  In biomedical studies it is of substantial interest to develop risk
prediction scores using high-dimensional data such as gene expression data for
clinical endpoints that are subject to censoring. In the presence of
well-established clinical risk factors, investigators often prefer a procedure
that also adjusts for these clinical variables. While accelerated failure time
(AFT) models are a useful tool for the analysis of censored outcome data, it
assumes that covariate effects on the logarithm of time-to-event are linear,
which is often unrealistic in practice. We propose to build risk prediction
scores through regularized rank estimation in partly linear AFT models, where
high-dimensional data such as gene expression data are modeled linearly and
important clinical variables are modeled nonlinearly using penalized regression
splines. We show through simulation studies that our model has better operating
characteristics compared to several existing models. In particular, we show
that there is a nonnegligible effect on prediction as well as feature selection
when nonlinear clinical effects are misspecified as linear. This work is
motivated by a recent prostate cancer study, where investigators collected gene
expression data along with established prognostic clinical variables and the
primary endpoint is time to prostate cancer recurrence.

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