Folic acid and chromosome breakage. IV. Variance estimates from longitudinal studies of normal individuals and their implications for sample size and power to detect differences between populations

The frequency of chromosome aberrations was studied in minimal essential medium (MEM) with and without folic acid (FA) in lymphocytes of 4 normal individuals, each sampled 12 times over a 1-year period. The cells cultured without FA had significantly more breaks and gaps. In both media about 75% of aberrations were classified as gaps. Calculations based on variance estimates suggest that the use of medium without FA could enhance the statistical power to distinguish differences in proportions of chromosome breakage between groups in the same study.     

Statistical optimisation of medium components for chitinase production byPaenibacillus sabina strain JD2

Paenibacillus sabina strain JD2, a chitinolytic marine bacterium, was isolated from sea dumps collected at Sultanpur near Bhavnagar, India and its nutritional requirement for chitinase production was defined using statistical optimisation method. Effect of 8 different medium components on chitinase production byPaenibacillus sabina strain JD2 was screened by Plackett-Burman design. The screened medium components were further used in central composite design where chitinase production, pH and biomass responses were used in different models to evaluate fit ones. After performing power transformation, quadratic model was found to be fit for chitinase response and 2F1 model was found to be fit for biomass response. Whilst for pH response, quadratic model was found to be fit without any requirement of power transformation. In multiresponse analysis, medium formulation consisting of (g/l): chitin 18, yeast extract 0.50, and CaCl₂ 0.08, was found to predict 82.93 U/ml of chitinase with overall highest desirability of 0.842 as compared to other formulations. The selection of model was done on basis of high adjusted R² value and loweredp-value for each model in individual analysis of each response. Through desirability analysis, it was found that biomass and pH played an important role in increasing the chitinase production byPaenibacillus sabina strain JD2. Through statistical optimisation method, 2.74-fold increase in chitinase production was achieved as compared to unoptimised medium.     

Some properties of the angular power distribution of electromagnetic waves multiply scattered in a collisional magnetized turbulent plasma

A study is made of oblique incidence of a small-amplitude plane electromagnetic wave on a semi-infinite slab of a collisional turbulent plasma in an external uniform magnetic field. In the small-angle scattering approximation, the condition for neutralizing the effects of oblique incidence and plasma anisotropy on the statistical properties of radiation multiply scattered in the absorbing plasma medium is determined by using the methods of geometrical optics. The validity of this condition was confirmed by numerical calculations based on the statistical modeling technique. The effect of the shape of the spectrum of the electron density fluctuations on the shape of the angular power distribution of a multiply scattered radiation is investigated.     

A survey of the statistical power of research in behavioral ecology and animal behavior

We estimated the statistical power of the first and last statisticaltest presented in 697 papers from 10 behavioral journals. Firsttests had significantly greater statistical power and reportedmore significant results (smaller p values) than did last tests.This trend was consistent across journals, taxa, and the typeof statistical test used. On average, statistical power was13–16% to detect a small effect and 40–47% to detecta medium effect. This is far lower than the general recommendationof a power of 80%. By this criterion, only 2–3%, 13–21%,and 37–50% of the tests examined had the requisite powerto detect a small, medium, or large effect, respectively. Neitherp values nor statistical power varied significantly across the10 journals or 11 taxa. However, mean p values of first andlast tests were significantly correlated across journals ( ), with a similar trend for mean power ( ). There is therefore some evidence that power and p values are repeatable among journals. Mean p valuesor power of first and last tests were, however, uncorrelatedacross taxa. Finally, there was a significant correlation betweenpower and reported p value for both first ( ) and last tests ( ). If true effect sizes are unrelated to study sample sizes, the averagetrue effect size must be nonzero for this pattern to emerge.This suggests that failure to observe significant relationshipsis partly owing to small sample sizes, as power increases withsample size.     

Human performance and physiology: A statistical power analysis of ELF electromagnetic field research

Research examining the effects of electromagnetic fields (EMFs) on human performance and physiology has produced inconsistent results; this might be attributable to low statistical power. Statistical power refers to the probability of obtaining a statistically significant result, given the fact that a real effect exists. The results of a survey of published investigations of the effects of EMFs on human performance and physiology show that statistical power levels are very low, ranging from a mean of.08 for small effect sizes to .46 for large effect sizes. Implications of these findings for the interpretation of results are discussed along with suggestions for increasing statistical power. © 1996 Wiley-Liss, Inc.     

