Holm–Bonferroni method

Résumé

In statistics, the Holm–Bonferroni method, also called the Holm method or Bonferroni–Holm method, is used to counteract the problem of multiple comparisons. It is intended to control the family-wise error rate (FWER) and offers a simple test uniformly more powerful than the Bonferroni correction. It is named after Sture Holm, who codified the method, and Carlo Emilio Bonferroni. Motivation When considering several hypotheses, the problem of multiplicity arises: the more hypotheses are checked, the higher the probability of obtaining Type I errors (false positives). The Holm–Bonferroni method is one of many approaches for controlling the FWER, i.e., the probability that one or more Type I errors will occur, by adjusting the rejection criteria for each of the individual hypotheses. Formulation The method is as follows:

Suppose you have m p-values, sorted into order lowest-to-highest P_1,\ldots,P_m, and their corresponding hypotheses

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https://en.wikipedia.org/wiki/Holm%E2%80%93Bonferroni_method

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This course is neither an introduction to the mathematics of statistics nor an introduction to a statistics program such as R. The aim of the course is to understand statistics from its experimental design and to avoid common pitfalls of statistical reasoning. There is space to discuss ongoing work.

Ce cours enseigne les notions élémentaires de la théorie de probabilité et de la statistique, tels que l'inférence, les tests et la régression.

This course covers topics in applied biostatistics, with an emphasis on practical aspects of data analysis using R statistical software. Topics include types of studies and their design and analysis, high dimensional data analysis (genetic/genomic) and other topics as time and interest permit.

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Statistical inference in ensemble modeling of cellular metabolism

Marc-Olivier Boldi, Tuure Eelis Hameri, Vassily Hatzimanikatis

Kinetic models of metabolism can be constructed to predict cellular regulation and devise metabolic engineering strategies, and various promising computational workflows have been developed in recent years for this. Due to the uncertainty in the kinetic parameter values required to build kinetic models, these workflows rely on ensemble modeling (EM) principles for sampling and building populations of models describing observed physiologies. Sensitivity coefficients from metabolic control analysis (MCA) of kinetic models can provide important insight about cellular control around a given physiological steady state. However, despite considering populations of kinetic models and their model outputs, current approaches do not provide adequate tools for statistical inference. To derive conclusions from model outputs, such as MCA sensitivity coefficients, it is necessary to rank/compare populations of variables with each other. Currently existing workflows consider confidence intervals (CIs) that are derived independently for each comparable variable. Hence, it is important to derive simultaneous CIs for the variables that we wish to rank/compare. Herein, we used an existing large-scale kinetic model of Escherichia Coli metabolism to present how univariate CIs can lead to incorrect conclusions, and we present a new workflow that applies three different multivariate statistical approaches. We use the Bonferroni and the exact normal methods to build symmetric CIs using the normality assumptions. We then suggest how bootstrapping can compute asymmetric CIs whilst relaxing this normality assumption. We conclude that the Bonferroni and the exact normal methods can provide simple and efficient ways for constructing reliable CIs, with the exact normal method favored over the Bonferroni when the compared variables present dependencies. Bootstrapping, despite its significantly higher computational cost, is recommended when comparing non-normal distributions of variables. Additionally, we show how the Bonferroni method can readily be used to estimate required sample numbers to attain a certain CI size.

2019

Chargement

Statistical inference in ensemble modeling of cellular metabolism

Marc-Olivier Boldi, Tuure Eelis Hameri, Vassily Hatzimanikatis

2019