This paper reviews recent advances in missing data research using graphical models to represent multivariate dependencies. We first examine the limitations of traditional frameworks from three different perspectives: . We then show how procedures based on graphical models can overcome these limitations and provide meaningful performance guarantees even when data are Missing Not At Random (MNAR). In particular, we identify conditions that guarantee consistent estimation in broad categories of missing data problems, and derive procedures for implementing this estimation. Finally we derive testable implications for missing data models in both MAR (Missing At Random) and MNAR categories.
Weighting procedures for missing data are based on creating weighted copies of complete cases and are succinctly summarized in @cite_11 . These procedures that are primarily based on @cite_20 and have been generalized to address missing data problems in @cite_27 , @cite_53 and @cite_28 .
@cite_28 @cite_53 @cite_27 @cite_20 @cite_11
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In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased when there exist time-dependent confounders that are also affected by previous treatment. This paper introduces marginal structural models, a new class of causal mo Abstract We propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data. The proposed estimators do not require full specification of the likelihood. They can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random. These estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable. The likelihood-based parametric G-computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance. But because of possible model misspecification, the parametric G-computation algorithm estimator, in contrast with the proposed w... Abstract In applied problems it is common to specify a model for the conditional mean of a response given a set of regressors. A subset of the regressors may be missing for some study subjects either by design or happenstance. In this article we propose a new class of semiparametric estimators, based on inverse probability weighted estimating equations, that are consistent for parameter vector α0 of the conditional mean model when the data are missing at random in the sense of Rubin and the missingness probabilities are either known or can be parametrically modeled. We show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0, and then deriving a representation for the efficient score... Abstract This paper presents a general technique for the treatment of samples drawn without replacement from finite universes when unequal selection probabilities are used. Two sampling schemes are discussed in connection with the problem of determining optimum selection probabilities according to the information available in a supplementary variable. Admittedly, these two schemes have limited application. They should prove useful, however, for the first stage of sampling with multi-stage designs, since both permit unbiased estimation of the sampling variance without resorting to additional assumptions. * Journal Paper No. J2139 of the Iowa Agricultural Experiment Station, Ames, Iowa, Project 1005. Presented to the Institute of Mathematical Statistics, March 17, 1951. We review the class of inverse probability weighting (IPW) approaches for the analysis of missing data under various missing data patterns and mechanisms. The IPW methods rely on the intuitive idea of creating a pseudo-population of weighted copies of the complete cases to remove selection bias introduced by the missing data. However, different weighting approaches are required depending on the missing data pattern and mechanism. We begin with a uniform missing data pattern (i.e., a scalar missing indicator indicating whether or not the full data is observed) to motivate the approach. We then generalize to more complex settings. Our goal is to provide a conceptual overview of existing IPW approaches and illustrate the connections and differences among these approaches.