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

TL;DR

This paper develops a targeted maximum likelihood estimation method for continuous-time survival outcomes, introducing a new flexible estimation approach that improves bias and efficiency over traditional methods.

Contribution

It presents a novel TMLE procedure for continuous-time event data, incorporating a highly adaptive lasso for estimating intensities, advancing causal inference in survival analysis.

Findings

Estimator is unbiased and has proper coverage in simulations.

Achieves efficiency improvements over Kaplan-Meier methods.

Applicable to continuous-time survival data with stochastic interventions.

Abstract

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