Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes
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Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes. / Rytgaard, Helene C.; Gerds, Thomas A.; Laan, Mark J. van der.
In: Annals of Statistics, 2022.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes
AU - Rytgaard, Helene C.
AU - Gerds, Thomas A.
AU - Laan, Mark J. van der
N1 - 27 pages (excluding supplementary material), 1 figures
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - math.ST
KW - stat.ME
KW - stat.TH
UR - https://imstat.org/journals-and-publications/annals-of-statistics/annals-of-statistics-future-papers/
M3 - Journal article
JO - Annals of Statistics
JF - Annals of Statistics
SN - 0090-5364
ER -
ID: 274172516