Assessing the statistical significance of risk factors when screening large numbers of $urn:x-wiley:15410420:media:biom12957:biom12957-math-0003$ tables that cross-classify disease status with each type of exposure poses a challenging multiple testing problem. The problem is especially acute in large-scale genomic case-control studies. We develop a potentially more powerful and computationally efficient approach (compared with existing methods, including Bonferroni and permutation testing) by taking into account the presence of complex dependencies between the $urn:x-wiley:15410420:media:biom12957:biom12957-math-0004$ tables. Our approach gains its power by exploiting Monte Carlo simulation from the estimated null distribution of a maximally selected log-odds ratio. We apply the method to case-control data from a study of a large collection of genetic variants related to the risk of early onset stroke.

Supporting Information

References

Barber, R. F. and E. J. Candès (2015). Controlling the false discovery rate via knockoffs. Annals of Statistics 43, 2055–2085.
10.1214/15-AOS1337
Web of Science® Google Scholar
Cai, T. T., Ren, Z., and H. Zhou (2016). Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation. Electronic Journal of Statistics 10, 1–59.
10.1214/15-EJS1081
Web of Science® Google Scholar
Candès, E. J. , Fan, Y., Janson, L., and J. Lv (2018). Panning for gold: Model-free knockoffs for high-dimensional controlled variable selection. Journal of the Royal Statistical Society, Series B 80, 551–577.
10.1111/rssb.12265
Google Scholar
Carvajal-Rodriguez, A., de Una-Alvarez, J., and E. Rolan-Alvarez (2009). A new multitest correction (SGoF) that increases its statistical power when increasing the number of tests. BMC Bioinformatics 10, 209.
10.1186/1471-2105-10-209
CAS PubMed Web of Science® Google Scholar
Churchill, G. A. and R.W. Doerge (1994). Empirical threshold values for quantitative trait mapping. Genetics 138, 963–971.
10.1093/genetics/138.3.963
CAS PubMed Web of Science® Google Scholar
Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and Their Application. New York: Cambridge University Press.
10.1017/CBO9780511802843
Google Scholar
Donoho, D. and Jin, J. (2004). Higher criticism for detecting sparse heterogeneous mixtures. Annals of Statistics 32, 962–994.
10.1214/009053604000000265
Web of Science® Google Scholar
Donoho, D. and Jin, J. (2015). Higher criticism for large-scale inference, especially for rare and weak effects. Statistical Science 30, 1–25.
10.1214/14-STS506
Web of Science® Google Scholar
Dudoit, S. and van der Laan, M. J. (2008). Multiple Testing Procedures with Applications to Genomics.New York: Springer.
10.1007/978-0-387-49317-6
Google Scholar
Efron, B. (2010). Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction. Cambridge New York: University Press.
10.1017/CBO9780511761362
Google Scholar
Guinness, J. and M. Fuentes (2017). Circulant embedding of approximate covariances for inference from Gaussian data on large lattices. Journal of Computational and Graphical Statistics 26, 88–97.
10.1080/10618600.2016.1164534
Web of Science® Google Scholar
Keogh, R. H. and Cox, D. R. (2014). Case-Control Studies. New York: Cambridge University Press.
10.1017/CBO9781139094757
Google Scholar
Kou, S. G. and Ying, Z. (1996). Asymptotics for a $urn:x-wiley:15410420:media:biom12957:biom12957-math-0241$ table with fixed margins. Statistica Sinica 6, 809–829.
Web of Science® Google Scholar
Kou, S. G. and Ying, Z. (2006). Analysis of sequences of dependent $urn:x-wiley:15410420:media:biom12957:biom12957-math-0242$ tables. In Random Walk, Sequential Analysis and Related Topics, A. C. Hsiung, Z. Ying, and C.-H. Zhang (eds), 171–198. Singapore: World Scientific.
10.1142/9789812772558_0012
Google Scholar
McKeague, I. W. and M. Qian (2015a). An adaptive resampling test for detecting the presence of significant predictors (with discussion). Journal of the American Statistical Association 110, 1422–1433.
10.1080/01621459.2015.1095099
CAS PubMed Web of Science® Google Scholar
McKeague, I. W. and M. Qian (2015b). Rejoinder to the discussants of An Adaptive Resampling Test for Detecting the Presence of Significant Predictors.Journal of the American Statistical Association 110, 1459–1462.
10.1080/01621459.2015.1107431
CAS Web of Science® Google Scholar
Risk Assessment of Cerebrovascular Events (RACE) Study (2017). https://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000456.v1.p1 [accession number ph s000456.v1.p1].
Google Scholar
Reis, I. M., Hirji, K. F. and Afifi, A. A. (1999). Exact and asymptotic tests for homogeneity in several $urn:x-wiley:15410420:media:biom12957:biom12957-math-0243$ tables. Statistics in Medicine, 18, 893–906.
10.1002/(SICI)1097-0258(19990430)18:8<893::AID-SIM84>3.0.CO;2-5
CAS PubMed Web of Science® Google Scholar
Sham, P. C., and Purcell, S. M. (2014). Statistical power and significance testing in large-scale genetic studies. Nature Reviews Genetics 15, 335–346.
10.1038/nrg3706
CAS PubMed Web of Science® Google Scholar
Taylor, J. and Tibshirani, R. (2018). Post-selection inference for $urn:x-wiley:15410420:media:biom12957:biom12957-math-0244$ –penalized likelihood models. Canadian Journal of Statistics 46, 41–61.
10.1002/cjs.11313
PubMed Web of Science® Google Scholar
Wen, X. and M. Stephens (2010). Using linear predictors to impute allele frequencies from summary or pooled genotype data. Annals of Applied Statistics, 4, 1158–1182.
10.1214/10-AOAS338
PubMed Web of Science® Google Scholar
Wu, M. C., Kraft, P., Epstein, M. P., Taylor, D. M., Chanock, S. J., Hunter, D. J. et al. (2010). Powerful SNP-set analysis for case-control genome-wide association studies. American Journal of Human Genetics 86, 929–942.
10.1016/j.ajhg.2010.05.002
CAS PubMed Web of Science® Google Scholar