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Estimation of the false discovery proportion with unknown dependence.

ABSTRACT: Large-scale multiple testing with correlated test statistics arises frequently in many scientific research. Incorporating correlation information in approximating false discovery proportion has attracted increasing attention in recent years. When the covariance matrix of test statistics is known, Fan, Han & Gu (2012) provided an accurate approximation of False Discovery Proportion (FDP) under arbitrary dependence structure and some sparsity assumption. However, the covariance matrix is often unknown in many applications and such dependence information has to be estimated before approximating FDP. The estimation accuracy can greatly affect FDP approximation. In the current paper, we aim to theoretically study the impact of unknown dependence on the testing procedure and establish a general framework such that FDP can be well approximated. The impacts of unknown dependence on approximating FDP are in the following two major aspects: through estimating eigenvalues/eigenvectors and through estimating marginal variances. To address the challenges in these two aspects, we firstly develop general requirements on estimates of eigenvalues and eigenvectors for a good approximation of FDP. We then give conditions on the structures of covariance matrices that satisfy such requirements. Such dependence structures include banded/sparse covariance matrices and (conditional) sparse precision matrices. Within this framework, we also consider a special example to illustrate our method where data are sampled from an approximate factor model, which encompasses most practical situations. We provide a good approximation of FDP via exploiting this specific dependence structure. The results are further generalized to the situation where the multivariate normality assumption is relaxed. Our results are demonstrated by simulation studies and some real data applications.

SUBMITTER: Fan J

PROVIDER: S-EPMC5648371 | biostudies-literature | 2017 Sep

REPOSITORIES: biostudies-literature

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Estimation of the false discovery proportion with unknown dependence.

Fan Jianqing J Han Xu X

Journal of the Royal Statistical Society. Series B, Statistical methodology 20160926 4

Large-scale multiple testing with correlated test statistics arises frequently in many scientific research. Incorporating correlation information in approximating false discovery proportion has attracted increasing attention in recent years. When the covariance matrix of test statistics is known, Fan, Han & Gu (2012) provided an accurate approximation of False Discovery Proportion (FDP) under arbitrary dependence structure and some sparsity assumption. However, the covariance matrix is often unk ...[more]

PMID: 29056863

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Project description:BackgroundIn the analysis of microarray data one generally produces a vector of p-values that for each gene give the likelihood of obtaining equally strong evidence of change by pure chance. The distribution of these p-values is a mixture of two components corresponding to the changed genes and the unchanged ones. The focus of this article is how to estimate the proportion unchanged and the false discovery rate (FDR) and how to make inferences based on these concepts. Six published methods for estimating the proportion unchanged genes are reviewed, two alternatives are presented, and all are tested on both simulated and real data. All estimates but one make do without any parametric assumptions concerning the distributions of the p-values. Furthermore, the estimation and use of the FDR and the closely related q-value is illustrated with examples. Five published estimates of the FDR and one new are presented and tested. Implementations in R code are available.ResultsA simulation model based on the distribution of real microarray data plus two real data sets were used to assess the methods. The proposed alternative methods for estimating the proportion unchanged fared very well, and gave evidence of low bias and very low variance. Different methods perform well depending upon whether there are few or many regulated genes. Furthermore, the methods for estimating FDR showed a varying performance, and were sometimes misleading. The new method had a very low error.ConclusionThe concept of the q-value or false discovery rate is useful in practical research, despite some theoretical and practical shortcomings. However, it seems possible to challenge the performance of the published methods, and there is likely scope for further developing the estimates of the FDR. The new methods provide the scientist with more options to choose a suitable method for any particular experiment. The article advocates the use of the conjoint information regarding false positive and negative rates as well as the proportion unchanged when identifying changed genes.

Dataset Information

Estimation of the false discovery proportion with unknown dependence.

Publications

Estimation of the false discovery proportion with unknown dependence.

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