Very large sample sizes

BMJ ◽  
2009 ◽  
Vol 338 (feb25 2) ◽  
pp. b737-b737 ◽  
Author(s):  
J. Fletcher
Keyword(s):  
Sample Sizes ◽  
Large Sample

scholarly journals High heterogeneity undermines generalization of differential expression results in RNA-Seq analysis

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Weitong Cui ◽  
Huaru Xue ◽  
Lei Wei ◽  
Jinghua Jin ◽  
Xuewen Tian ◽  
...  
Keyword(s):  
Gene Expression ◽  
Differential Expression ◽  
Small Sample ◽  
Differentially Expressed ◽  
Cancer Type ◽  
Rna Seq ◽  
Sample Sizes ◽  
Large Sample ◽  
Expression Levels ◽  
Gene Expression Levels

Abstract Background RNA sequencing (RNA-Seq) has been widely applied in oncology for monitoring transcriptome changes. However, the emerging problem that high variation of gene expression levels caused by tumor heterogeneity may affect the reproducibility of differential expression (DE) results has rarely been studied. Here, we investigated the reproducibility of DE results for any given number of biological replicates between 3 and 24 and explored why a great many differentially expressed genes (DEGs) were not reproducible. Results Our findings demonstrate that poor reproducibility of DE results exists not only for small sample sizes, but also for relatively large sample sizes. Quite a few of the DEGs detected are specific to the samples in use, rather than genuinely differentially expressed under different conditions. Poor reproducibility of DE results is mainly caused by high variation of gene expression levels for the same gene in different samples. Even though biological variation may account for much of the high variation of gene expression levels, the effect of outlier count data also needs to be treated seriously, as outlier data severely interfere with DE analysis. Conclusions High heterogeneity exists not only in tumor tissue samples of each cancer type studied, but also in normal samples. High heterogeneity leads to poor reproducibility of DEGs, undermining generalization of differential expression results. Therefore, it is necessary to use large sample sizes (at least 10 if possible) in RNA-Seq experimental designs to reduce the impact of biological variability and DE results should be interpreted cautiously unless soundly validated.

Concentration inequalities for the empirical distribution of discrete distributions: beyond the method of types

2019 ◽  
Vol 9 (4) ◽  
pp. 813-850 ◽  
Author(s):  
Jay Mardia ◽  
Jiantao Jiao ◽  
Ervin Tánczos ◽  
Robert D Nowak ◽  
Tsachy Weissman
Keyword(s):  
Sample Size ◽  
Empirical Distribution ◽  
Discrete Distributions ◽  
Concentration Inequalities ◽  
Sample Sizes ◽  
Alphabet Size ◽  
Large Sample ◽  
Kl Divergence ◽  
The Difference ◽  
True Distribution

Abstract We study concentration inequalities for the Kullback–Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes of sample size $n$ and alphabet size $k$, and the improvement becomes more significant when $k$ is large. We discuss the applications of our results in obtaining tighter concentration inequalities for $L_1$ deviations of the empirical distribution from the true distribution, and the difference between concentration around the expectation or zero. We also obtain asymptotically tight bounds on the variance of the KL divergence between the empirical and true distribution, and demonstrate their quantitatively different behaviours between small and large sample sizes compared to the alphabet size.

What's the Score?

2000 ◽  
Vol 21 (1) ◽  
pp. 57-58
Author(s):  
David Birnbaum
Keyword(s):  
Confidence Interval ◽  
Infection Rate ◽  
Binomial Distribution ◽  
Sample Sizes ◽  
Negative Numbers ◽  
Large Sample ◽  
Infection Surveillance

AbstractIf you have calculated a confidence interval for an infection rate and found the interval extending into meaningless negative numbers, chances are the error is due to use of approximation formulae. Many of us unknowingly were taught to use the Wald approximation, which does not always approximate the exact binomial distribution accurately. Poor approximation can occur in infection surveillance at both small and large sample sizes.

scholarly journals Simple Recoder (SRc): Alat Bantu Pengkodean Hasil Kuesioner Online

