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Quantify and control reproducibility in high-throughput experiments


Ensuring reproducibility of results in high-throughput experiments is crucial for biomedical research. Here, we propose a set of computational methods, INTRIGUE, to evaluate and control reproducibility in high-throughput settings. Our approaches are built on a new definition of reproducibility that emphasizes directional consistency when experimental units are assessed with signed effect size estimates. The proposed methods are designed to (1) assess the overall reproducible quality of multiple studies and (2) evaluate reproducibility at the individual experimental unit levels. We demonstrate the proposed methods in detecting unobserved batch effects via simulations. We further illustrate the versatility of the proposed methods in transcriptome-wide association studies: in addition to reproducible quality control, they are also suited to investigating genuine biological heterogeneity. Finally, we discuss the potential extensions of the proposed methods in other vital areas of reproducible research (for example, publication bias and conceptual replications).

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Fig. 1: Accuracy and performance of the proposed methods in simulations.
Fig. 2: Highly reproducible TWAS signals identified from the height GWAS data in the UK Biobank and the GIANT consortium.
Fig. 3: Tissue-consistent and -specific height TWAS signals identified from whole blood and skeletal muscle tissues.

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Data availability

All processed data for simulations and real data analysis are available at GWAS summary statistics for the UK Biobank and the GIANT consortium are available at eQTL data for TWAS analysis are available at

Code availability

The source code for software implementation (in R and C/C++), simulation studies and real data processing are provided in A Docker image that duplicates the complete computational environment for reproducing the reported results can be freely downloaded from


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This work was supported by National Institutes of Health grant nos. R35GM138121, R01DK108805 and R01DK119380.

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Authors and Affiliations



Y.Z., M.G.S. and X.W. conceived the ideas. Y.Z. and X.W. designed the experiments. Y.Z. and X.W. developed methods, implemented software and performed analyses. Y.Z., M.G.S. and X.W. wrote the manuscript.

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Correspondence to Xiaoquan Wen.

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The authors declare no competing interests.

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Peer review information Lin Tang was the primary editor on this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Proportion estimates from batch effect affected high-throughput experiments with no genuine biological signals.

Each simulated dataset consists of 1,000 genes. No gene is differentially expressed in the case (N = 20) and the control (N = 20) samples. In each replication dataset, 500 genes are affected by the unobserved batch effects with various magnitudes (η/σ). The figure shows the estimates of (πIR, πR) from the CEFN and the META models for all magnitudes of batch effects examined. The reproducible proportions across all datasets remain close to 0, while the estimates of the irreproducible proportions monotonically increases as the batch effects become stronger.

Extended Data Fig. 2 A directed acyclic graph representation of the proposed Bayesian hierarchical model.

The estimated effects, \({\hat{\beta }}_{i,j}\)’s are observed, \({\bar{\beta }}_{i}\)’s and βi,j’s are latent random variables. ω, k (or r) are hyper-parameters.

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Supplementary Table 1 and Notes.

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Zhao, Y., Sampson, M.G. & Wen, X. Quantify and control reproducibility in high-throughput experiments. Nat Methods 17, 1207–1213 (2020).

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