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Summary Randomized experiments have been the gold standard for drawing causal inference. The conventional model-based approach has been one of the most popular methods of analysing treatment effects from randomized experiments, which is often carried out through inference for certain model parameters. In this paper, we provide a systematic investigation of model-based analyses for treatment effects under the randomization-based inference framework. This framework does not impose any distributional assumptions on the outcomes, covariates and their dependence, and utilizes only randomization as the reasoned basis. We first derive the asymptotic theory for $ Z $-estimation in completely randomized experiments, and propose sandwich-type conservative covariance estimation. We then apply the developed theory to analyse both average and individual treatment effects in randomized experiments. For the average treatment effect, we consider model-based, model-imputed and model-assisted estimation strategies, where the first two strategies can be sensitive to model misspecification or require specific methods for parameter estimation. The model-assisted approach is robust to arbitrary model misspecification and always provides consistent average treatment effect estimation. We propose optimal ways to conduct model-assisted estimation using generally nonlinear least squares for parameter estimation. For the individual treatment effects, we propose directly modelling the relationship between individual effects and covariates, and discuss the model’s identifiability, inference and interpretation allowing for model misspecification.
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Covariate‐adjusted response‐adaptive designs based on semiparametric approaches
Abstract We consider theoretical and practical issues for innovatively using a large number of covariates in clinical trials to achieve various design objectives without model misspecification. Specifically, we propose a new family of semiparametric covariate‐adjusted response‐adaptive randomization (CARA) designs and we use the target maximum likelihood estimation (TMLE) to analyze the correlated data from CARA designs. Our approach can flexibly achieve multiple objectives and correctly incorporate the effect of a large number of covariates on the responses without model misspecification. We also obtain the consistency and asymptotic normality of the target parameters, allocation probabilities, and allocation proportions. Numerical studies demonstrate that our approach has advantages over existing approaches, even when the data‐generating distribution is complicated.
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- Award ID(s):
- 2014951
- PAR ID:
- 10419842
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- ISSN:
- 0006-341X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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