Nonparametric efficient causal estimation of the intervention-specific expected number of recurrent events with continuous-time targeted maximum likelihood and highly adaptive lasso estimation

Longitudinal settings involving outcome, competing risks and censoring events occurring and recurring in continuous time are common in medical research, but are often analyzed with methods that do not allow for taking post-baseline information into account. In this work, we define statistical and causal target parameters via the g-computation formula by carrying out interventions directly on the product integral representing the observed data distribution in a continuous-time counting process model framework. In recurrent events settings our target parameter identifies the expected number of recurrent events also in settings where the censoring mechanism or post-baseline treatment decisions depend on past information of post-baseline covariates such as the recurrent event process. We propose a flexible estimation procedure based on targeted maximum likelihood estimation coupled with highly adaptive lasso estimation to provide a novel approach for double robust and nonparametric inference for the considered target parameter. We illustrate the methods in a simulation study.