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Biostatistics Advance Access originally published online on June 20, 2006
Biostatistics 2007 8(2):306-322; doi:10.1093/biostatistics/kxl011
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Adaptive design: estimation and inference with censored data in a semiparametric model

Yu Shen*

Department of Biostatistics, M. D. Anderson Cancer Center, Houston, TX 77030, USA yshen{at}mdanderson.org

Yi Cheng

Department of Mathematical Sciences, Indiana University at South Bend, IN 46634, USA

* To whom correspondence should be addressed.

In this article, we provide a method of estimation for the treatment effect in the adaptive design for censored survival data with or without adjusting for risk factors other than the treatment indicator. Within the semiparametric Cox proportional hazards model, we propose a bias-adjusted parameter estimator for the treatment coefficient and its asymptotic confidence interval at the end of the trial. The method for obtaining an asymptotic confidence interval and point estimator is based on a general distribution property of the final test statistic from the weighted linear rank statistics at the interims with or without considering the nuisance covariates. The computation of the estimates is straightforward. Extensive simulation studies show that the asymptotic confidence intervals have reasonable nominal probability of coverage, and the proposed point estimators are nearly unbiased with practical sample sizes.

Keywords: Confidence interval; Cox model; Martingale; Nuisance covariates; Point estimator; Self-designing

Received December 5, 2005; revised April 7, 2006; accepted for publication June 16, 2006.


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