Rank-based meta-analysis: signal reconstruction versus rank aggregation Seminar

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Abstract: Rank data have the advantage of being invariant to transformation and normalisation as long as the relative orderings are preserved and therefore they are most suitable for certain tasks such as the meta-analysis of genomic data obtained from different sources or experiments. Various rank aggregation techniques are readily available and covered in the recently published R package TopKLists [Schimek et al. (2015) DOI 10.1515/sagmb-2014-0093]. Here we propose an alternative approach that aims at the statistical reconstruction of the common signals that have informed those ranks observed in the experiments of interest. This can be achieved by indirect inference. The thus obtained signal estimates represent the consensus of several rankings in the sense of meta-analysis or data integration. A simple but flexible signal plus noise model of the unobserved multiple measurements causal for the observed rankings is assumed. For the evaluation of the model based on the empirical matrix of ranks we apply a distribution function approach in combination with an adaptive Metropolis algorithm for numerical optimisation. Moreover, under the empirical distribution function we can employ non-parametric bootstrap to estimate the standard errors of the signal parameters. As a by-product, rank aggregation results can be obtained from the signal estimates. In a real data problem the new approach is compared to conventional rank aggregation techniques.