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Biostatistics Advance Access published online on May 2, 2006
Biostatistics, 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
Received December 20, 2005
Revised April 24, 2006
Accepted April 28, 2006

Article

A Semiparametric Approach for the Nonparametric Transformation Survival Model With Multiple Covariates

Xiao Song 1, Shuangge Ma 1 *, Jian Huang 2, and Xiao-Hua Zhou 3

1 Department of Biostatistics, University of Washington, Box 357232, 1705 NE Pacific Street, Seattle, WA 98195, U.S.A.
2 Department of Statistics and Actuarial Science and Program in Public Health Genetics, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, U.S.A.
3 Department of Biostatistics, University of Washington, Box 357232, 1705 NE Pacific Street, Seattle, WA 98195, U.S.A.; Puget Sound Health Care System, 1660 S. Columbian Way, Seattle, WA 98018, U.S.A.

* To whom correspondence should be addressed.
Shuangge Ma, E-mail: shuangge{at}u.washington.edu


  Abstract

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 estimator (Khan and Tamer, 2004), we propose a smoothed partial rank estimator which maximizes a smooth approximation of the partial rank objective function. The estimator is shown to be asymptotically equivalent to the partial rank 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 VA lung cancer data set.

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