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There is growing interest in developing causal inference methods for multi-valued treatments with a focus on pairwise average treatment effects. Here we focus on a clinically important, yet less-studied estimand: causal drug-drug interactions (DDIs), which quantifies the degree to which the causal effect of drug A is altered by the presence versus the absence of drug B. Confounding adjustment when studying the effects of DDIs can be accomplished via inverse probability of treatment weighting (IPTW), a standard approach originally developed for binary treatments and later generalized to multi-valued treatments. However, this approach generally results in biased results when the propensity score model is misspecified. Motivated by the need for more robust techniques, we propose two empirical likelihood-based weighting approaches that allow for specifying a set of propensity score models, with the second method balancing user-specified covariates directly, by incorporating additional, nonparametric constraints. The resulting estimators from both methods are consistent when the postulated set of propensity score models contains a correct one; this property has been termed multiple robustness. We then evaluate their finite sample performance through simulation. The results demonstrate that the proposed estimators outperform the standard IPTW method in terms of both robustness and efficiency. Finally, we apply the proposed methods to evaluate the impact of renin-angiotensin system inhibitors (RAS-I) on the comparative nephrotoxicity of nonsteroidal anti-inflammatory drugs (NSAID) and opioids, using data derived from electronic medical records from a large multi-hospital health system.

In a completely randomized experiment, the variances of treatment effect estimators in the finite population are usually not identifiable and hence not estimable. Although some estimable bounds of the variances have been established in the literature, few of them are derived in the presence of covariates. In this paper, the difference-in-means estimator and the Wald estimator are considered in the completely randomized experiment with perfect compliance and noncompliance, respectively. Sharp bounds for the variances of these two estimators are established when covariates are available. Furthermore, consistent estimators for such bounds are obtained, which can be used to shorten the confidence intervals and improve the power of tests. Confidence intervals are constructed based on the consistent estimators of the upper bounds, whose coverage rates are uniformly asymptotically guaranteed. Simulations were conducted to evaluate the proposed methods. The proposed methods are also illustrated with two real data analyses.

We study the offline reinforcement learning (RL) in the face of unmeasured confounders. Due to the lack of online interaction with the environment, offline RL is facing the following two significant challenges: (i) the agent may be confounded by the unobserved state variables; (ii) the offline data collected a prior does not provide sufficient coverage for the environment. To tackle the above challenges, we study the policy learning in the confounded MDPs with the aid of instrumental variables. Specifically, we first establish value function (VF)-based and marginalized importance sampling (MIS)-based identification results for the expected total reward in the confounded MDPs. Then by leveraging pessimism and our identification results, we propose various policy learning methods with the finite-sample suboptimality guarantee of finding the optimal in-class policy under minimal data coverage and modeling assumptions. Lastly, our extensive theoretical investigations and one numerical study motivated by the kidney transplantation demonstrate the promising performance of the proposed methods.

Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model fitting algorithm as a function of the data. However, exchangeability is often violated when predictive models are deployed in practice. For example, if the data distribution drifts over time, then the data points are no longer exchangeable; moreover, in such settings, we might want to use a nonsymmetric algorithm that treats recent observations as more relevant. This paper generalizes conformal prediction to deal with both aspects: we employ weighted quantiles to introduce robustness against distribution drift, and design a new randomization technique to allow for algorithms that do not treat data points symmetrically. Our new methods are provably robust, with substantially less loss of coverage when exchangeability is violated due to distribution drift or other challenging features of real data, while also achieving the same coverage guarantees as existing conformal prediction methods if the data points are in fact exchangeable. We demonstrate the practical utility of these new tools with simulations and real-data experiments on electricity and election forecasting.

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased away from the ground-truth. Due to this asymptotic bias, traditional inference methods may in practice yield parameters that generalize poorly and misestimate uncertainty. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high-quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real data-sets.

We propose a new sensitivity analysis model that combines copulas and normalizing flows for causal inference under unobserved confounding. We refer to the new model as $\rho$-GNF ($\rho$-Graphical Normalizing Flow), where $\rho{\in}[-1,+1]$ is a bounded sensitivity parameter representing the backdoor non-causal association due to unobserved confounding modeled using the most well studied and widely popular Gaussian copula. Specifically, $\rho$-GNF enables us to estimate and analyse the frontdoor causal effect or average causal effect (ACE) as a function of $\rho$. We call this the $\rho_{curve}$. The $\rho_{curve}$ enables us to specify the confounding strength required to nullify the ACE. We call this the $\rho_{value}$. Further, the $\rho_{curve}$ also enables us to provide bounds for the ACE given an interval of $\rho$ values. We illustrate the benefits of $\rho$-GNF with experiments on simulated and real-world data in terms of our empirical ACE bounds being narrower than other popular ACE bounds.

To estimate causal effects, analysts performing observational studies in health settings utilize several strategies to mitigate bias due to confounding by indication. There are two broad classes of approaches for these purposes: use of confounders and instrumental variables (IVs). Because such approaches are largely characterized by untestable assumptions, analysts must operate under an indefinite paradigm that these methods will work imperfectly. In this tutorial, we formalize a set of general principles and heuristics for estimating causal effects in the two approaches when the assumptions are potentially violated. This crucially requires reframing the process of observational studies as hypothesizing potential scenarios where the estimates from one approach are less inconsistent than the other. While most of our discussion of methodology centers around the linear setting, we touch upon complexities in non-linear settings and flexible procedures such as target minimum loss-based estimation (TMLE) and double machine learning (DML). To demonstrate the application of our principles, we investigate the use of donepezil off-label for mild cognitive impairment (MCI). We compare and contrast results from confounder and IV methods, traditional and flexible, within our analysis and to a similar observational study and clinical trial.

Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.