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In the absence of data from a randomized trial, researchers may aim to use observational data to draw causal inference about the effect of a treatment on a time-to-event outcome. In this context, interest often focuses on the treatment-specific survival curves, that is, the survival curves were the population under study to be assigned to receive the treatment or not. Under certain conditions, including that all confounders of the treatment-outcome relationship are observed, the treatment-specific survival curve can be identified with a covariate-adjusted survival curve. In this article, we propose a novel cross-fitted doubly-robust estimator that incorporates data-adaptive (e.g. machine learning) estimators of the conditional survival functions. We establish conditions on the nuisance estimators under which our estimator is consistent and asymptotically linear, both pointwise and uniformly in time. We also propose a novel ensemble learner for combining multiple candidate estimators of the conditional survival estimators. Notably, our methods and results accommodate events occurring in discrete or continuous time, or an arbitrary mix of the two. We investigate the practical performance of our methods using numerical studies and an application to the effect of a surgical treatment to prevent metastases of parotid carcinoma on mortality.
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Multiply robust estimators in longitudinal studies with missing data under control-based imputation
ABSTRACT Longitudinal studies are often subject to missing data. The recent guidance from regulatory agencies, such as the ICH E9(R1) addendum addresses the importance of defining a treatment effect estimand with the consideration of intercurrent events. Jump-to-reference (J2R) is one classical control-based scenario for the treatment effect evaluation, where the participants in the treatment group after intercurrent events are assumed to have the same disease progress as those with identical covariates in the control group. We establish new estimators to assess the average treatment effect based on a proposed potential outcomes framework under J2R. Various identification formulas are constructed, motivating estimators that rely on different parts of the observed data distribution. Moreover, we obtain a novel estimator inspired by the efficient influence function, with multiple robustness in the sense that it achieves n1/2-consistency if any pairs of multiple nuisance functions are correctly specified, or if the nuisance functions converge at a rate not slower than n−1/4 when using flexible modeling approaches. The finite-sample performance of the proposed estimators is validated in simulation studies and an antidepressant clinical trial.
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- Award ID(s):
- 2242776
- PAR ID:
- 10492218
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 80
- Issue:
- 1
- ISSN:
- 0006-341X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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