The nonparametric transformation model for survival time that makes no parametric assumptions on both the transformation function and the error is appealing in its flexibility. The nonparametric transformation model makes no assumption 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 in the case of multiple covariates. Based on the partial rank estimator (Khan & 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 by application to real data.
Song, Xiao; Ma, Shuangge; Huang, Jian; and Zhou, Xiao-Hua, "A Semiparametric Approach for the Nonparametric Transformation Survival Model With Multiple Covariates" (December 2006). UW Biostatistics Working Paper Series. Working Paper 302.