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Register a new userRobust semiparametric inference with missing data
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Added by
Xavier de Luna
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is exacerbated when inverse probability weighting methods are used, which may overweight contaminated observations. We introduce inverse probability weighted, double robust and outcome regression estimators of location and scale parameters, which are robust to contamination in the sense that their influence function is bounded. We give asymptotic properties and study finite sample behaviour. Our simulated experiments show that contamination can be more serious a threat to the quality of inference than model misspecification. An interesting aspect of our results is that the auxiliary outcome model used to adjust for ignorable missingness by some of the estimators, is also useful to protect against contamination. We also illustrate through a case study how both adjustment to ignorable missingness and protection against contamination are achieved through weighting schemes, which can be contrasted to gain further insights.
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We study the identification and estimation of statistical functionals of multivariate data missing non-monotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what has been previously called no self-censoring or itemwise conditionally independent nonresponse, which roughly corresponds to the assumption that no partially-observed variable directly determines its own missingness status. We show that this assumption, combined with an odds ratio parameterization of the joint density, enables identification of functionals of interest, and we establish the semiparametric efficiency bound for the nonparametric model satisfying this assumption. We propose a practical augmented inverse probability weighted estimator, and in the setting with a (possibly high-dimensional) always-observed subset of covariates, our proposed estimator enjoys a certain double-robustness property. We explore the performance of our estimator with simulation experiments and on a previously-studied data set of HIV-positive mothers in Botswana.
Spatial extent inference (SEI) is widely used across neuroimaging modalities to study brain-phenotype associations that inform our understanding of disease. Recent studies have shown that Gaussian random field (GRF) based tools can have inflated family-wise error rates (FWERs). This has led to fervent discussion as to which preprocessing steps are necessary to control the FWER using GRF-based SEI. The failure of GRF-based methods is due to unrealistic assumptions about the covariance function of the imaging data. The permutation procedure is the most robust SEI tool because it estimates the covariance function from the imaging data. However, the permutation procedure can fail because its assumption of exchangeability is violated in many imaging modalities. Here, we propose the (semi-) parametric bootstrap joint (PBJ; sPBJ) testing procedures that are designed for SEI of multilevel imaging data. The sPBJ procedure uses a robust estimate of the covariance function, which yields consistent estimates of standard errors, even if the covariance model is misspecified. We use our methods to study the association between performance and executive functioning in a working fMRI study. The sPBJ procedure is robust to variance misspecification and maintains nominal FWER in small samples, in contrast to the GRF methods. The sPBJ also has equal or superior power to the PBJ and permutation procedures. We provide an R package https://github.com/simonvandekar/pbj to perform inference using the PBJ and sPBJ procedures
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.
Skepticism about the assumption of no unmeasured confounding, also known as exchangeability, is often warranted in making causal inferences from observational data; because exchangeability hinges on an investigators ability to accurately measure covariates that capture all potential sources of confounding. In practice, the most one can hope for is that covariate measurements are at best proxies of the true underlying confounding mechanism operating in a given observational study. In this paper, we consider the framework of proximal causal inference introduced by Tchetgen Tchetgen et al. (2020), which while explicitly acknowledging covariate measurements as imperfect proxies of confounding mechanisms, offers an opportunity to learn about causal effects in settings where exchangeability on the basis of measured covariates fails. We make a number of contributions to proximal inference including (i) an alternative set of conditions for nonparametric proximal identification of the average treatment effect; (ii) general semiparametric theory for proximal estimation of the average treatment effect including efficiency bounds for key semiparametric models of interest; (iii) a characterization of proximal doubly robust and locally efficient estimators of the average treatment effect. Moreover, we provide analogous identification and efficiency results for the average treatment effect on the treated. Our approach is illustrated via simulation studies and a data application on evaluating the effectiveness of right heart catheterization in the intensive care unit of critically ill patients.
Practical problems with missing data are common, and statistical methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism governing data missingness, and correctly deciding the appropriate mechanism is crucially relevant for conducting proper practical investigations. The conventional notions include the three common potential classes -- missing completely at random, missing at random, and missing not at random. In this paper, we present a new hypothesis testing approach for deciding between missing at random and missing not at random. Since the potential alternatives of missing at random are broad, we focus our investigation on a general class of models with instrumental variables for data missing not at random. Our setting is broadly applicable, thanks to that the model concerning the missing data is nonparametric, requiring no explicit model specification for the data missingness. The foundational idea is to develop appropriate discrepancy measures between estimators whose properties significantly differ only when missing at random does not hold. We show that our new hypothesis testing approach achieves an objective data oriented choice between missing at random or not. We demonstrate the feasibility, validity, and efficacy of the new test by theoretical analysis, simulation studies, and a real data analysis.
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