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Instrumental variables are widely used in econometrics and epidemiology for identifying and estimating causal effects when an exposure of interest is confounded by unmeasured factors. Despite this popularity, the assumptions invoked to justify the use of instruments differ substantially across the literature. Similarly, statistical approaches for estimating the resulting causal quantities vary considerably, and often rely on strong parametric assumptions. In this work, we compile and organize structural conditions that nonparametrically identify conditional average treatment effects, average treatment effects among the treated, and local average treatment effects, with a focus on identification formulae invoking the conditional Wald estimand. Moreover, we build upon existing work and propose nonparametric efficient estimators of functionals corresponding to marginal and conditional causal contrasts resulting from the various identification paradigms. We illustrate the proposed methods on an observational study examining the effects of operative care on adverse events for cholecystitis patients, and a randomized trial assessing the effects of market participation on political views., Comment: 46 pages, 2 figures

Laparoscopic surgery has been shown through a number of randomized trials to be an effective form of treatment for cholecystitis. Given this evidence, one natural question for clinical practice is: does the effectiveness of laparoscopic surgery vary among patients? It might be the case that, while the overall effect is positive, some patients treated with laparoscopic surgery may respond positively to the intervention while others do not or may be harmed. In our study, we focus on conditional average treatment effects to understand whether treatment effects vary systematically with patient characteristics. Recent methodological work has developed a meta-learner framework for flexible estimation of conditional causal effects. In this framework, nonparametric estimation methods can be used to avoid bias from model misspecification while preserving statistical efficiency. In addition, researchers can flexibly and effectively explore whether treatment effects vary with a large number of possible effect modifiers. However, these methods have certain limitations. For example, conducting inference can be challenging if black-box models are used. Further, interpreting and visualizing the effect estimates can be difficult when there are multi-valued effect modifiers. In this paper, we develop new methods that allow for interpretable results and inference from the meta-learner framework for heterogeneous treatment effects estimation. We also demonstrate methods that allow for an exploratory analysis to identify possible effect modifiers. We apply our methods to a large database for the use of laparoscopic surgery in treating cholecystitis. We also conduct a series of simulation studies to understand the relative performance of the methods we develop. Our study provides key guidelines for the interpretation of conditional causal effects from the meta-learner framework., Comment: 48 pages, 7 figures

Comparative effectiveness research frequently employs the instrumental variable design since randomized trials can be infeasible for many reasons. In this study, we investigate and compare treatments for emergency cholecystitis -- inflammation of the gallbladder. A standard treatment for cholecystitis is surgical removal of the gallbladder, while alternative non-surgical treatments include managed care and pharmaceutical options. As randomized trials are judged to violate the principle of equipoise, we consider an instrument for operative care: the surgeon's tendency to operate. Standard instrumental variable estimation methods, however, often rely on parametric models that are prone to bias from model misspecification. We outline instrumental variable estimation methods based on the doubly robust machine learning framework. These methods enable us to employ various machine learning techniques for nuisance parameter estimation and deliver consistent estimates and fast rates of convergence for valid inference. We use these methods to estimate the primary target causal estimand in an IV design. Additionally, we expand these methods to develop estimators for heterogeneous causal effects, profiling principal strata, and a sensitivity analyses for a key instrumental variable assumption. We conduct a simulation study to demonstrate scenarios where more flexible estimation methods outperform standard methods. Our findings indicate that operative care is generally more effective for cholecystitis patients, although the benefits of surgery can be less pronounced for key patient subgroups.

Quantifying treatment effect heterogeneity is a crucial task in many areas of causal inference, e.g. optimal treatment allocation and estimation of subgroup effects. We study the problem of estimating the level sets of the conditional average treatment effect (CATE), identified under the no-unmeasured-confounders assumption. Given a user-specified threshold, the goal is to estimate the set of all units for whom the treatment effect exceeds that threshold. For example, if the cutoff is zero, the estimand is the set of all units who would benefit from receiving treatment. Assigning treatment just to this set represents the optimal treatment rule that maximises the mean population outcome. Similarly, cutoffs greater than zero represent optimal rules under resource constraints. The level set estimator that we study follows the plug-in principle and consists of simply thresholding a good estimator of the CATE. While many CATE estimators have been recently proposed and analysed, how their properties relate to those of the corresponding level set estimators remains unclear. Our first goal is thus to fill this gap by deriving the asymptotic properties of level set estimators depending on which estimator of the CATE is used. Next, we identify a minimax optimal estimator in a model where the CATE, the propensity score and the outcome model are Holder-smooth of varying orders. We consider data generating processes that satisfy a margin condition governing the probability of observing units for whom the CATE is close to the threshold. We investigate the performance of the estimators in simulations and illustrate our methods on a dataset used to study the effects on mortality of laparoscopic vs open surgery in the treatment of various conditions of the colon., Comment: 38 pages, 4 figures

