Biomedical subjects

David R Bickel

Publications and source records attributed to David R Bickel.

4 recordsLinked to original sources

PubMed2004

Probabilities of spurious connections in gene networks: application to expression time series.

MOTIVATION: The reconstruction of gene networks from gene-expression microarrays is gaining popularity as methods improve and as more data become available. The reliability of such networks could be judged by the probability that a connection between genes is spurious, resulting from chance fluctuations rather than from a true biological relationship. RESULTS: Unlike the false discovery rate and positive false discovery rate, the decisive false discovery rate (dFDR) is exactly equal to a conditional probability without assuming independence or the randomness of hypothesis truth values. This property is useful not only in the common application to the detection of differential gene expression, but also in determining the probability of a spurious connection in a reconstructed gene network. Estimators of the dFDR can estimate each of three probabilities: (1) The probability that two genes that appear to be associated with each other lack such association. (2) The probability that a time ordering observed for two associated genes is misleading. (3) The probability that a time ordering observed for two genes is misleading, either because they are not associated or because they are associated without a lag in time. The first probability applies to both static and dynamic gene networks, and the other two only apply to dynamic gene networks.

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PubMed2004

Error-rate and decision-theoretic methods of multiple testing: which genes have high objective probabilities of differential expression?

Given a multiple testing situation, the null hypotheses that appear to have sufficiently low probabilities of truth may be rejected using a simple, nonparametric method based on decision theory. This applies not only to posterior levels of belief, but also to conditional probabilities in the sense of relative frequencies, as seen from their equality to local false discovery rates (dFDRs). This approach neither requires the estimation of probability densities, nor of their ratios. Decision theory can also inform the selection of false discovery rate weights. An application to gene expression microarrays is presented with a discussion of the applicability of the assumption of "clumpy dependence."

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PubMed2004

Degrees of differential gene expression: detecting biologically significant expression differences and estimating their magnitudes.

MOTIVATION: Many methods of identifying differential expression in genes depend on testing the null hypotheses of exactly equal means or distributions of expression levels for each gene across groups, even though a statistically significant difference in the expression level does not imply the occurrence of any difference of biological or clinical significance. This is because a mathematical definition of 'differential expression' as any non-zero difference does not correspond to the differential expression biologists seek. Furthermore, while some current methods account for multiple comparisons in hypothesis tests, they do not accordingly adjust estimates of the degrees to which genes are differentially expressed. Both problems lead to overstating the relevance of findings. RESULTS: Testing whether genes have relevant differential expression can be accomplished with customized null hypotheses, thereby redefining 'differential expression' in a way that is more biologically meaningful. When such tests control the false discovery rate, they effectively discover genes based on a desired quantile of differential gene expression. Estimation of the degree to which genes are differentially expressed has been corrected for multiple comparisons. AVAILABILITY: R code is freely available from http://www.davidbickel.com and may become available from www.r-project.org or www.bioconductor.org SUPPLEMENTARY INFORMATION: Applications to cancer microarrays, an application in the absence of differential expression, pseudocode, and a guide to customizing the methods may be found at www.davidbickel.com and www.mathpreprints.com

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PubMed2003

Robust cluster analysis of microarray gene expression data with the number of clusters determined biologically.

MOTIVATION: The success of each method of cluster analysis depends on how well its underlying model describes the patterns of expression. Outlier-resistant and distribution-insensitive clustering of genes are robust against violations of model assumptions. RESULTS: A measure of dissimilarity that combines advantages of the Euclidean distance and the correlation coefficient is introduced. The measure can be made robust using a rank order correlation coefficient. A robust graphical method of summarizing the results of cluster analysis and a biological method of determining the number of clusters are also presented. These methods are applied to a public data set, showing that rank-based methods perform better than log-based methods. AVAILABILITY: Software is available from http://www.davidbickel.com.

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