  This paper studies the generalization of the targeted minimum loss-based
estimation (TMLE) framework to estimation of effects of time-varying
interventions in settings where both interventions, covariates, and outcome can
happen at subject-specific time-points on an arbitrarily fine time-scale. TMLE
is a general template for constructing asymptotically linear substitution
estimators for smooth low-dimensional parameters in infinite-dimensional
models. Existing longitudinal TMLE methods are developed for data where
observations are made on a discrete time-grid.
  We consider a continuous-time counting process model where intensity measures
track the monitoring of subjects, and focus on a low-dimensional target
parameter defined as the intervention-specific mean outcome at the end of
follow-up. To construct our TMLE algorithm for the given statistical estimation
problem we derive an expression for the efficient influence curve and represent
the target parameter as a functional of intensities and conditional
expectations. The high-dimensional nuisance parameters of our model are
estimated and updated in an iterative manner according to separate targeting
steps for the involved intensities and conditional expectations.
  The resulting estimator solves the efficient influence curve equation. We
state a general efficiency theorem and describe a highly adaptive lasso
estimator for nuisance parameters that allows us to establish asymptotic
linearity and efficiency of our estimator under minimal conditions on the
underlying statistical model.
