  Semiparametric accelerated failure time (AFT) models directly relate the
predicted failure times to covariates and are a useful alternative to models
that work on the hazard function or the survival function. For case-cohort
data, much less development has been done with AFT models. In addition to the
missing covariates outside of the sub-cohort in controls, challenges from AFT
model inferences with full cohort are retained. The regression parameter
estimator is hard to compute because the most widely used rank-based estimating
equations are not smooth. Further, its variance depends on the unspecified
error distribution, and most methods rely on computationally intensive
bootstrap to estimate it. We propose fast rank-based inference procedures for
AFT models, applying recent methodological advances to the context of
case-cohort data. Parameters are estimated with an induced smoothing approach
that smooths the estimating functions and facilitates the numerical solution.
Variance estimators are obtained through efficient resampling methods for
nonsmooth estimating functions that avoids full blown bootstrap. Simulation
studies suggest that the recommended procedure provides fast and valid
inferences among several competing procedures. Application to a tumor study
demonstrates the utility of the proposed method in routine data analysis.
