arXiv subjects

Eric Tchetgen Tchetgen

Publications and source records attributed to Eric Tchetgen Tchetgen.

68 records · Page 4Linked to original sources

arXiv2019

Identification, Doubly Robust Estimation, and Semiparametric Efficiency Theory of Nonignorable Missing Data With a Shadow Variable

We consider identification and estimation with an outcome missing not at random (MNAR). We study an identification strategy based on a so-called shadow variable. A shadow variable is assumed to be correlated with the outcome, but independent of the missingness process conditional on the outcome and fully observed covariates. We describe a general condition for nonparametric identification of the full data law under MNAR using a valid shadow variable. Our condition is satisfied by many commonly-used models; moreover, it is imposed on the complete cases, and therefore has testable implications with observed data only. We describe semiparametric estimation methods and evaluate their performance on both simulation data and a real data example. We characterize the semiparametric efficiency bound for the class of regular and asymptotically linear estimators, and derive a closed form for the efficient influence function.

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arXiv2018

Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder

We consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the con- founder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014) that rests on identification of the measurement error mechanism. When only one proxy for the confounder is available, or the required rank condition is not met, we develop a strategy to test the null hypothesis of no causal effect.

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arXiv2018

A stochastic second-order generalized estimating equations approach for estimating intraclass correlation coefficient in the presence of informative missing data

Design and analysis of cluster randomized trials must take into account correlation among outcomes from the same clusters. When applying standard generalized estimating equations (GEE), the first-order (e.g. treatment) effects can be estimated consistently even with a misspecified correlation structure. In settings for which the correlation is of interest, one could estimate this quantity via second-order generalized estimating equations (GEE2). We build upon GEE2 in the setting of missing data, for which we incorporate a "second-order" inverse-probability weighting (IPW) scheme and "second-order" doubly robust (DR) estimating equations that guard against partial model misspecification. We highlight the need to model correlation among missing indicators in such settings. In addition, the computational difficulties in solving these second-order equations have motivated our development of more computationally efficient algorithms for solving GEE2, which alleviates reliance on parameter starting values and provides substantially faster and higher convergence rates than the more widely used deterministic root-solving methods.

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arXiv2018

Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables

Instrumental variables (IVs) are widely used for estimating causal effects in the presence of unmeasured confounding. Under the standard IV model, however, the average treatment effect (ATE) is only partially identifiable. To address this, we propose novel assumptions that allow for identification of the ATE. Our identification assumptions are clearly separated from model assumptions needed for estimation, so that researchers are not required to commit to a specific observed data model in establishing identification. We then construct multiple estimators that are consistent under three different observed data models, and multiply robust estimators that are consistent in the union of these observed data models. We pay special attention to the case of binary outcomes, for which we obtain bounded estimators of the ATE that are guaranteed to lie between -1 and 1. Our approaches are illustrated with simulations and a data analysis evaluating the causal effect of education on earnings.

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arXiv2017

Quantifying an Adherence Path-Specific Effect of Antiretroviral Therapy in the Nigeria PEPFAR Program

Since the early 2000s, evidence has accumulated for a significant differential effect of first-line antiretroviral therapy (ART) regimens on human immunodeficiency virus (HIV) viral load suppression. This finding was replicated in our data from the Harvard President's Emergency Plan for AIDS Relief (PEPFAR) program in Nigeria. Investigators were interested in finding the source of these differences, i.e., understanding the mechanisms through which one regimen outperforms another, particularly via adherence. This question can be naturally formulated via mediation analysis with adherence playing the role of a mediator. Existing mediation analysis results, however, have relied on an assumption of no exposure-induced confounding of the intermediate variable, and generally require an assumption of no unmeasured confounding for nonparametric identification. Both assumptions are violated by the presence of drug toxicity. In this paper, we relax these assumptions and show that certain path-specific effects remain identified under weaker conditions. We focus on the path-specific effect solely mediated by adherence and not by toxicity and propose an estimator for this effect. We illustrate with simulations and present results from a study applying the methodology to the Harvard PEPFAR data. Supplementary materials are available online.

