Generalized Redistribute-to-the-Right Algorithm: Application to the Analysis of Censored Cost Data

Medical cost estimation is a challenging task when censoring of data is present. Although researchers have proposed methods for estimating mean costs, these are often derived from theory and are not always easy to understand. We provide an alternative method, based on a replace-from-the-right algorithm, for estimating mean costs more efficiently. We show that our estimator is equivalent to an existing one that is based on the inverse probability weighting principle and semiparametric efficiency theory. We also propose an alternative method for estimating the survival function of costs, based on the redistribute-to-the-right algorithm, that was originally used for explaining the Kaplan-Meier estimator. We show that this second proposed estimator is equivalent to a simple weighted survival estimator of costs. Finally, we develop a more efficient survival estimator of costs, using the same redistribute-to-the-right principle. This estimator is naturally monotone, more efficient than some existing survival estimators, and has a quite small bias in many realistic settings. We conduct numerical studies to examine the finite sample property of the survival estimators for costs, and show that our new estimator has small mean squared errors when the sample size is not too large. We apply both existing and new estimators to a data example from a randomized cardiovascular clinical trial.