Assessment of Cultivation Factors that Affect Biomass and Geraniol Production in Transgenic Tobacco Cell Suspension Cultures

A large-scale statistical experimental design was used to determine essential cultivation parameters that affect biomass accumulation and geraniol production in transgenic tobacco (Nicotiana tabacum cv. Samsun NN) cell suspension cultures. The carbohydrate source played a major role in determining the geraniol yield and factors such as filling volume, inoculum size and light were less important. Sucrose, filling volume and inoculum size had a positive effect on geraniol yield by boosting growth of plant cell cultures whereas illumination of the cultures stimulated the geraniol biosynthesis. We also found that the carbohydrates sucrose and mannitol showed polarizing effects on biomass and geraniol accumulation. Factors such as shaking frequency, the presence of conditioned medium and solubilizers had minor influence on both plant cell growth and geraniol content. When cells were cultivated under the screened conditions for all the investigated factors, the cultures produced ∼5.2 mg/l geraniol after 12 days of cultivation in shaking flasks which is comparable to the yield obtained in microbial expression systems. Our data suggest that industrial experimental designs based on orthogonal arrays are suitable for the selection of initial cultivation parameters prior to the essential medium optimization steps. Such designs are particularly beneficial in the early optimization steps when many factors must be screened, increasing the statistical power of the experiments without increasing the demand on time and resources.     

MSACompro: protein multiple sequence alignment using predicted secondary structure, solvent accessibility, and residue-residue contacts

Background

Estimation of allele frequency is of fundamental importance in population genetic analyses and in association mapping. In most studies using next-generation sequencing, a cost effective approach is to use medium or low-coverage data (e.g., < 15X). However, SNP calling and allele frequency estimation in such studies is associated with substantial statistical uncertainty because of varying coverage and high error rates.

Results

We evaluate a new maximum likelihood method for estimating allele frequencies in low and medium coverage next-generation sequencing data. The method is based on integrating over uncertainty in the data for each individual rather than first calling genotypes. This method can be applied to directly test for associations in case/control studies. We use simulations to compare the likelihood method to methods based on genotype calling, and show that the likelihood method outperforms the genotype calling methods in terms of: (1) accuracy of allele frequency estimation, (2) accuracy of the estimation of the distribution of allele frequencies across neutrally evolving sites, and (3) statistical power in association mapping studies. Using real re-sequencing data from 200 individuals obtained from an exon-capture experiment, we show that the patterns observed in the simulations are also found in real data.

Conclusions

Overall, our results suggest that association mapping and estimation of allele frequencies should not be based on genotype calling in low to medium coverage data. Furthermore, if genotype calling methods are used, it is usually better not to filter genotypes based on the call confidence score.     

Multi-locus test conditional on confirmed effects leads to increased power in genome-wide association studies

Complex diseases or phenotypes may involve multiple genetic variants and interactions between genetic, environmental and other factors. Current genome-wide association studies (GWAS) mostly used single-locus analysis and had identified genetic effects with multiple confirmations. Such confirmed single-nucleotide polymorphism (SNP) effects were likely to be true genetic effects and ignoring this information in testing new effects of the same phenotype results in decreased statistical power due to increased residual variance that has a component of the omitted effects. In this study, a multi-locus association test (MLT) was proposed for GWAS analysis conditional on SNPs with confirmed effects to improve statistical power. Analytical formulae for statistical power were derived and were verified by simulation for MLT accounting for confirmed SNPs and for single-locus test (SLT) without accounting for confirmed SNPs. Statistical power of the two methods was compared by case studies with simulated and the Framingham Heart Study (FHS) GWAS data. Results showed that the MLT method had increased statistical power over SLT. In the GWAS case study on four cholesterol phenotypes and serum metabolites, the MLT method improved statistical power by 5% to 38% depending on the number and effect sizes of the conditional SNPs. For the analysis of HDL cholesterol (HDL-C) and total cholesterol (TC) of the FHS data, the MLT method conditional on confirmed SNPs from GWAS catalog and NCBI had considerably more significant results than SLT.     