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arXiv2017

Semiparametric Estimation with Data Missing Not at Random Using an Instrumental Variable

Missing data occur frequently in empirical studies in health and social sciences, often compromising our ability to make accurate inferences. An outcome is said to be missing not at random (MNAR) if, conditional on the observed variables, the missing data mechanism still depends on the unobserved outcome. In such settings, identification is generally not possible without imposing additional assumptions. Identification is sometimes possible, however, if an instrumental variable (IV) is observed for all subjects which satisfies the exclusion restriction that the IV affects the missingness process without directly influencing the outcome. In this paper, we provide necessary and sufficient conditions for nonparametric identification of the full data distribution under MNAR with the aid of an IV. In addition, we give sufficient identification conditions that are more straightforward to verify in practice. For inference, we focus on estimation of a population outcome mean, for which we develop a suite of semiparametric estimators that extend methods previously developed for data missing at random. Specifically, we propose inverse probability weighted estimation, outcome regression-based estimation and doubly robust estimation of the mean of an outcome subject to MNAR. For illustration, the methods are used to account for selection bias induced by HIV testing refusal in the evaluation of HIV seroprevalence in Mochudi, Botswana, using interviewer characteristics such as gender, age and years of experience as IVs.

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arXiv2017

Mediation Analysis for Censored Survival Data under an Accelerated Failure Time Model

Recent advances in causal mediation analysis have formalized conditions for estimating direct and indirect effects in various contexts. These approaches have been extended to a number of models for survival outcomes including accelerated failure time (AFT) models which are widely used in a broad range of health applications given their intuitive interpretation. In this setting, it has been suggested that under standard assumptions, the "difference" and "product" methods produce equivalent estimates of the indirect effect of exposure on the survival outcome. We formally show that these two methods may produce substantially different estimates in the presence of censoring or truncation, due to a form of model misspecification. Specifically, we establish that while the product method remains valid under standard assumptions in the presence of independent censoring, the difference method can be biased in the presence of such censoring whenever the error distribution of the AFT model fails to be collapsible upon marginalizing over the mediator. This will invariably be the case for most choices of mediator and outcome error distributions. A notable exception arises in case of normal mediator-normal outcome where we show consistency of both difference and product estimators in the presence of independent censoring. These results are confirmed in simulation studies and two data applications.

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arXiv2016

Identification and Inference for Marginal Average Treatment Effect on the Treated With an Instrumental Variable

In observational studies, treatments are typically not randomized and therefore estimated treatment effects may be subject to confounding bias. The instrumental variable (IV) design plays the role of a quasi-experimental handle since the IV is associated with the treatment and only affects the outcome through the treatment. In this paper, we present a novel framework for identification and inference using an IV for the marginal average treatment effect amongst the treated (ETT) in the presence of unmeasured confounding. For inference, we propose three different semiparametric approaches: (i) inverse probability weighting (IPW), (ii) outcome regression (OR), and (iii) doubly robust (DR) estimation, which is consistent if either (i) or (ii) is consistent, but not necessarily both. A closed-form locally semiparametric efficient estimator is obtained in the simple case of binary IV and outcome and the efficiency bound is derived for the more general case.

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arXiv2016

Accounting for interactions and complex inter-subject dependency in estimating treatment effect in cluster randomized trials with missing outcomes

Semi-parametric methods are often used for the estimation of intervention effects on correlated outcomes in cluster-randomized trials (CRTs). When outcomes are missing at random (MAR), Inverse Probability Weighted (IPW) methods incorporating baseline covariates can be used to deal with informative missingness. Also, augmented generalized estimating equations (AUG) correct for imbalance in baseline covariates but need to be extended for MAR outcomes. However, in the presence of interactions between treatment and baseline covariates, neither method alone produces consistent estimates for the marginal treatment effect if the model for interaction is not correctly specified. We propose an AUG-IPW estimator that weights by the inverse of the probability of being a complete case and allows different outcome models in each intervention arm. This estimator is doubly robust (DR), it gives correct estimates whether the missing data process or the outcome model is correctly specified. We consider the problem of covariate interference which arises when the outcome of an individual may depend on covariates of other individuals. When interfering covariates are not modeled, the DR property prevents bias as long as covariate interference is not present simultaneously for the outcome and the missingness. An R package is developed implementing the proposed method. An extensive simulation study and an application to a CRT of HIV risk reduction-intervention in South Africa illustrate the method.

