Inference under covariate-adaptive randomization with multiple treatments
By Federico A. Bugni, Ivan A. Canay, A. Shaikh. Quantitative Economics, 2018
90 citations recorded by the source corpus.
This paper studies inference in randomized controlled trials with covariate‐adaptive randomization when there are multiple treatments. More specifically, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni, Canay, and Shaikh (2018), covariate‐adaptive randomization refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve “balance” within each stratum. Importantly, in contrast to Bugni, Canay, and Shaikh (2018), we not only allow for multiple treatments, but further allow for the proportion of units being assigned to each of the treatments to vary across strata. We first study the properties of estimators derived from a “fully saturated” linear regression, that is, a linear regression of the outcome on all interactions between indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are invalid in the sense that they may have limiting rejection probability under the null hypothesis strictly greater than the nominal level; on the other hand, tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact in the sense that they have limiting rejection probability under the null hypothesis equal to the nominal level. For the special case in which the target proportion of units being assigned to each of the treatments does not vary across strata, we additionally consider tests based on estimators derived from a linear regression with “strata fixed effects,” that is, a linear regression of the outcome on indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are conservative in the sense that they have limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level, but tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact, thereby generalizing results in Bugni, Canay, and Shaikh (2018) for the case of a single treatment to multiple treatments. A simulation study and an empirical application illustrate the practical relevance of our theoretical results.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/be92cd291dee033612ca71b46360be7f585096da
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Citations in the corpus
- Stratification Trees for Adaptive Randomization in Randomized Controlled Trials (2018, methodology): “By a slight modification of the argument in Lemma C1 in Bugni et al. (2018), we have that OpT̂ q d“ rOpT̂ q , where rOpT q :“ » — — — — — — — — — — — — — – rΩ0p1;T q rΩ1p1;T q rΩ0p2;T q ... Θp1;T q ... ΘpK;T q fi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi fl , (2) with rΩapk;T q “ Npk;T q…”
- Factorial Designs, Model Selection, and (Incorrect) Inference in Randomized Experiments (2019, background): “The choice between the short and the long model (with interactions between the treatment and strata indicators) is also relevant in stratified experiments (e.g., Imbens & Rubin, 2015; Ansel et al., 2018; Bugni et al., 2018, 2019).”