Using public control genotype data to increase power and decrease cost of case–control genetic association studies

Genome-wide association (GWA) studies are a powerful approach for identifying novel genetic risk factors associated with human disease. A GWA study typically requires the inclusion of thousands of samples to have sufficient statistical power to detect single nucleotide polymorphisms that are associated with only modest increases in risk of disease given the heavy burden of a multiple test correction that is necessary to maintain valid statistical tests. Low statistical power and the high financial cost of performing a GWA study remains prohibitive for many scientific investigators anxious to perform such a study using their own samples. A number of remedies have been suggested to increase statistical power and decrease cost, including the utilization of free publicly available genotype data and multi-stage genotyping designs. Herein, we compare the statistical power and relative costs of alternative association study designs that use cases and screened controls to study designs that are based only on, or additionally include, free public control genotype data. We describe a novel replication-based two-stage study design, which uses free public control genotype data in the first stage and follow-up genotype data on case-matched controls in the second stage that preserves many of the advantages inherent when using only an epidemiologically matched set of controls. Specifically, we show that our proposed two-stage design can substantially increase statistical power and decrease cost of performing a GWA study while controlling the type-I error rate that can be inflated when using public controls due to differences in ancestry and batch genotype effects.     

脑膜炎球菌多糖疫苗培养基的标准化研究

目的用干粉原料完全替代以消化液为主要原料的培养基配方,实现脑膜炎球菌多糖疫苗培养基的标准化生产。方法用筛选改良的酪蛋白酸水解物干粉替代50%盐酸酪蛋白水解液,以改良酵母浸出粉替代酵母透析液和酵母浸出粉,适当调整培养基配方,改进并稳定培养基制备工艺,确定适宜质量指标,并对各项质量指标数据进行分析。结果改进后的脑膜炎球菌多糖疫苗干粉培养基有效地降低了批间差异,各项质量指标均符合脑膜炎球菌培养要求,培养基的各项质量指标更加稳定可控,在生产中得到了良好、稳定的生长结果。结论用干粉原料完全替代脑膜炎球菌多糖疫苗培养基中的消化液和酵母透析液是成功的,同时改良的干粉培养基进一步明确了配方标准,使原料准备、制备工艺、质量指标控制更加标准化,有效提高了培养基质量,有利于规模化生产,促进了脑膜炎球菌多糖疫苗生产用培养基的标准化工作。     

Development of a serum-free medium for <Emphasis Type="Italic">in vitro</Emphasis> expansion of human cytotoxic T lymphocytes using a statistical design

Background  

Serum-containing medium (SCM), which has a number of poorly defined components with varying concentrations, hampers standardization of lymphocyte cultures. In order to develop a serum-free medium (SFM) for the expansion of human lymphocytes from peripheral blood mononuclear cells (PBMCs), a statistical optimization approach based on a fractional factorial method and a response surface method was adopted. A basal medium was prepared by supplementing RPMI1640 medium with insulin, albumin, ferric citrate, ethanolamine, fatty acids, glutamine, sodium pyruvate, 2-mercaptoethanol, 1-thioglycerol, nonessential amino acids, and vitamins. We identified additional positive determinants and their optimal concentrations for cell growth through a statistical analysis.     

powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions

Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years, effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight. In order to greatly decrease the barriers to using good statistical methods for fitting power law distributions, we developed the powerlaw Python package. This software package provides easy commands for basic fitting and statistical analysis of distributions. Notably, it also seeks to support a variety of user needs by being exhaustive in the options available to the user. The source code is publicly available and easily extensible.     

The prevalence of negative studies with inadequate statistical power: an analysis of the plastic surgery literature.

