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Biostatistics Advance Access originally published online on May 2, 2006
Biostatistics 2007 8(2):197-211; doi:10.1093/biostatistics/kxl001
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

A semiparametric approach for the nonparametric transformation survival model with multiple covariates

Xiao Song* and Shuangge Ma

Department of Biostatistics, University of Washington, Box 357232, 1705 Northeast Pacific Street, Seattle, WA 98195, USA songx{at}u.washington.edu

Jian Huang

Department of Statistics and Actuarial Science and Program in Public Health Genetics, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA

Xiao-Hua Zhou

Department of Biostatistics, University of Washington, Box 357232, 1705 Northeast Pacific Street, Seattle, WA 98195, USA and Puget Sound Health Care System, 1660 South Columbian Way, Seattle, WA 98018, USA

* To whom correspondence should be addressed.

The nonparametric transformation model makes no parametric assumptions on the forms of the transformation function and the error distribution. This model is appealing in its flexibility for modeling censored survival data. Current approaches for estimation of the regression parameters involve maximizing discontinuous objective functions, which are numerically infeasible to implement with multiple covariates. Based on the partial rank (PR) estimator (Khan and Tamer, 2004), we propose a smoothed PR estimator which maximizes a smooth approximation of the PR objective function. The estimator is shown to be asymptotically equivalent to the PR estimator but is much easier to compute when there are multiple covariates. We further propose using the weighted bootstrap, which is more stable than the usual sandwich technique with smoothing parameters, for estimating the standard error. The estimator is evaluated via simulation studies and illustrated with the Veterans Administration lung cancer data set.

Keywords: Nonparametric transformation model; Partial rank estimator; Survival analysis; Weighted bootstrap

Received December 20, 2005; revised April 24, 2006; accepted for publication April 28, 2006.


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