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1. An instrumental variable method for point processes: generalized Wald estimation based on deconvolution

   https://doi.org/10.1093/biomet/asad005  

   Jiang, Zhichao; Chen, Shizhe; Ding, Peng (January 2023, Biometrika)

   Summary Point processes are probabilistic tools for modelling event data. While there exists a fast-growing literature on the relationships between point processes, how such relationships connect to causal effects remains unexplored. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define causal quantities based on potential outcomes and establish nonparametric identification results with a binary instrumental variable. We extend the traditional Wald estimation to deal with point process treatment and outcome, showing that it should be performed after a Fourier transform of the intention-to-treat effects on the treatment and outcome, and thus takes the form of deconvolution. We refer to this approach as generalized Wald estimation and propose an estimation strategy based on well-established deconvolution methods. 

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2. 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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3. Semiparametric estimation of structural nested mean models with irregularly spaced longitudinal observations

   https://doi.org/10.1111/biom.13471  

   Yang, Shu (April 2021, Biometrics)

   Abstract Structural nested mean models (SNMMs) are useful for causal inference of treatment effects in longitudinal observational studies. Most existing works assume that the data are collected at prefixed time points for all subjects, which, however, may be restrictive in practice. To deal with irregularly spaced observations, we assume a class of continuous‐time SNMMs and a martingale condition of no unmeasured confounding (NUC) to identify the causal parameters. We develop the semiparametric efficiency theory and locally efficient estimators for continuous‐time SNMMs. This task is nontrivial due to the restrictions from the NUC assumption imposed on the SNMM parameter. In the presence of ignorable censoring, we show that the complete‐case estimator is optimal among a class of weighting estimators including the inverse probability of censoring weighting estimator, and it achieves a double robustness feature in that it is consistent if at least one of the models for the potential outcome mean function and the treatment process is correctly specified. The new framework allows us to conduct causal analysis respecting the underlying continuous‐time nature of data processes. The simulation study shows that the proposed estimator outperforms existing approaches. We estimate the effect of time to initiate highly active antiretroviral therapy on the CD4 count at year 2 from the observational Acute Infection and Early Disease Research Program database. 

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4. Causal imputation via synthetic interventions”, Causal Learning and Reasoning

   Squires, C.; Shen, D.; Shah, D.; Uhler, C. (January 2022, Proceedings of Machine Learning Research)

   Consider the problem of determining the effect of a compound on a specific cell type. To answer this question, researchers traditionally need to run an experiment applying the drug of interest to that cell type. This approach is not scalable: given a large number of different actions (compounds) and a large number of different contexts (cell types), it is infeasible to run an experiment for every action-context pair. In such cases, one would ideally like to predict the outcome for every pair while only needing outcome data for a small _subset_ of pairs. This task, which we label "causal imputation", is a generalization of the causal transportability problem. To address this challenge, we extend the recently introduced _synthetic interventions_ (SI) estimator to handle more general data sparsity patterns. We prove that, under a latent factor model, our estimator provides valid estimates for the causal imputation task. We motivate this model by establishing a connection to the linear structural causal model literature. Finally, we consider the prominent CMAP dataset in predicting the effects of compounds on gene expression across cell types. We find that our estimator outperforms standard baselines, thus confirming its utility in biological applications. 

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5. Design‐robust two‐way‐fixed‐effects regression for panel data

   https://doi.org/10.3982/QE1962  

   Arkhangelsky, Dmitry; Imbens, Guido W; Lei, Lihua; Luo, Xiaoman (November 2024, Quantitative Economics)

   We propose a new estimator for average causal effects of a binary treatment with panel data in settings with general treatment patterns. Our approach augments the popular two‐way‐fixed‐effects specification with unit‐specific weights that arise from a model for the assignment mechanism. We show how to construct these weights in various settings, including the staggered adoption setting, where units opt into the treatment sequentially but permanently. The resulting estimator converges to an average (over units and time) treatment effect under the correct specification of the assignment model, even if the fixed‐ effect model is misspecified. We show that our estimator is more robust than the conventional two‐way estimator: it remains consistent if either the assignment mechanism or the two‐way regression model is correctly specified. In addition, the proposed estimator performs better than the two‐way‐fixed‐effect estimator if the outcome model and assignment mechanism are locally misspecified. This strong robustness property underlines and quantifies the benefits of modeling the assignment process and motivates using our estimator in practice. We also discuss an extension of our estimator to handle dynamic treatment effects. 

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