2019 ◽  
Vol 1 (4) ◽  
Author(s):  
R. Pasifikus Christa Wijaya
Keyword(s):  
Online Survey ◽  
Effective Means ◽  
Research Data ◽  
The Internet ◽  
Sample Sizes ◽  
Online Surveys ◽  
Large Sample ◽  
Current Survey ◽  
Survey Results ◽  
Use Of The Internet

Online survey is considered as an effective means to collect research data. The use of the internet benefits researchers to get large sample sizes in almost unlimited reach. Unfortunately, the editing and coding of the results of the current survey is often constrained by outcomes that are still in the form of word responses. We introduce Simple Recoder (SRc) to make it easier for researchers to provide codes on response responses, especially on the results of online surveys. This tool will make it easier for researchers and students to organize data from online survey results.

scholarly journals Fast model-based ordination with copulas

2021 ◽  
Author(s):  
Gordana C. Popovic ◽  
Francis K.C. Hui ◽  
David I. Warton
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Current Model ◽  
Sample Sizes ◽  
Major Drawback ◽  
Large Sample ◽  
Model Based ◽  
Ordination Methods ◽  
Order Of Magnitude ◽  
Taxonomic Groups

Visualising data is a vital part of analysis, allowing researchers to find patterns, and assess and communicate the results of statistical modeling. In ecology, visualisation is often challenging when there are many variables (often for different species or other taxonomic groups) and they are not normally distributed (often counts or presence-absence data). Ordination is a common and powerful way to overcome this hurdle by reducing data from many response variables to just two or three, to be easily plotted. Ordination is traditionally done using dissimilarity-based methods, most commonly non-metric multidimensional scaling (nMDS). In the last decade however, model-based methods for unconstrained ordination have gained popularity. These are primarily based on latent variable models, with latent variables estimating the underlying, unobserved ecological gradients. Despite some major benefits, a major drawback of model-based ordination methods is their speed, as they typically taking much longer to return a result than dissimilarity-based methods, especially for large sample sizes. We introduce copula ordination, a new, scalable model-based approach to unconstrained ordination. This method has all the desirable properties of model-based ordination methods, with the added advantage that it is computationally far more efficient. In particular, simulations show copula ordination is an order of magnitude faster than current model-based methods, and can even be faster than nMDS for large sample sizes, while being able to produce similar ordination plots and trends as these methods.

scholarly journals SEAGLE: A Scalable Exact Algorithm for Large-Scale Set-Based Gene-Environment Interaction Tests in Biobank Data

2021 ◽  
Vol 12 ◽  
Author(s):  
Jocelyn T. Chi ◽  
Ilse C. F. Ipsen ◽  
Tzu-Hung Hsiao ◽  
Ching-Heng Lin ◽  
Li-San Wang ◽  
...  
Keyword(s):  
Large Scale ◽  
Exact Algorithm ◽  
Large Sample Size ◽  
Environment Interaction ◽  
Sample Sizes ◽  
Computationally Efficient ◽  
Test Statistic ◽  
Large Sample ◽  
Gene Environment Interaction ◽  
Gene Environment

The explosion of biobank data offers unprecedented opportunities for gene-environment interaction (GxE) studies of complex diseases because of the large sample sizes and the rich collection in genetic and non-genetic information. However, the extremely large sample size also introduces new computational challenges in G×E assessment, especially for set-based G×E variance component (VC) tests, which are a widely used strategy to boost overall G×E signals and to evaluate the joint G×E effect of multiple variants from a biologically meaningful unit (e.g., gene). In this work, we focus on continuous traits and present SEAGLE, a Scalable Exact AlGorithm for Large-scale set-based G×E tests, to permit G×E VC tests for biobank-scale data. SEAGLE employs modern matrix computations to calculate the test statistic and p-value of the GxE VC test in a computationally efficient fashion, without imposing additional assumptions or relying on approximations. SEAGLE can easily accommodate sample sizes in the order of 105, is implementable on standard laptops, and does not require specialized computing equipment. We demonstrate the performance of SEAGLE using extensive simulations. We illustrate its utility by conducting genome-wide gene-based G×E analysis on the Taiwan Biobank data to explore the interaction of gene and physical activity status on body mass index.

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