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      Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap

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          Abstract

          To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the "missing at random" and "no unmeasured confounder" assumptions. However, these assumptions are unverifiable using empirical data and pose serious threats to the validity of the qualitative conclusions of the statistical inference. A sensitivity analysis asks how the conclusions may change if the unverifiable assumptions are violated to a certain degree. In this paper we consider a marginal sensitivity model which is a natural extension of Rosenbaum's sensitivity model for matched observational studies. We aim to construct confidence intervals based on inverse probability weighting estimators, such that the intervals have asymptotically nominal coverage of the estimand whenever the data generating distribution is in the collection of marginal sensitivity models. We use a percentile bootstrap and a generalized minimax/maximin inequality to transform this intractable problem to a linear fractional programming problem, which can be solved very efficiently. We illustrate our method using a real dataset to estimate the causal effect of fish consumption on blood mercury level.

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          Most cited references 25

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          Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

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            Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study.

            Estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics. The propensity score, the probability of treatment exposure conditional on covariates, is the basis for two approaches to adjusting for confounding: methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores. We review popular versions of these approaches and related methods offering improved precision, describe theoretical properties and highlight their implications for practice, and present extensive comparisons of performance that provide guidance for practical use. 2004 John Wiley & Sons, Ltd.
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              Programming with linear fractional functionals

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                Author and article information

                Journal
                30 November 2017
                Article
                1711.11286

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                30 pages, 1 figure
                stat.ME math.ST stat.TH

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