Rank-based estimating equations with general weight for accelerated failure time models: An induced smoothing approach

The induced smoothing technique overcomes the difficulties caused by the non-smoothness in rank-based estimating functions for accelerated failure time models, but it is only natural when the estimating function has Gehan's weight. For a general weight, the induced smoothing method does not provide smooth estimating functions that can be easily evaluated. We propose an iterative-induced smoothing procedure for general weights with the estimator from Gehan's weight initial value. The resulting estimators have the same asymptotic properties as those from the non-smooth estimating equations with the same weight. Their variances are estimated with an efficient resampling approach that avoids solving estimating equations repeatedly. The methodology is generalized to incorporate an additional weight to accommodate missing data and various sampling schemes. In a numerical study, the proposed estimators were obtained much faster without losing accuracy in comparison to those from non-smooth estimating equations, and the variance estimators provided good approximation of the variation in estimation. The methodology was applied to two real datasets, the first one from an adolescent depression study and the second one from a cancer study with missing covariates by design. The implementation is available in an R package aftgee.