Department of Mathematics
When testing a large number of hypotheses, estimating the proportion of true nulls, denoted by π0, becomes increasingly important. This quantity has many applications in practice. For instance, a reliable estimate of π0 can eliminate the conservative bias of the Benjamini-Hochberg procedure on controlling the false discovery rate. It is known that most methods in the literature for estimating π0 are conservative. Recently, some attempts have been paid to reduce such estimation bias. Nevertheless, they are either over bias corrected or suffering from an unacceptably large estimation variance. In this paper, we propose a new method for estimating π0 that aims to reduce the bias and variance of the estimation simultaneously. To achieve this, we first utilize the probability density functions of false-null p-values and then propose a novel algorithm to estimate the quantity of π0. The statistical behavior of the proposed estimator is also investigated. Finally, we carry out extensive simulation studies and several real data analysis to evaluate the performance of the proposed estimator. Both simulated and real data demonstrate that the proposed method may improve the existing literature significantly.
Effect size, False-null p-value, Microarray data, Multiple testing, Probability density function, Upper tail probability
Source Publication Title
Oxford University Press
This is a pre-copyedited, author-produced version of an article accepted for publication in Biostatistics following peer review. The version of record Yebin Cheng, Dexiang Gao, Tiejun Tong; Bias and variance reduction in estimating the proportion of true-null hypotheses. Biostatistics 2015; 16 (1): 189-204. doi: 10.1093/biostatistics/kxu029 is available online at: https://doi.org/10.1093/biostatistics/kxu029.
Yebin Cheng’s research was supported in part by National Natural Science Foundation of China grant No.11271241) and Shanghai Leading Academic Discipline Project No.863. Dexiang Gao’s research was supported in part by NIH grant R01 CA 157850-02 and 51P30 CA46934. Tiejun Tong’s research was supported in part by Hong Kong Research grant HKBU202711 and Hong Kong Baptist University FRG grants FRG2/11-12/110 and FRG1/13-14/018.
Link to Publisher's Edition
Cheng, Y., Gao, D., & Tong, T. (2015). Bias and variance reduction in estimating the proportion of true-null hypotheses. Biostatistics, 16 (1), 189-204. https://doi.org/10.1093/biostatistics/kxu029