A note on rank-preserving structural failure time models to account for crossover

In randomized trials where some standard-treatment arm patients cross to the experimental treatment, it is frequently of interest to estimate the between-arm survival difference as if no patients on the standard-treatment arm had crossed over to the experimental treatment. Rank-preserving structural failure time models, an extension of semiparametric accelerated-failure-time models, are a popular method for accomplishing this because they do not require modeling which patients will crossover.

In trying to apply the rank-preserving structural failure time model in practice, we noted some unusual behavior of the estimated acceleration parameter (differential treatment effect). Simple examples and limited simulations are provided to examine and understand this behavior.

The simulations show that rank-preserving structural failure time model estimator of the acceleration parameter can take on extreme values, especially when the intent-to-treat analysis favors the standard-treatment arm. Furthermore, the addition of censoring is paradoxically shown to reduce the estimator's variability compared to the uncensored data when the underlying observations are exponentially distributed. Use of a Weibull distribution with short tails for the survival times eliminates this unusual behavior.

The rank-preserving structural failure time model estimators of the acceleration parameter are not based on the joint ranks of the original data, and it is suggested that this makes acceleration-parameter estimator unstable with long-tailed survival distributions.