Studies published in the medical literature often neglect to consider the statistical power needed to detect a meaningful difference between study groups. Small sample sizes tend to produce negative results because of low statistical power. Studies that cannot make conclusive statements about their hypotheses can waste resources, deter further research, and impede advances in clinical treatment. The current study reviewed three of the most frequently read plastic surgery journals from 1976 to 1996 to determine the prevalence of inadequately (<80 percent) powered clinical trials and experimental studies that found no difference (negative studies) in the response variable of interest between comparison groups. The statistical power of 54 negative studies using continuous response variables was calculated to detect a difference of 1 SD (+/-1 SD) in means between the comparative groups. The power of another 57 negative studies with dichotomous response (yes/no) variables was calculated to detect a relative change in proportions of 25 percent and 50 percent from the experimental to the control group. It was found that 85 percent of the studies with continuous response variables had inadequate power to detect the desired mean difference of +/-1 SD. In studies with dichotomous response variables, 98 percent had inadequate power to detect a desired 25 percent relative change in proportions, and 74 percent had inadequate power to detect a desired 50 percent relative change in proportions. These results indicate that many of the studies in the plastic surgery literature lack adequate power to detect a moderate-to-large difference between groups. The lack of power makes the interpretation of the studies with negative findings inconclusive. Proper study design dictates that investigators consider a priori the difference between groups that is of clinical interest, and the sample size per group that is needed to provide adequate statistical power to detect the desired difference.     

Development of a serum-free medium for the production of erythropoietin by suspension culture of recombinant Chinese hamster ovary cells using a statistical design.

In order to develop a serum-free (SF) medium for the production of erythropoietin (EPO) by suspension culture of recombinant Chinese hamster ovary (rCHO) cells, a statistical optimization approach based on a Plackett-Burman design was adopted. A basal medium was prepared by supplementing Iscove's modified Dulbecco's medium (IMDM) with Fe(NO3)3.9H2O, CuCl2 and ZnSO4.7H2O which are generally contained in SF medium formulations. Insulin, transferrin and ethanolamine were also supplemented to the basal medium to determine their optimal concentrations. From this statistical analysis, glutamate, serine, methionine, phosphatidylcholine, hydrocortisone and pluronic F68 were identified as positive determinants for cell growth. The SF medium was formulated by supplementing the basal medium with components showing positive effects on cell growth in suspension culture. An EPO titer in this optimized SF medium was 79% of that in IMDM supplemented with 5% dialyzed fetal bovine serum (dFBS). Furthermore, the in vitro and in vivo biological activities of EPO produced in the SF medium were comparable to those produced in the serum-supplemented medium. Taken together, the results obtained here show that a Plackett-Burman design facilitates the development of SF media for the production of EPO by suspension culture of rCHO cells.     

QTL detection power of multi-parental RIL populations in Arabidopsis thaliana

A major goal of today's biology is to understand the genetic basis of quantitative traits. This can be achieved by statistical methods that evaluate the association between molecular marker variation and phenotypic variation in different types of mapping populations. The objective of this work was to evaluate the statistical power of quantitative trait loci (QTL) detection of various multi-parental mating designs, as well as to assess the reasons for the observed differences. Our study was based on an empirical data of 20 Arabidopsis thaliana accessions, which have been selected to capture the maximum genetic diversity. The examined mating designs differed strongly with respect to the statistical power to detect QTL. We observed the highest power to detect QTL for the diallel cross with random mating design. The results of our study suggested that performing sibling mating within subpopulations of joint-linkage mapping populations has the potential to considerably increase the power for QTL detection. Our results, however, revealed that using designs in which more than two parental alleles segregate in each subpopulation increases the power even more.     

Estimating plant allometric relationships in a power model with a minimum size of allocation

The allocation of resources among plant structures depends on size. For example, plants need to have a certain minimum size before they allocate resources into producing seeds. Furthermore, the allometric relationship between different plant structures and size has often been found to be adequately described by power functions. Allometric power functions have traditionally led to a bias when estimating and predicting e.g. seed production as a function of size using classical linear statistical methods. The statistical problems of using the linear models when estimating a power function with a threshold value have been solved but due to the relative complexity of the statistical solutions, the solutions are often not used in the ecological literature. Here, an intuitive and simple power model with a minimum size of allocation is investigated using a Bayesian estimation method on a simulated data set. The Bayesian estimation provided satisfactory estimates of the parameters in the model, and the model is suggested as a simple alternative when fitting allometric power functions to ecological data.     

