery-powered resonator arrays f...

Shape-choice partition and size-determination method for the blanks for the drawing of boxes

Through experimental comparison and comprehensive analysis of the shape- and size-determination method for several box blanks used commonly at present, a set of choice- and size-calculation methods for the ideal box-blank shapes is assessed. Experimental results show that the choice partition for the given reasonable method of the shape- and size-determination of the box blank for two types of blanks cannot only determine the reasonable blank shape conveniently, but also can standardize the choice of the blank shape and the calculation method of the sizes.