Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes

This paper generalizes the targeted minimum loss-based estimation (TMLE) framework to allow for estimating 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 constructing asymptotically linear substitution estimators smooth low-dimensional parameters infinite-dimensional models. Existing longitudinal methods are developed data observations made discrete time-grid. We consider continuous-time counting process model intensity measures track monitoring subjects, focus target parameter defined as intervention-specific mean end follow-up. To construct our algorithm given statistical problem, we derive expression efficient influence curve represent functional intensities conditional expectations. The high-dimensional nuisance estimated updated iterative manner according separate targeting steps involved resulting estimator solves equation. state efficiency theorem describe highly adaptive lasso that allows us establish asymptotic linearity under minimal conditions underlying model.