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Register a new userHigh-dimensional Model-assisted Inference for Local Average Treatment Effects with Instrumental Variables
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Zhiqiang Tan
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Consider the problem of estimating the local average treatment effect with an instrument variable, where the instrument unconfoundedness holds after adjusting for a set of measured covariates. Several unknown functions of the covariates need to be estimated through regression models, such as instrument propensity score and treatment and outcome regression models. We develop a computationally tractable method in high-dimensional settings where the numbers of regression terms are close to or larger than the sample size. Our method exploits regularized calibrated estimation, which involves Lasso penalties but carefully chosen loss functions for estimating coefficient vectors in these regression models, and then employs a doubly robust estimator for the treatment parameter through augmented inverse probability weighting. We provide rigorous theoretical analysis to show that the resulting Wald confidence intervals are valid for the treatment parameter under suitable sparsity conditions if the instrument propensity score model is correctly specified, but the treatment and outcome regression models may be misspecified. For existing high-dimensional methods, valid confidence intervals are obtained for the treatment parameter if all three models are correctly specified. We evaluate the proposed methods via extensive simulation studies and an empirical application to estimate the returns to education.
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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.
This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method is non-asymptotic in the sense that it provides a finite sample bound on the difference between the true and nominal probabilities of rejecting a correct null hypothesis. The method is a non-Studentized version of the Anderson-Rubin test but is motivated and analyzed differently. In contrast to the conventional Anderson-Rubin test, the method proposed here does not require restrictive distributional assumptions, linearity of the estimated model, or simultaneous equations. Nor does it require knowledge of whether the instruments are strong or weak. It does not require testing or estimating the strength of the instruments. The method can be applied to quantile IV models that may be nonlinear and can be used to test a parametric IV model against a nonparametric alternative. The results presented here hold in finite samples, regardless of the strength of the instruments.
We consider the setting in which a strong binary instrument is available for a binary treatment. The traditional LATE approach assumes the monotonicity condition stating that there are no defiers (or compliers). Since this condition is not always obvious, we investigate the sensitivity and testability of this condition. In particular, we focus on the question: does a slight violation of monotonicity lead to a small problem or a big problem? We find a phase transition for the monotonicity condition. On one of the boundary of the phase transition, it is easy to learn the sign of LATE and on the other side of the boundary, it is impossible to learn the sign of LATE. Unfortunately, the impossible side of the phase transition includes data-generating processes under which the proportion of defiers tends to zero. This boundary of phase transition is explicitly characterized in the case of binary outcomes. Outside a special case, it is impossible to test whether the data-generating process is on the nice side of the boundary. However, in the special case that the non-compliance is almost one-sided, such a test is possible. We also provide simple alternatives to monotonicity.
Labeling patients in electronic health records with respect to their statuses of having a disease or condition, i.e. case or control statuses, has increasingly relied on prediction models using high-dimensional variables derived from structured and unstructured electronic health record data. A major hurdle currently is a lack of valid statistical inference methods for the case probability. In this paper, considering high-dimensional sparse logistic regression models for prediction, we propose a novel bias-corrected estimator for the case probability through the development of linearization and variance enhancement techniques. We establish asymptotic normality of the proposed estimator for any loading vector in high dimensions. We construct a confidence interval for the case probability and propose a hypothesis testing procedure for patient case-control labelling. We demonstrate the proposed method via extensive simulation studies and application to real-world electronic health record data.
Randomization (a.k.a. permutation) inference is typically interpreted as testing Fishers sharp null hypothesis that all effects are exactly zero. This hypothesis is often criticized as uninteresting and implausible. We show, however, that many randomization tests are also valid for a bounded null hypothesis under which effects are all negative (or positive) for all units but otherwise heterogeneous. The bounded null is closely related to important concepts such as monotonicity and Pareto efficiency. Inverting tests of this hypothesis yields confidence intervals for the maximum (or minimum) individual treatment effect. We then extend randomization tests to infer other quantiles of individual effects, which can be used to infer the proportion of units with effects larger (or smaller) than any threshold. The proposed confidence intervals for all quantiles of individual effects are simultaneously valid, in the sense that no correction due to multiple analyses is needed. In sum, we provide a broader justification for Fisher randomization tests, and develop exact nonparametric inference for quantiles of heterogeneous individual effects. We illustrate our methods with simulations and applications, where we find that Stephenson rank statistics often provide the most informative results.
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