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Many experiments conducted in molecular biology compare intensity values obtained by micro-RNA transcriptomics, proteomics or metabolomics ('Omics') procedures between two groups of independent biological samples differing in an experimental condition or in the health status of the subjects the samples were taken from. A special characteristic of such data is the frequent occurrence of zero intensity values caused by compounds (e.g., micro RNAs, peptides or metabolites) that cannot be detected in some samples. Zero intensities can arise either by true absence of a compound or by a signal that is below a technical limit of detection.

The distribution of observed signals is often viewed either as a mixture of a binomial distribution (absence or presence of a detectable signal) and a continuous subdistribution (intensity if signal is present) or as a left-censored continuous distribution. While one-part tests such as the T-test or Wilcoxon's rank-sum test treat the zero-inflated distributions as left-censored, so-called two-part tests compare mixture distributions between groups. R codes for the two-part T-test and the two-part Wilcoxon test as well as the non-parametric Empirical Likelihood Ratio Test are given in Appendix 2 of Taylor and Pollard (2009).

The Left-Inflated Mixture model combines one- and two-part approaches under the assumption of a log-normal subdistribution (cf. Moulton and Halsey, 1995). For a vector of intensity values (including? zeros?) and a vector of group codes our R function calculates a likelihood ratio p-value and an estimate of the log fold change. Furthermore, direct estimates for the proportions of the two considered types of zero intensities (biological, technical) are provided.

References:

**Gleiss, A., Dakna, M., Mischak, H., Heinze, G.** (2015): "Two-group comparisons of zero-inflated intensity values: the choice of test statistic matters" *Bioinformatics*, Bioinformatics, 31(14), 2015, 2310-2317 (doi:10.1093/bioinformatics/btv154)

**Moulton, L.U. and Halsey, N.A. **(1995): "A mixture model with detection limits for regression analyses of antibody response to vaccine", *Biometrics* 51, 1570-1578

**Taylor, S. and Pollard, K.** (2009): "Hypothesis tests for point-mass mixture data with application to ´omics data with many zero values", *Stat. Appl. Genet. Mo. B*. 8, 1-43

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