Direct Bootstrapping and Permuting of Observations fail for Aalen-Johansen Estimators

TL;DR

This paper proves that common resampling methods like bootstrap and permutation fail to produce consistent tests for transition probabilities in finite-state Markov processes, due to their impact on the covariance structure of Aalen-Johansen estimators.

Contribution

It provides rigorous proofs demonstrating the failure of Efron's bootstrap and permutation methods for Aalen-Johansen estimators in Markov processes.

Findings

Bootstrap and permutation alter covariance functions of estimators.

These methods do not yield consistent resampling tests.

Failure illustrated with competing risks and cumulative incidence functions.

Abstract

This article provides rigorous proofs that neither Efron's bootstrap nor permutation techniques can be applied directly to the observations to construct consistent resampling tests for transition probability matrices of finite-state Markov processes. These methods modify the covariance functions of the limiting distributions of the involved Aalen-Johansen processes, even in the case of fully observable individuals. An example for the failure of these resampling methods is given by cumulative incidence functions in competing risks set-ups.