Comment: Performance of Double-Robust Estimators When “Inverse Probability” Weights Are Highly Variable

Robins, James M.; Sued, Mariela; Lei-Gomez, Quanhong; Rotnitzky, Andrea

doi:10.1214/07-sts227d

Cited by 340 publications

(370 citation statements)

References 12 publications

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“…Previous examples of Proposition 12 are given in Newey (1990, p. 116), Newey (1999, and Robins et. al.…”

Section: Vector Of Instrumental Variables Andλmentioning

confidence: 97%

Locally robust semiparametric estimation

Chernozhukov¹,

Escanciano²,

Ichimura³

et al. 2016

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This paper shows how to construct locally robust semiparametric GMM estimators, meaning equivalently moment conditions have zero derivative with respect to the first step and the first step does not affect the asymptotic variance. They are constructed by adding to the moment functions the adjustment term for first step estimation. Locally robust estimators have several advantages. They are vital for valid inference with machine learning in the first step, see Belloni et. al. (2012Belloni et. al. ( , 2014, and are less sensitive to the specification of the first step. They are doubly robust for affine moment functions, so moment conditions continue to hold when one first step component is incorrect. Locally robust moment conditions also have smaller bias that is flatter as a function of first step smoothing leading to improved small sample properties. Series first step estimators confer local robustness on any moment conditions and are doubly robust for affine moments, in the direction of the series approximation. Many new locally and doubly robust estimators are given here, including for economic structural models. We give simple asymptotic theory for estimators that use cross-fitting in the first step, including machine learning.

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“…Previous examples of Proposition 12 are given in Newey (1990, p. 116), Newey (1999, and Robins et. al.…”

Section: Vector Of Instrumental Variables Andλmentioning

confidence: 97%

Locally robust semiparametric estimation

Chernozhukov¹,

Escanciano²,

Ichimura³

et al. 2016

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show abstract

“…The second models, incorrectly specified, were as the first ones, but with covariate X instead of L. In the second experiment, as in Robins et al (2007), we recoded A as 1 − A and replicated the first experiment. We conducted this experiment because Robins et al (2007) noted that the favourable performance ofβ reg (η) compared withβ(η,α) reported by Kang & Schafer (2007) was reversed when the observed data were {1 − A, (1 − A)Y, L}; thus, our study includes scenarios favourable toβ reg (η) and tô β (η,α).…”

Section: Simulation Studiesmentioning

confidence: 99%

“…Several authors (Robins & Wang, 2000;Kang & Schafer, 2007;Rubin & van der Laan, 2008) have noted that standard double-robust estimators may have substantial bias and large variance, even under correct specification of the missingness model, if the estimated missingness probabilities are highly variable and/or the outcome regression model is misspecified. Alternative double-robust estimators have been recently developed to address these problems (van der Laan & Rubin, 2006;Tan, 2006Tan, , 2007Tan, , 2008Tan, , 2010aTan, , 2010bRobins et al, 2007;Cao et al, 2009). In particular, Tan (2008Tan ( , 2010a and Cao et al (2009) derived double-robust estimators of E(Y ) = β 0 , i.e., in the special case in which Z is absent and h(Z ; β) = β, which satisfy Properties 1 and 2 and have the enhanced efficiency benefit that:…”

Section: Introductionmentioning

confidence: 99%

Improved double-robust estimation in missing data and causal inference models

et al. 2012

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SUMMARYRecently proposed double-robust estimators for a population mean from incomplete data and for a finite number of counterfactual means can have much higher efficiency than the usual double-robust estimators under misspecification of the outcome model. In this paper, we derive a new class of double-robust estimators for the parameters of regression models with incomplete cross-sectional or longitudinal data, and of marginal structural mean models for cross-sectional data with similar efficiency properties. Unlike the recent proposals, our estimators solve outcome regression estimating equations. In a simulation study, the new estimator shows improvements in variance relative to the standard double-robust estimator that are in agreement with those suggested by asymptotic theory.Some key words: Drop-out; Marginal structural model; Missing at random.

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“…It is known that when both models are correct, then the inference is an expected one. Also, it is known that when both models are incorrect, the estimates are severely biased and lead to an incorrect inference [22]. Finally, the impact of ignoring the left-censoring of the outcome was examined by replacing censored values either by half of the lower limit of detection or by a randomly imputed value with the models a WMM h and a WMM r , respectively.…”

Section: Simulation Study For Non-ignorable Missing and Left-censoredmentioning

confidence: 99%

Analysis of non‐ignorable missing and left‐censored longitudinal data using a weighted random effects tobit model

Sattar

Weissfeld

Molenberghs

2011

Statistics in Medicine

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In a longitudinal study with response data collected during a hospital stay, observations may be missing because of the subject's discharge from the hospital prior to completion of the study or the death of the subject, resulting in non-ignorable missing data. In addition to non-ignorable missingness, there is left-censoring in the response measurements because of the inherent limit of detection. For analyzing non-ignorable missing and left-censored longitudinal data, we have proposed to extend the theory of random effects tobit regression model to weighted random effects tobit regression model. The weights are computed on the basis of inverse probability weighted augmented methodology. An extensive simulation study was performed to compare the performance of the proposed model with a number of competitive models. The simulation study shows that the estimates are consistent and that the root mean square errors of the estimates are minimal for the use of augmented inverse probability weights in the random effects tobit model. The proposed method is also applied to the non-ignorable missing and left-censored interleukin-6 biomarker data obtained from the Genetic and Inflammatory Markers of Sepsis study.

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Comment: Performance of Double-Robust Estimators When “Inverse Probability” Weights Are Highly Variable

Cited by 340 publications

References 12 publications

Locally robust semiparametric estimation

Locally robust semiparametric estimation

Improved double-robust estimation in missing data and causal inference models

Analysis of non‐ignorable missing and left‐censored longitudinal data using a weighted random effects tobit model

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