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1. Measurement errors in the binary instrumental variable model

   https://doi.org/10.1093/biomet/asz060  

   Jiang, Zhichao; Ding, Peng (November 2019, Biometrika)

   Summary Instrumental variable methods can identify causal effects even when the treatment and outcome are confounded. We study the problem of imperfect measurements of the binary instrumental variable, treatment and outcome. We first consider nondifferential measurement errors, that is, the mismeasured variable does not depend on other variables given its true value. We show that the measurement error of the instrumental variable does not bias the estimate, that the measurement error of the treatment biases the estimate away from zero, and that the measurement error of the outcome biases the estimate toward zero. Moreover, we derive sharp bounds on the causal effects without additional assumptions. These bounds are informative because they exclude zero. We then consider differential measurement errors, and focus on sensitivity analyses in those settings. 

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2. 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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3. Analysis of regression-discontinuity designs with multiple cutoffs or multiple scores

   https://doi.org/10.1177/1536867X20976320  

   Cattaneo, Matias D.; Titiunik, Rocío; Vazquez-Bare, Gonzalo (December 2020, The Stata Journal: Promoting communications on statistics and Stata)

   In this article, we introduce the Stata (and R) package rdmulti, which consists of three commands (rdmc, rdmcplot, rdms) for analyzing regression-discontinuity (RD) designs with multiple cutoffs or multiple scores. The command rdmc applies to noncumulative and cumulative multicutoff RD settings. It calculates pooled and cutoff-specific RD treatment effects and provides robust biascorrected inference procedures. Postestimation and inference is allowed. The command rdmcplot offers RD plots for multicutoff settings. Finally, the command rdms concerns multiscore settings, covering in particular cumulative cutoffs and two running variable contexts. It also calculates pooled and cutoff-specific RD treatment effects, provides robust bias-corrected inference procedures, and allows for postestimation and inference. These commands use the Stata (and R) package rdrobust for plotting, estimation, and inference. Companion R functions with the same syntax and capabilities are provided. 

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4. 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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5. An Efficient Way to Find Optimal Crossover Designs Using CVX for Precision Medicine: Optimal Crossover Designs via CVX

   https://doi.org/10.52933/jdssv.v4i3.83  

   Li, Yin; Wong, Weng Kee; Zhou, Hua; Chough_Carriere, Keumhee (June 2024, Journal of Data Science, Statistics, and Visualisation)

   Crossover designs play an increasingly important role in precision medicine. We show the search of an optimal crossover design can be formulated as a convex optimization problem and convex optimization tools, such as CVX, can be directly used to search for an optimal crossover design.  We first demonstrate how to transform crossover design problems into convex optimization problems and show CVX can effortlessly find optimal crossover designs that coincide with a few theoretical crossover optimal designs in the literature. The proposed approach is especially useful when it becomes problematic to construct optimal designs analytically for complicated models. We then apply CVX to find crossover designs for models with auto-correlated error structures or when the information matrices may be singular and analytical answers are unavailable. We also construct N-of-1 trials frequently used in precision medicine to estimate treatment effects on the individuals or to estimate average treatment effects, including finding dual-objective optimal crossover designs. 

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