Lasso-adjusted treatment effect estimation under covariate-adaptive randomization

Abstract

We consider the problem of estimating and inferring treatment effects in randomized experiments. In practice, stratified randomization, or more generally, covariate-adaptive randomization, is routinely used in the design stage to balance treatment allocations with respect to a few variables that are most relevant to the outcomes. Then, regression is performed in the analysis stage to adjust the remaining imbalances to yield more efficient treatment effect estimators. Building upon and unifying the recent results obtained for ordinary least squares adjusted estimators under covariate-adaptive randomization, this paper presents a general theory of regression adjustment that allows for model misspecification and the presence of a large number of baseline covariates. We exemplify the theory on two lasso-adjusted treatment effect estimators, both of which are optimal in their respective classes. In addition, nonparametric consistent variance estimators are proposed to facilitate valid inferences, which work irrespective of the specific randomization methods used. The robustness and improved efficiency of the proposed estimators are demonstrated through numerical studies.

Regression analysis for covariate‐adaptive randomization: A robust and efficient inference perspective

“…We leave to future work the investigation of semi‐parametric efficiency under covariate‐adaptive randomization. Second, to further improve efficiency, one can use the stratum‐specific adjusted vectors $$$ {\hat{\beta}}_{\left[k\right]}(1) $$$ and $$$ {\hat{\beta}}_{\left[k\right]}(0) $$$ within stratum $$$ k $$$ instead of the common adjusted vectors $$$ \hat{\beta}(1) $$$ and $$$ \hat{\beta}(0) $$$ for all strata, 33,34 which is equivalent to adding higher‐order interactions, such as $$$ {A}_i{I}_{i\in \left[k\right]}{\boldsymbol{X}}_i $$$, to the regression models. We do not explore this approach further in this work because such models, in our experience, are seldom specified as primary analyses in statistical analysis plans for clinical trials.…”

“…We do not explore this approach further in this work because such models, in our experience, are seldom specified as primary analyses in statistical analysis plans for clinical trials. Also, evidence suggested that it may lead to inferior performance when there exists a large number of strata 19,34 …”

“…Also, evidence suggested that it may lead to inferior performance when there exists a large number of strata. 19,34…”

Network and covariate adjusted response‐adaptive design for binary response

“…It is at the same time challenging when considering response, network, and covariate information altogether. One may refer to studies that address inference under response-adaptive designs 33,[47][48][49] and covariate-adaptive designs [50][51][52][53][54][55] for potential solutions for inference under the proposed design. It is beyond the scope of this study and is postponed to future work.…”

Regression-Based Multiple Treatment Effect Estimation under Covariate-Adaptive Randomization

“…This approach produces a valid inference by using a working model between responses and covariates, regardless of whether the working model is correct or not. To consider the regression adjustment for baseline covariates in addition to stratification covariates, stratum-common estimators and stratum-specific estimators have been developed, mainly for the case in which the allocation ratios are the same across strata (Liu et al, 2023;Ma et al, 2022;Ye et al, 2022aYe et al, , 2022b. However, little attention has been paid to the case in which the allocation ratios are different across strata, especially when additional baseline covariates are included, although different allocation ratios are commonly used in practice and are more flexible (Angrist et al, 2014;Chong et al, 2016).…”