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1. Partial Identifiability in Discrete Data with Measurement Error

   Noam Finkelstein ; Roy Adams ; Suchi Saria ; Ilya Shpitser ( July 2021 , Proceedings of the Thirty Seventh Conference on Uncertainty in Artificial Intelligence)

   Cassio de Campos ; Marloes H. Maathuis (Ed.)

   When data contains measurement errors, it is necessary to make modeling assumptions relating the error-prone measurements to the unobserved true values. Work on measurement error has largely focused on models that fully identify the parameter of interest. As a result, many practically useful models that result in bounds on the target parameter -- known as partial identification -- have been neglected. In this work, we present a method for partial identification in a class of measurement error models involving discrete variables. We focus on models that impose linear constraints on the tar- get parameter, allowing us to compute partial identification bounds using off-the-shelf LP solvers. We show how several common measurement error assumptions can be composed with an extended class of instrumental variable-type models to create such linear constraint sets. We further show how this approach can be used to bound causal parameters, such as the average treatment effect, when treatment or outcome variables are measured with error. Using data from the Oregon Health Insurance Experiment, we apply this method to estimate bounds on the effect Medicaid enrollment has on depression when depression is measured with error. 

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2. Using Post-Outcome Measurement Information in Censoring-by-Death Problems

   https://doi.org/10.1111/rssb.12113  

   Yang, Fan ; Small, Dylan S. ( April 2015 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Many clinical studies on non-mortality outcomes such as quality of life suffer from the problem that the non-mortality outcome can be censored by death, i.e. the non-mortality outcome cannot be measured if the subject dies before the time of measurement. To address the problem that this censoring by death is informative, it is of interest to consider the average effect of the treatment on the non-mortality outcome among subjects whose measurement would not be censored under either treatment or control, which is called the survivor average causal effect (SACE). The SACE is not point identified under usual assumptions but bounds can be constructed. The previous literature on bounding the SACE uses only the survival information before the measurement of the non-mortality outcome. However, survival information after the measurement of the non-mortality outcome could also be informative. For randomized trials, we propose a set of ranked average score assumptions that make use of survival information before and after the measurement of the non-mortality outcome which are plausibly satisfied in many studies and we develop a two-step linear programming approach to obtain the closed form for bounds on the SACE under our assumptions. We also extend our method to randomized trials with non-compliance or observational studies with a valid instrumental variable to obtain bounds on the complier SACE which is presented in on-line supplementary material. We apply our method to a randomized trial of the effect of mechanical ventilation with lower tidal volume versus traditional tidal volume for acute lung injury patients. Our bounds on the SACE are much shorter than the bounds that are obtained by using only the survival information before the measurement of the non-mortality outcome.

    

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3. Double Machine Learning Density Estimation for Local Treatment Effects with Instruments

   Jung, Y. ; Tian, J. ; Bareinboim, E. ( January 2021 , Advances in neural information processing systems)

   It is common to quantify causal effects with mean values, which, however, may fail to capture significant distribution differences of the outcome under different treatments. We study the problem of estimating the density of the causal effect of a binary treatment on a continuous outcome given a binary instrumental variable in the presence of covariates. Specifically, we consider the local treatment effect, which measures the effect of treatment among those who comply with the assignment under the assumption of monotonicity (only the ones who were offered the treatment take it). We develop two families of methods for this task, kernel-smoothing and model-based approximations -- the former smoothes the density by convoluting with a smooth kernel function; the latter projects the density onto a finite-dimensional density class. For both approaches, we derive double/debiased machine learning (DML) based estimators. We study the asymptotic convergence rates of the estimators and show that they are robust to the biases in nuisance function estimation. We illustrate the proposed methods on synthetic data and a real dataset called 401(k). 

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4. Two robust tools for inference about causal effects with invalid instruments

   https://doi.org/10.1111/biom.13415  

   Kang, Hyunseung ; Lee, Youjin ; Cai, T. Tony ; Small, Dylan S. ( December 2020 , Biometrics)

   Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This paper presents two tools to conduct valid inference and tests in the presence of invalid instruments. First, we propose a simple and general approach to construct confidence intervals based on taking unions of well‐known confidence intervals. Second, we propose a novel test for the null causal effect based on a collider bias. Our two proposals outperform traditional instrumental variable confidence intervals when invalid instruments are present and can also be used as a sensitivity analysis when there is concern that instrumental variables assumptions are violated. The new approach is applied to a Mendelian randomization study on the causal effect of low‐density lipoprotein on globulin levels.

    

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5. Conditional differential measurement error: partial identifiability and estimation

   Huang, Pengrun ; Makar, Maggie ( January 2022 , NeurIPS workshop on causal machine learning for real world impact)

   Differential measurement error, which occurs when the error in the measured outcome is correlated with the treatment renders the causal effect unidentifiable from observational data. In this work, we study conditional differential measurement error, where a subgroup of the population is known to be prone to differential measurement error. Under an assumption about the direction (but not magnitude) of the measurement error, we derive sharp bounds on the conditional average treatment effect, and present an approach to estimate them. We empirically validate our approach on semi-synthetic da, showing that it gives more credible and informative bound than other approaches. In addition, we implement our approach on real data, showing its utility in guiding decisions about dietary modification intervals to improve nutritional intake. 

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