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Borrowing strength: a likelihood ratio test for related sparse signals.

ABSTRACT: Cancer biology is a field where the complexity of the phenomena battles against the availability of data. Often only a few observations per signal source, i.e. genes, are available. Such scenarios are becoming increasingly more relevant as modern sensing technologies generally have no trouble in measuring lots of channels, but where the number of subjects, such as patients or samples, is limited. In statistics, this problem falls under the heading 'large p, small n'. Moreover, in such situations the use of asymptotic analytical results should generally be mistrusted.We consider two cancer datasets, with the aim to mine the activity of functional groups of genes. We propose a hierarchical model with two layers in which the individual signals share a common variance component. A likelihood ratio test is defined for the difference between two collections of corresponding signals. The small number of observations requires a careful consideration of the bias of the statistic, which is corrected through an explicit Bartlett correction. The test is validated on Monte Carlo simulations, which show improved detection of differences compared with other methods. In a leukaemia study and a cancerous fibroblast cell line, we find that the method also works better in practice, i.e. it gives a richer picture of the underlying biology.The MATLAB code is available from the authors or on http://www.math.rug.nl/stat/Software.e.c.wit@rug.nl d.bakewell@liv.ac.uk.

SUBMITTER: Wit EC

PROVIDER: S-EPMC3400963 | biostudies-literature | 2012 Aug

REPOSITORIES: biostudies-literature

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Borrowing strength: a likelihood ratio test for related sparse signals.

Wit Ernst C EC Bakewell David J G DJ

Bioinformatics (Oxford, England) 20120604 15

<h4>Motivation</h4>Cancer biology is a field where the complexity of the phenomena battles against the availability of data. Often only a few observations per signal source, i.e. genes, are available. Such scenarios are becoming increasingly more relevant as modern sensing technologies generally have no trouble in measuring lots of channels, but where the number of subjects, such as patients or samples, is limited. In statistics, this problem falls under the heading 'large p, small n'. Moreover, ...[more]

PMID: 22668791

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Project description:The assumption of Hardy-Weinberg equilibrium (HWE) is generally required for association analysis using case-control design on autosomes; otherwise, the size may be inflated. There has been an increasing interest of exploring the association between diseases and markers on X chromosome and the effect of the departure from HWE on association analysis on X chromosome. Note that there are two hypotheses of interest regarding the X chromosome: (i) the frequencies of the same allele at a locus in males and females are equal and (ii) the inbreeding coefficient in females is zero (without excess homozygosity). Thus, excess homozygosity and significantly different minor allele frequencies between males and females are used to filter X-linked variants. There are two existing methods to test for (i) and (ii), respectively. However, their size and powers have not been studied yet. Further, there is no existing method to simultaneously detect both hypotheses till now. Therefore, in this article, we propose a novel likelihood ratio test for both (i) and (ii) on X chromosome. To further investigate the underlying reason why the null hypothesis is statistically rejected, we also develop two likelihood ratio tests for detecting (i) and (ii), respectively. Moreover, we explore the effect of population stratification on the proposed tests. From our simulation study, the size of the test for (i) is close to the nominal significance level. However, the size of the excess homozygosity test and the test for both (i) and (ii) is conservative. So, we propose parametric bootstrap techniques to evaluate their validity and performance. Simulation results show that the proposed methods with bootstrap techniques control the size well under the respective null hypothesis. Power comparison demonstrates that the methods with bootstrap techniques are more powerful than those without bootstrap procedure and the existing methods. The application of the proposed methods to a rheumatoid arthritis dataset indicates their utility.

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Borrowing strength: a likelihood ratio test for related sparse signals.

Publications

Borrowing strength: a likelihood ratio test for related sparse signals.

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