Abstract
Multiple correlated time-to-event endpoints often occur in clinical trials and some time-to-event endpoints are more important than others. Most weighted multiple testing adjustment methods have been proposed to control family-wise type I error rates either only consider the correlation among continuous or binary endpoints or totally disregard the correlation among the endpoints. For continuous or binary endpoints, the correlation matrix can be directly estimated from the corresponding correlated endpoints. However, it is challenging to directly estimate the correlation matrix from the multiple endpoints in survival data since censoring is involved. In this chapter, we propose a weighted multiple testing correction method for correlated time-to-event endpoints in survival data, based on the correlation matrix estimated from the WLW method proposed by Wei, Lin, and Weissfeld. Simulations are conducted to study the family-wise type I error rate of the proposed method and to compare the power performance of the proposed method to the nonparametric multiple testing methods such as the alpha-exhaustive fallback (AEF), fixed-sequence (FS), and the weighted Holm-Bonferroni method when used for the correlated time-to-event endpoints. The proposed method and others are illustrated using a real dataset from Fernald Community Cohort (formerly known as the Fernald Medical Monitoring Program).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alosh, M., Huque, M.F.: A flexible strategy for testing subgroups and overall population. Stat. Med. 28, 3–23 (2009)
Conneely, K.N., Boehnke, M.: So many correlated tests, so little time! Rapid adjustment of p values for multiple correlated tests. Am. J. Hum. Genet. 81, 1158–1168 (2007)
Fan, J., Gijbels, I., King, M.: Local likelihood and local partial likelihood in hazard regression. Ann. Stat. 25(4), 1661–1690 (1997)
Fernald Medical Monitoring Program Website: https://urldefense.proofpoint.com/v2/url?u=http- 3A__www.eh.uc.edu_fmmp&d=AAIGAQ&c=4sF48jRmVAe_CH-k9mXYXEGfSnM3bY53 YSKuLUQRxhA&r=656gLa67DL3AtCWt3Jb0tIRzTwk1qCp1OB7YsvvcToI&m=6W9WCE ZFMxFnHnV55uMK2eK2NDafDEWbmZP_2DcdldA&s=HjK4SFlUlSnSDz50bfhJBuDPUC EfjPDRzFZTbg0sAl0&e= (2014). Cited 15 Nov 2014
Genz, A.: Numerical computation of multivariate normal probabilities. J. Comput. Graph. Stat. 1, 141–149 (1992)
Genz, A.: Comparison of methods for the computation of multivariate normal probabilities. Comput. Sci. Stat. 25, 400–405 (1993)
Genz, A., Bretz, F., Hothorn, T.: mvtnorm: multivariate normal and t distribution. R package version 2.12.0. Available at https://urldefense.proofpoint.com/v2/url?u=http-3A__cran.r-2Dproject.org_web_packages_mvtnorm_&d=AAIGAQ&c=4sF48jRmVAe_CH-k9mXYXEGfSn M3bY53YSKuLUQRxhA&r=656gLa67DL3AtCWt3Jb0tIRzTwk1qCp1OB7YsvvcToI&m=6 W9WCEZFMxFnHnV55uMK2eK2NDafDEWbmZP_2DcdldA&s=4LjNlTNOcwwRiQYj7_ CHG0qMaZIphbnaImMOKgYfryk&e=\index.html (2014). Cited 15 Nov 2014
Higham, N.J.: Computing the nearest correlation matrix - A problem from finance. IMA J. Numer. Anal. 22(3), 329–343 (2002)
Holm, S.: A simple sequentially rejective multiple test procedure. Scand. J. Stat. 6, 65–70 (1979)
Huque, M.F., Alosh, M.: A flexible fixed-sequence testing method for hierarchically ordered correlated multiple endpoints in clinical trials. J. Stat. Plann. Inference 138, 321–335 (2008)
Pocock, S.J., Geller, N.L., Tsiatis, A.A.: The analysis of multiple endpoints in clinical trials. Biometrics 43, 487–498 (1987)
R Development Core Team: R: a language and environment for statistical computing. R Foundation for Statistical Computing. Aavailable at https://urldefense.proofpoint.com/v2/url?u=http-3A__www.r-2Dproject.org_&d=AAIGAQ&c=4sF48jRmVAe_CH-k9mXYXEGfSnM3bY53YSKuL UQRxhA&r=656gLa67DL3AtCWt3Jb0tIRzTwk1qCp1OB7YsvvcToI&m=6W9WCEZFMxFn HnV55uMK2eK2NDafDEWbmZP_2DcdldA&s=k45dskHmTjrjhL-mG248jkpbB-Vc6UP2wX W0uveFHtw&e= (2014). Cited 15 Nov 2014
The ORIGIN Trial Investigators: Rationale, design and baseline characteristics for a large simple international trial of cardiovascular disease prevention in people with dysglycaemia: the ORIGIN trial. Am. Heart J. 155, 26–32 (2008)
Wei, L.J., Lin, D.Y., Weissfeld, L.: Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J. Am. Stat. Assoc. 84, 1065–1073 (1989)
Westfall, P.H., Kropf, S., Finos, L.: Weighted FWE-controlling methods in high-dimensional situations. In: Recent Developments in Multiple Comparison Procedures. IML Lecture Notes and Monograph Series, vol. 47, pp. 143–154. Institute of Mathematical Statistics, Beachwood (2004)
Wiens, B.L.: A fixed sequence Bonferroni procedure for testing multiple endpoints. Pharm. Stat. 2, 211–215 (2003)
Wiens, B.L., Dmitrienko, A.: The fallback procedure for evaluating a single family of hypotheses. J. Biopharm. Stat. 15, 929–942 (2005)
Wiens, B.L., Dmitrienko, A.: On selecting a multiple comparison procedure for analysis of a clinical trial: fallback, fixed sequence, and related procedures. Stat. Biopharm. Res. 2, 22–32 (2010)
Wones, R., Pinney, S.M., Buckholz, J., Deck-Tebbe, C., Freyberg, R., Pesce, A.: Medical monitoring: a beneficial remedy for residents living near an environmental hazard site. J. Occup. Environ. Med. 51(12), 1374–1383 (2009)
Xie, C.: Weighted multiple testing correction for correlated tests. Stat. Med. 31, 341–352 (2012)
Xie, C., Lu, X., Pogue, J., Chen, D.: Weighted multiple testing corrections for correlated binary endpoints. Commun. Stat. Simul. Comput. 42(8), 1693–1702 (2013)
Xie, C.: Relations among three parametric multiple testing methods for correlated tests. J. Stat. Comput. Simul. 84(4), 812–818 (2014)
Acknowledgements
This project was supported by the National Center for Research Resources and the National Center for Advancing Translational Sciences, National Institutes of Health, through Grant 8 UL1 TR000077-04 and National Institute for Environmental Health Sciences, Grant P30-ES006096 (UC Center for Environmental Genetics). The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Xie, C., Ghulam, E., Chen, A., Wang, K., Pinney, S.M., Lindsell, C. (2015). Weighted Multiple Testing Correction for Correlated Endpoints in Survival Data. In: Chen, DG., Wilson, J. (eds) Innovative Statistical Methods for Public Health Data. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-18536-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-18536-1_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18535-4
Online ISBN: 978-3-319-18536-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)