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arXiv2016

On Varieties of Doubly Robust Estimators Under Missingness Not at Random With a Shadow Variable

Suppose we are interested in the mean of an outcome variable missing not at random. Suppose however that one has available a fully observed shadow variable, which is associated with the outcome but independent of the missingness process conditional on covariates and the possibly unobserved outcome. Such a variable may be a proxy or a mismeasured version of the outcome available for all individuals. We have previously established necessary and sufficient conditions for identification of the full data law in such a setting, and have described semiparametric estimators including a doubly robust estimator of the outcome mean. Here, we propose two alternative doubly robust estimators for the outcome mean, which may be viewed as extensions of analogous methods under missingness at random, but enjoy different properties. We assess correctness of the required working models via straightforward goodness-of-fit tests.

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arXiv2016

Lepski's Method and Adaptive Estimation of Nonlinear Integral Functionals of Density

We study the adaptive minimax estimation of non-linear integral functionals of a density and extend the results obtained for linear and quadratic functionals to general functionals. The typical rate optimal non-adaptive minimax estimators of "smooth" non-linear functionals are higher order U-statistics. Since Lepski's method requires tight control of tails of such estimators, we bypass such calculations by a modification of Lepski's method which is applicable in such situations. As a necessary ingredient, we also provide a method to control higher order moments of minimax estimator of cubic integral functionals. Following a standard constrained risk inequality method, we also show the optimality of our adaptation rates.

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arXiv2016

Technical Report: Higher Order Influence Functions and Minimax Estimation of Nonlinear Functionals

Robins et al, 2008, published a theory of higher order influence functions for inference in semi- and non-parametric models. This paper is a comprehensive manuscript from which Robins et al, was drawn. The current paper includes many results and proofs that were not included in Robins et al due to space limitation. Particular results contained in the present paper that were not reported in Robins et al include the following. Given a set of functionals and their corresponding higher order influence functions, we show how to derive the higher order influence function of their product. We apply this result to obtain higher order influence functions and associated estimators for the mean of a response Y subject to monotone missingness under missing at random. These results also apply to estimating the causal effect of a time dependent treatment on an outcome Y in the presence of time-varying confounding. Finally, we include an appendix that contains proofs for all theorems that were stated without proof in Robins et al, 2008. The initial part of the paper is closely related to Robins et al, the latter parts differ.

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arXiv2015

Asymptotic Normality of Quadratic Estimators

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.

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arXiv2015

Causal Inference with a Graphical Hierarchy of Interventions

Identifying causal parameters from observational data is fraught with subtleties due to the issues of selection bias and confounding. In addition, more complex questions of interest, such as effects of treatment on the treated and mediated effects may not always be identified even in data where treatment assignment is known and under investigator control, or may be identified under one causal model but not another. Increasingly complex effects of interest, coupled with a diversity of causal models in use resulted in a fragmented view of identification. This fragmentation makes it unnecessarily difficult to determine if a given parameter is identified (and in what model), and what assumptions must hold for this to be the case. This, in turn, complicates the development of estimation theory and sensitivity analysis procedures. In this paper, we give a unifying view of a large class of causal effects of interest in terms of a hierarchy of interventions, and show that identification theory for this large class reduces to an identification theory of random variables under interventions from this hierarchy. Moreover, we show that one type of intervention in the hierarchy is naturally associated with queries identified under the Finest Fully Randomized Causally Interpretable Structure Tree Graph (FFRCISTG) model of Robins (via the extended g-formula), and another is naturally associated with queries identified under the Non-Parametric Structural Equation Model with Independent Errors (NPSEM-IE) of Pearl, via a more general functional we call the edge g-formula. Our results motivate the study of estimation theory for the edge g-formula, since we show it arises both in mediation analysis, and in settings where treatment assignment has unobserved causes, such as models associated with Pearl's front-door criterion.

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