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Register a new userInference on Average Treatment Effect under Minimization and Other Covariate-Adaptive Randomization Methods
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Added by
Ting Ye
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Covariate-adaptive randomization schemes such as the minimization and stratified permuted blocks are often applied in clinical trials to balance treatment assignments across prognostic factors. The existing theoretical developments on inference after covariate-adaptive randomization are mostly limited to situations where a correct model between the response and covariates can be specified or the randomization method has well-understood properties. Based on stratification with covariate levels utilized in randomization and a further adjusting for covariates not used in randomization, in this article we propose several estimators for model free inference on average treatment effect defined as the difference between response means under two treatments. We establish asymptotic normality of the proposed estimators under all popular covariate-adaptive randomization schemes including the minimization whose theoretical property is unclear, and we show that the asymptotic distributions are invariant with respect to covariate-adaptive randomization methods. Consistent variance estimators are constructed for asymptotic inference. Asymptotic relative efficiencies and finite sample properties of estimators are also studied. We recommend using one of our proposed estimators for valid and model free inference after covariate-adaptive randomization.
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In this paper, we study the estimation and inference of the quantile treatment effect under covariate-adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error under-rejects. But for method (2), its asymptotic size equals the nominal level. We also show that, for both methods, the asymptotic size of the Wald test using a covariate-adaptive bootstrap standard error equals the nominal level. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.
Standard Mendelian randomization analysis can produce biased results if the genetic variant defining the instrumental variable (IV) is confounded and/or has a horizontal pleiotropic effect on the outcome of interest not mediated by the treatment. We provide novel identification conditions for the causal effect of a treatment in presence of unmeasured confounding, by leveraging an invalid IV for which both the IV independence and exclusion restriction assumptions may be violated. The proposed Mendelian Randomization Mixed-Scale Treatment Effect Robust Identification (MR MiSTERI) approach relies on (i) an assumption that the treatment effect does not vary with the invalid IV on the additive scale; and (ii) that the selection bias due to confounding does not vary with the invalid IV on the odds ratio scale; and (iii) that the residual variance for the outcome is heteroscedastic and thus varies with the invalid IV. We formally establish that their conjunction can identify a causal effect even with an invalid IV subject to pleiotropy. MiSTERI is shown to be particularly advantageous in presence of pervasive heterogeneity of pleiotropic effects on additive scale, a setting in which two recently proposed robust estimation methods MR GxE and MR GENIUS can be severely biased. In order to incorporate multiple, possibly correlated and weak IVs, a common challenge in MR studies, we develop a MAny Weak Invalid Instruments (MR MaWII MiSTERI) approach for strengthened identification and improved accuracy MaWII MiSTERI is shown to be robust to horizontal pleiotropy, violation of IV independence assumption and weak IV bias. Both simulation studies and real data analysis results demonstrate the robustness of the proposed MR MiSTERI methods.
Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two sample t-test for treatment effect is typically conservative, in the sense that the actual test size is smaller than the nominal level. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.
We consider the estimation of the average treatment effect in the treated as a function of baseline covariates, where there is a valid (conditional) instrument. We describe two doubly robust (DR) estimators: a locally efficient g-estimator, and a targeted minimum loss-based estimator (TMLE). These two DR estimators can be viewed as generalisations of the two-stage least squares (TSLS) method to semi-parametric models that make weaker assumptions. We exploit recent theoretical results that extend to the g-estimator the use of data-adaptive fits for the nuisance parameters. A simulation study is used to compare standard TSLS with the two DR estimators finite-sample performance, (1) when fitted using parametric nuisance models, and (2) using data-adaptive nuisance fits, obtained from the Super Learner, an ensemble machine learning method. Data-adaptive DR estimators have lower bias and improved coverage, when compared to incorrectly specified parametric DR estimators and TSLS. When the parametric model for the treatment effect curve is correctly specified, the g-estimator outperforms all others, but when this model is misspecified, TMLE performs best, while TSLS can result in large biases and zero coverage. Finally, we illustrate the methods by reanalysing the COPERS (COping with persistent Pain, Effectiveness Research in Self-management) trial to make inference about the causal effect of treatment actually received, and the extent to which this is modified by depression at baseline.
Covariate-specific treatment effects (CSTEs) represent heterogeneous treatment effects across subpopulations defined by certain selected covariates. In this article, we consider marginal structural models where CSTEs are linearly represented using a set of basis functions of the selected covariates. We develop a new approach in high-dimensional settings to obtain not only doubly robust point estimators of CSTEs, but also model-assisted confidence intervals, which are valid when a propensity score model is correctly specified but an outcome regression model may be misspecified. With a linear outcome model and subpopulations defined by discrete covariates, both point estimators and confidence intervals are doubly robust for CSTEs. In contrast, confidence intervals from existing high-dimensional methods are valid only when both the propensity score and outcome models are correctly specified. We establish asymptotic properties of the proposed point estimators and the associated confidence intervals. We present simulation studies and empirical applications which demonstrate the advantages of the proposed method compared with competing ones.
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