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Generalized Mann–Whitney Type Tests for Microarray Experiments

Author

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  • Daniel Fischer
  • Hannu Oja
  • Johanna Schleutker
  • Pranab K. Sen
  • Tiina Wahlfors

Abstract

type="main" xml:id="sjos12055-abs-0001"> New statistical procedures are introduced to analyse typical microRNA expression data sets. For each separate microRNA expression, the null hypothesis to be tested is that there is no difference between the distributions of the expression in different groups. The test statistics are then constructed having certain type of alternatives in mind. To avoid strong (parametric) distributional assumptions, the alternatives are formulated using probabilities of different orders of pairs or triples of observations coming from different groups, and the test statistics are then constructed using corresponding several-sample U-statistics, natural estimates of these probabilities. Classical several-sample rank test statistics, such as the Kruskal–Wallis and Jonckheere–Terpstra tests, are special cases in our approach. Also, as the number of variables (microRNAs) is huge, we confront a serious simultaneous testing problem. Different approaches to control the family-wise error rate or the false discovery rate are shortly discussed, and it is shown how the Chen–Stein theorem can be used to show that family-wise error rate can be controlled for cluster-dependent microRNAs under weak assumptions. The theory is illustrated with an analysis of real data, a microRNA expression data set on Finnish (aggressive and non-aggressive) prostate cancer patients and their controls.

Suggested Citation

  • Daniel Fischer & Hannu Oja & Johanna Schleutker & Pranab K. Sen & Tiina Wahlfors, 2014. "Generalized Mann–Whitney Type Tests for Microarray Experiments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 672-692, September.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:3:p:672-692
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    References listed on IDEAS

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    1. B.M. Brown & T.P. Hettmansperger, 2002. "Kruskal–Wallis, Multiple Comparisons and Efron Dice," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(4), pages 427-438, December.
    2. Olivier Thas & Jan De Neve & Lieven Clement & Jean-Pierre Ottoy, 2012. "Probabilistic index models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(4), pages 623-671, September.
    3. Sen, Pranab K. & Kang, Moonsu, 2013. "Bivariate high-level exceedance and the Chen–Stein theorem in genomics multiple hypothesis testing perspectives," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1725-1730.
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    2. Edgar Brunner & Frank Konietschke & Markus Pauly & Madan L. Puri, 2017. "Rank-based procedures in factorial designs: hypotheses about non-parametric treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1463-1485, November.

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