Primary Submission Category: Machine Learning and Causal Inference
On the estimation of the mean number of counterfactual recurrent events before failure
Authors: Benjamin Baer, Ashkan Ertefaie, Robert Strawderman,
Presenting Author: Benjamin Baer*
On any time interval, the marginal increment in the expected number of recurrent events before failure can be decomposed as a product of two terms: the survival probability evaluated at the beginning of the time interval, multiplied by the increment in the expected number of recurrent events before failure conditional on surviving to the beginning of the time interval. For a fixed set of landmark times, the expected number of recurrent events before failure can be similarly decomposed as a sum of such terms. The resulting expression can be viewed as a generalization of the cumulative incidence function arising in semi-competing risks problems, and allows one to quantify the relative contributions of the failure time and recurrent event count distributions to the expected number of recurrent events before failure.
We define our estimand as the vector comprising each function evaluated along a sequence of landmark times. We identify the estimand in the presence of right-censoring and causal selection as an observed data functional under coarsening at random, derive the nonparametric efficiency bound, and propose a multiply-robust estimator that achieves the bound and permits nonparametric estimation of nuisance parameters. Additionally, we derive the class of influence functions when the coarsening distribution is known and frame previously published estimators as belonging to the class. Along the way, we highlight some inconsistencies in the causal survival literature.