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Targeted maximum likelihood estimation is a general methodology combiningflexible ensemble learning and semiparametric efficiency theory in a two-stepprocedure for estimation of causal parameters. Proposed targeted maximumlikelihood procedures for survival and competing risks analysis have so farfocused on events taken values in discrete time. We here present a targetedmaximum likelihood estimation procedure for event times that take values in R+.We focuson the estimation of intervention-specific mean outcomes withstochastic interventions on a time-fixed treatment. For data-adaptiveestimation of nuisance parameters, we propose a new flexible highly adaptivelasso estimation method for continuous-time intensities that can be implementedwith L1-penalized Poisson regression. In a simulation study the targetedmaximum likelihood estimator based on the highly adaptive lasso estimatorproves to be unbiased and achieve proper coverage in agreement with theasymptotic theory and further displays efficiency improvements relative to aKaplan-Meier approach.

Estimation of time-specific intervention effects on continuously distributed time-to-event outcomes by targeted maximum likelihood estimation