Efficient Nonparametric Causal Inference with Missing Exposure Information

Kennedy, Edward H.

doi:10.1515/ijb-2019-0087

Cited by 6 publications

(7 citation statements)

References 33 publications

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“…for any smooth parametric submodel Q (Kennedy, 2020). Thus, the candidate influence function satisfies the above pathwise differentiability condition and hence, is an efficient influence function.…”

Section: (X=x)mentioning

confidence: 89%

Doubly robust capture-recapture methods for estimating population size

Manjari¹,

Kennedy²,

Jewell³

2021

Preprint

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Estimation of population size using incomplete lists (also called the capture-recapture problem) has a long history across many biological and social sciences. For example, human rights and other groups often construct partial and overlapping lists of victims of armed conflicts, with the hope of using this information to estimate the total number of victims. Earlier statistical methods for this setup either use potentially restrictive parametric assumptions, or else rely on typically suboptimal plug-in-type nonparametric estimators; however, both approaches can lead to substantial bias, the former via model misspecification and the latter via smoothing. Under an identifying assumption that two lists are conditionally independent given measured covariate information, we make several contributions. First we derive the nonparametric efficiency bound for estimating the capture probability, which indicates the best possible performance of any estimator, and sheds light on the statistical limits of capture-recapture methods. Then we present a new estimator, and study its finite-sample properties, showing that it has a double robustness property new to capture-recapture, and that it is near-optimal in a non-asymptotic sense, under relatively mild nonparametric conditions. Next, we give a method for constructing confidence intervals for total population size from generic capture probability estimators, and prove non-asymptotic nearvalidity. Finally, we study our methods in simulations, and apply them to estimate the number of killings and disappearances attributable to different groups in Peru during its internal armed conflict between 1980 and 2000.

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Section: (X=x)mentioning

confidence: 89%

Doubly robust capture-recapture methods for estimating population size

Manjari¹,

Kennedy²,

Jewell³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…To proceed, we appeal to semiparametric theory, and derive the nonparametric influence function for τ a (P ), and the semiparametric efficient influence function for τ * a (P ) (Bickel et al, 1993;Tsiatis, 2007). By modeling the necessary components to estimate these theoretical influence functions, and performing sample splitting, we present estimators that efficiently and robustly target τ a (P ) and τ * a (P ), akin to many recently developed methods (Chernozhukov et al, 2018;Kennedy, 2019Kennedy, , 2020.…”

Section: Estimators Based On Efficient Influence Functionsmentioning

confidence: 99%

Double sampling and semiparametric methods for informatively missing data

Levis¹,

Mukherjee²,

Wang³

et al. 2022

Preprint

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Missing data arise almost ubiquitously in applied settings, and can pose a substantial threat to the validity of statistical analyses. In the context of comparative effectiveness research, such as in large observational databases (e.g., those derived from electronic health records), outcomes may be missing not at random with respect to measured covariates. In this setting, we propose a double sampling method, in which outcomes are obtained via intensive follow-up on a subsample of subjects for whom data were initially missing. We describe assumptions under which the joint distribution of confounders, treatment, and outcome is identified under this design, and derive efficient estimators of the average treatment effect under a nonparametric model, as well as a model assuming outcomes were initially missing at random. We compare these in simulations to an approach that adaptively selects an estimator based on evidence of violation of the missing at random assumption. We also show that the proposed double sampling design can be extended to handle arbitrary coarsening mechanisms, and derive consistent, asymptotically normal, and nonparametric efficient estimators of any smooth full data functional of interest, and prove that these estimators often are multiply robust.

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“…Although one-sided noncompliance is often associated with RCTs, some observational studies also fit with the framework (Frölich and Melly 2013;Kennedy 2020). In the case of one-sided noncompliance, we can also consider our problem as the estimation of the average treatment effect on the treated (ATT) since LATE is equal to ATT under onesided noncompliance and the other standard assumptions (Frölich and Melly 2013;Donald, Hsu, and Lieli 2014).…”

Section: Identificationmentioning

confidence: 99%

Estimation of Local Average Treatment Effect by Data Combination

Shinoda

Hoshino

2022

AAAI

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It is important to estimate the local average treatment effect (LATE) when compliance with a treatment assignment is incomplete. The previously proposed methods for LATE estimation required all relevant variables to be jointly observed in a single dataset; however, it is sometimes difficult or even impossible to collect such data in many real-world problems for technical or privacy reasons. We consider a novel problem setting in which LATE, as a function of covariates, is nonparametrically identified from the combination of separately observed datasets. For estimation, we show that the direct least squares method, which was originally developed for estimating the average treatment effect under complete compliance, is applicable to our setting. However, model selection and hyperparameter tuning for the direct least squares estimator can be unstable in practice since it is defined as a solution to the minimax problem. We then propose a weighted least squares estimator that enables simpler model selection by avoiding the minimax objective formulation. Unlike the inverse probability weighted (IPW) estimator, the proposed estimator directly uses the pre-estimated weight without inversion, avoiding the problems caused by the IPW methods. We demonstrate the effectiveness of our method through experiments using synthetic and real-world datasets.

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Efficient Nonparametric Causal Inference with Missing Exposure Information

Cited by 6 publications

References 33 publications

Doubly robust capture-recapture methods for estimating population size

Doubly robust capture-recapture methods for estimating population size

Double sampling and semiparametric methods for informatively missing data

Estimation of Local Average Treatment Effect by Data Combination

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