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1. Analysis of regression discontinuity designs with censored data

   Cho, Youngjoo ; Hu, Chen ; Ghosh, Debashis ( January 2021 , Journal of statistical research University of Dacca Institute of Statistical Research and Training)

   In many medical and scientific settings, the choice of treatment or intervention may be de-termined by a covariate threshold. For example, elderly men may receive more thoroughdiagnosis if their prostate-specific antigen (PSA) level is high. In these cases, the causaltreatment effect is often of great interest, especially when there is a lack of evidence fromrandomized clinical trials. From the social science literature, a class of methods known asregression discontinuity (RD) designs can be used to estimate the treatment effect in thissituation. Under certain assumptions, such an estimand enjoys a causal interpretation. Weshow how to estimate causal effects under the regression discontinuity design for censoreddata. The proposed estimation procedure employs a class of censoring unbiased transfor-mations that includes inverse probability censored weighting and doubly robust transfor-mation schemes. Simulation studies are used to evaluate the finite-sample properties of theproposed estimator. We also illustrate the proposed method by evaluating the causal effectof PSA-dependent screening strategies 

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2. Causal Inference with Noisy and Missing Covariates via Matrix Factorization

   Kallus, Nathan ; Mao, Xiaojie ; Madeleine, Udell ( January 2018 , Advances in neural information processing systems)

   Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce bias induced by measurement noise using a large number of noisy measurements of the underlying confounders. We propose the use of matrix factorization to infer the confounders from noisy covariates. This flexible and principled framework adapts to missing values, accommodates a wide variety of data types, and can enhance a wide variety of causal inference methods. We bound the error for the induced average treatment effect estimator and show it is consistent in a linear regression setting, using Exponential Family Matrix Completion preprocessing. We demonstrate the effectiveness of the proposed procedure in numerical experiments with both synthetic data and real clinical data. 

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3. Multiply robust estimators in longitudinal studies with missing data under control-based imputation

   https://doi.org/10.1093/biomtc/ujad036  

   Liu, Siyi ; Yang, Shu ; Zhang, Yilong ; Liu, Guanghan ( February 2024 , Biometrics)

   Longitudinal studies are often subject to missing data. The recent guidance from regulatory agencies, such as the ICH E9(R1) addendum addresses the importance of defining a treatment effect estimand with the consideration of intercurrent events. Jump-to-reference (J2R) is one classical control-based scenario for the treatment effect evaluation, where the participants in the treatment group after intercurrent events are assumed to have the same disease progress as those with identical covariates in the control group. We establish new estimators to assess the average treatment effect based on a proposed potential outcomes framework under J2R. Various identification formulas are constructed, motivating estimators that rely on different parts of the observed data distribution. Moreover, we obtain a novel estimator inspired by the efficient influence function, with multiple robustness in the sense that it achieves n1/2-consistency if any pairs of multiple nuisance functions are correctly specified, or if the nuisance functions converge at a rate not slower than n−1/4 when using flexible modeling approaches. The finite-sample performance of the proposed estimators is validated in simulation studies and an antidepressant clinical trial.

    

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4. Propensity Score Weighting for Causal Inference with Clustered Data

   https://doi.org/10.1515/jci-2017-0027  

   Yang, Shu ( September 2018 , Journal of Causal Inference)

   Abstract Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-level covariates that are related to both the treatment assignment and outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a calibration technique for propensity score estimation under the latent ignorable treatment assignment mechanism, i. e., the treatment-outcome relationship is unconfounded given the observed covariates and the latent cluster-specific confounders. We impose novel balance constraints which imply exact balance of the observed confounders and the unobserved cluster-level confounders between the treatment groups. We show that the proposed calibrated propensity score weighting estimator is doubly robust in that it is consistent for the average treatment effect if either the propensity score model is correctly specified or the outcome follows a linear mixed effects model. Moreover, the proposed weighting method can be combined with sampling weights for an integrated solution to handle confounding and sampling designs for causal inference with clustered survey data. In simulation studies, we show that the proposed estimator is superior to other competitors. We estimate the effect of School Body Mass Index Screening on prevalence of overweight and obesity for elementary schools in Pennsylvania. 

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5. 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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