Farm Scale Evaluations of spring-sown genetically modified herbicide-tolerant crops: a statistical assessment

Primary results from the Farm Scale Evaluations (FSEs) of spring-sown genetically modified herbicide-tolerant crops were published in 2003. We provide a statistical assessment of the results for count data, addressing issues of sample size (n), efficiency, power, statistical significance, variability and model selection. Treatment effects were consistent between rare and abundant species. Coefficients of variation averaged 73% but varied widely. High variability in vegetation indicators was usually offset by large n and treatment effects, whilst invertebrate indicators often had smaller n and lower variability; overall, achieved power was broadly consistent across indicators. Inferences about treatment effects were robust to model misspecification, justifying the statistical model adopted. As expected, increases in n would improve detectability of effects whilst, for example, halving n would have resulted in a loss of significant results of about the same order. 40% of the 531 published analyses had greater than 80% power to detect a 1.5-fold effect; reducing n by one-third would most likely halve the number of analyses meeting this criterion. Overall, the data collected vindicated the initial statistical power analysis and the planned replication. The FSEs provide a valuable database of variability and estimates of power under various sample size scenarios to aid planning of more efficient future studies.     

Enhanced statistical tests for GWAS in admixed populations: assessment using African Americans from CARe and a Breast Cancer Consortium

While genome-wide association studies (GWAS) have primarily examined populations of European ancestry, more recent studies often involve additional populations, including admixed populations such as African Americans and Latinos. In admixed populations, linkage disequilibrium (LD) exists both at a fine scale in ancestral populations and at a coarse scale (admixture-LD) due to chromosomal segments of distinct ancestry. Disease association statistics in admixed populations have previously considered SNP association (LD mapping) or admixture association (mapping by admixture-LD), but not both. Here, we introduce a new statistical framework for combining SNP and admixture association in case-control studies, as well as methods for local ancestry-aware imputation. We illustrate the gain in statistical power achieved by these methods by analyzing data of 6,209 unrelated African Americans from the CARe project genotyped on the Affymetrix 6.0 chip, in conjunction with both simulated and real phenotypes, as well as by analyzing the FGFR2 locus using breast cancer GWAS data from 5,761 African-American women. We show that, at typed SNPs, our method yields an 8% increase in statistical power for finding disease risk loci compared to the power achieved by standard methods in case-control studies. At imputed SNPs, we observe an 11% increase in statistical power for mapping disease loci when our local ancestry-aware imputation framework and the new scoring statistic are jointly employed. Finally, we show that our method increases statistical power in regions harboring the causal SNP in the case when the causal SNP is untyped and cannot be imputed. Our methods and our publicly available software are broadly applicable to GWAS in admixed populations.     

稀有变异遗传关联性研究中常用负担检验方法比较

为比较稀有变异遗传关联研究中常用负担检验方法(CMC、WST、SUM及其扩展)在不同遗传情境下的统计性能,本文通过计算机模拟产生不同样本量、连锁不平衡(linkage disequilibrium, LD)参数、混杂非关联变异的个数和不同效应的关联变异等条件的稀有变异病例对照数据集,运用各种负担检验方法进行分析,分别计算各方法的一类错误和效能。结果表明,各方法一类错误均在0.05附近;当稀有变异效应方向一致时,除aSUM法外,LD参数越大、混杂非关联变异越少、各法效能越高;当效应方向不一致时,各法效能则显著降低。除强LD外,有方向考虑的方法效能均比无方向考虑的方法高,且样本量越大效能越高。负担检验的统计性能受效应大小和方向、噪音变异和连锁不平衡等多种因素影响。在实际应用中,在各类方法选择、确定集合单位,权重等时最好结合遗传变异的生物信息先验以提高研究效能。     

A simple method for calculating the statistical power for detecting a QTL located in a marker interval

We developed a simple method for calculating the statistical power for detecting a QTL located in an interval flanked by two markers. The statistical method for QTL detection is assumed to be the Haley and Knott's simple regression method of interval mapping. This method allows us to answer one of the fundamental questions in designing a QTL mapping experiment: What is the minimum marker density required to detect a QTL explaining a certain heritable proportion of the phenotypic variance (denoted by h(2)) with a power gamma under a Type I error alpha in an F(2) or other mating designs with a sample size n? Computing the statistical power only requires the ability to evaluate a non-central F-distribution function and the inverse function of this distribution.