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1. Causal inference with confounders missing not at random

   https://doi.org/10.1093/biomet/asz048  

   Yang, S; Wang, L; Ding, P (September 2019, Biometrika)

   Summary It is important to draw causal inference from observational studies, but this becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. In this article we propose a novel framework for nonparametric identification of causal effects with confounders subject to an outcome-independent missingness, which means that the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounders. We then propose a nonparametric two-stage least squares estimator and a parametric estimator for causal effects. 

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2. SMIM: A unified framework of survival sensitivity analysis using multiple imputation and martingale

   https://doi.org/10.1111/biom.13555  

   Yang, Shu; Zhang, Yilong; Liu, Guanghan Frank; Guan, Qian (September 2021, Biometrics)

   Abstract Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ‐adjusted and control‐based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets a broad class of treatment effect estimands defined as functionals of treatment‐specific survival functions, taking into account missing data due to censoring. Multiple imputation facilitates the use of simple full‐sample estimation; however, the standard Rubin's combining rule may overestimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of the estimator and propose the wild bootstrap inference by resampling the martingale series. The new bootstrap inference has a theoretical guarantee for consistency and is computationally efficient compared to the nonparametric bootstrap counterpart. We evaluate the finite‐sample performance of the proposed SMIM through simulation and an application on an HIV clinical trial. 

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3. The Decaying Missing-at-Random Framework: Model Doubly Robust Causal Inference with Partially Labeled Data

   Zhang, Yuqian; Chakrabortty, Abhishek; Bradic, Jelena (April 2025, arXiv.org)

   In modern large-scale observational studies, data collection constraints often result in partially labeled datasets, posing challenges for reliable causal inference, especially due to potential labeling bias and relatively small size of the labeled data. This paper introduces a decaying missing-at-random (decaying MAR) framework and associated approaches for doubly robust causal inference on treatment effects in such semi-supervised (SS) settings. This simultaneously addresses selection bias in the labeling mechanism and the extreme imbalance between labeled and unlabeled groups, bridging the gap between the standard SS and missing data literatures, while throughout allowing for confounded treatment assignment and high-dimensional confounders under appropriate sparsity conditions. To ensure robust causal conclusions, we propose a bias-reduced SS (BRSS) estimator for the average treatment effect, a type of 'model doubly robust' estimator appropriate for such settings, establishing asymptotic normality at the appropriate rate under decaying labeling propensity scores, provided that at least one nuisance model is correctly specified. Our approach also relaxes sparsity conditions beyond those required in existing methods, including standard supervised approaches. Recognizing the asymmetry between labeling and treatment mechanisms, we further introduce a de-coupled BRSS (DC-BRSS) estimator, which integrates inverse probability weighting (IPW) with bias-reducing techniques in nuisance estimation. This refinement further weakens model specification and sparsity requirements. Numerical experiments confirm the effectiveness and adaptability of our estimators in addressing labeling bias and model misspecification. 

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4. Distributional imputation for the analysis of censored recurrent events

   https://doi.org/10.1002/sim.10087  

   Fairfax, Sarah R; Yang, Shu (June 2024, Statistics in Medicine)

   Longitudinal clinical trials for which recurrent events endpoints are of interest are commonly subject to missing event data. Primary analyses in such trials are often performed assuming events are missing at random, and sensitivity analyses are necessary to assess robustness of primary analysis conclusions to missing data assumptions. Control‐based imputation is an attractive approach in superiority trials for imposing conservative assumptions on how data may be missing not at random. A popular approach to implementing control‐based assumptions for recurrent events is multiple imputation (MI), but Rubin's variance estimator is often biased for the true sampling variability of the point estimator in the control‐based setting. We propose distributional imputation (DI) with corresponding wild bootstrap variance estimation procedure for control‐based sensitivity analyses of recurrent events. We apply control‐based DI to a type I diabetes trial. In the application and simulation studies, DI produced more reasonable standard error estimates than MI with Rubin's combining rules in control‐based sensitivity analyses of recurrent events. 

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5. Evaluation of linear models and missing value imputation for the analysis of peptide-centric proteomics

   Berg, Philip McConnell (May 2019, BMC bioinformatics)

   Background Several methods to handle data generated from bottom-up proteomics via liquid chromatography-mass spectrometry, particularly for peptide-centric quantification dealing with post-translational modification (PTM) analysis like reversible cysteine oxidation are evaluated. The paper proposes a pipeline based on the R programming language to analyze PTMs from peptide-centric label-free quantitative proteomics data. Results Our methodology includes variance stabilization, normalization, and missing data imputation to account for the large dynamic range of PTM measurements. It also corrects biases from an enrichment protocol and reduces the random and systematic errors associated with label-free quantification. The performance of the methodology is tested by performing proteome-wide differential PTM quantitation using linear models analysis (limma). We objectively compare two imputation methods along with significance testing when using multiple-imputation for missing data. Conclusion Identifying PTMs in large-scale datasets is a problem with distinct characteristics that require new methods for handling missing data imputation and differential proteome analysis. Linear models in combination with multiple-imputation could significantly outperform a t-test-based decision method. 

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