Experiments studying get-out-the-vote (GOTV) efforts estimate the causal effect of various mobilization efforts on voter turnout. However, there is often substantial noncompliance in these studies. A usual approach is to use an instrumental variable (IV) analysis to estimate impacts for compliers, here being those actually contacted by the investigators. Unfortunately, popular IV estimators can be unstable in studies with a small fraction of compliers. We explore post-stratifying the data (e.g., taking a weighted average of IV estimates within each stratum) using variables that predict complier status (and, potentially, the outcome) to mitigate this. We present the benefits of post-stratification in terms of bias, variance, and improved standard error estimates, and provide a finite-sample asymptotic variance formula. We also compare the performance of different IV approaches and discuss the advantages of our design-based post-stratification approach over incorporating compliance-predictive covariates into the two-stage least squares estimator. In the end, we show that covariates predictive of compliance can increase precision, but only if one is willing to make a bias-variance trade-off by down-weighting or dropping strata with few compliers. By contrast, standard approaches such as two-stage least squares fail to use such information. We finally examine the benefits of our approach in two GOTV applications.

We present a practical guide for the analysis of regression discontinuity (RD) designs in biomedical contexts. We begin by introducing key concepts, assumptions, and estimands within both the continuity-based framework and the local randomization framework. We then discuss modern estimation and inference methods within both frameworks, including approaches for bandwidth or local neighborhood selection, optimal treatment effect point estimation, and robust bias-corrected inference methods for uncertainty quantification. We also overview empirical falsification tests that can be used to support key assumptions. Our discussion focuses on two particular features that are relevant in biomedical research: (i) fuzzy RD designs, which often arise when therapeutic treatments are based on clinical guidelines but patients with scores near the cutoff are treated contrary to the assignment rule; and (ii) RD designs with discrete scores, which are ubiquitous in biomedical applications. We illustrate our discussion with three empirical applications: the effect of CD4 guidelines for anti-retroviral therapy on retention of HIV patients in South Africa, the effect of genetic guidelines for chemotherapy on breast cancer recurrence in the United States, and the effects of age-based patient cost-sharing on healthcare utilization in Taiwan. We provide replication materials employing publicly available statistical software in Python, R and Stata, offering researchers all necessary tools to conduct an RD analysis.

When an exposure of interest is confounded by unmeasured factors, an instrumental variable (IV) can be used to identify and estimate certain causal contrasts. Identification of the marginal average treatment effect (ATE) from IVs relies on strong untestable structural assumptions. When one is unwilling to assert such structure, IVs can nonetheless be used to construct bounds on the ATE. Famously, Balke and Pearl (1997) proved tight bounds on the ATE for a binary outcome, in a randomized trial with noncompliance and no covariate information. We demonstrate how these bounds remain useful in observational settings with baseline confounders of the IV, as well as randomized trials with measured baseline covariates. The resulting bounds on the ATE are non-smooth functionals, and thus standard nonparametric efficiency theory is not immediately applicable. To remedy this, we propose (1) under a novel margin condition, influence function-based estimators of the bounds that can attain parametric convergence rates when the nuisance functions are modeled flexibly, and (2) estimators of smooth approximations of these bounds. We propose extensions to continuous outcomes, explore finite sample properties in simulations, and illustrate the proposed estimators in an observational study targeting the effect of higher education on wages., Comment: 42 pages, 2 figures

In a clustered observational study, a treatment is assigned to groups and all units within the group are exposed to the treatment. We develop a new method for statistical adjustment in clustered observational studies using approximate balancing weights, a generalization of inverse propensity score weights that solve a convex optimization problem to find a set of weights that directly minimize a measure of covariate imbalance, subject to an additional penalty on the variance of the weights. We tailor the approximate balancing weights optimization problem to both adjustment sets by deriving an upper bound on the mean square error for each case and finding weights that minimize this upper bound, linking the level of covariate balance to a bound on the bias. We implement the procedure by specializing the bound to a random cluster-level effects model, leading to a variance penalty that incorporates the signal signal-to-noise ratio and penalizes the weight on individuals and the total weight on groups differently according to the the intra-class correlation.

Inverse probability weights are commonly used in epidemiology to estimate causal effects in observational studies. Researchers can typically focus on either the average treatment effect or the average treatment effect on the treated with inverse probability weighting estimators. However, when overlap between the treated and control groups is poor, this can produce extreme weights that can result in biased estimates and large variances. One alternative to inverse probability weights are overlap weights, which target the population with the most overlap on observed characteristics. While estimates based on overlap weights produce less bias in such contexts, the causal estimand can be difficult to interpret. One alternative to inverse probability weights are balancing weights, which directly target imbalances during the estimation process. Here, we explore whether balancing weights allow analysts to target the average treatment effect on the treated in cases where inverse probability weights are biased due to poor overlap. We conduct three simulation studies and an empirical application. We find that in many cases, balancing weights allow the analyst to still target the average treatment effect on the treated even when overlap is poor. We show that while overlap weights remain a key tool for estimating causal effects, more familiar estimands can be targeted by using balancing weights instead of inverse probability weights.

Research documents that Black patients experience worse general surgery outcomes than white patients in the United States. In this paper, we focus on an important but less-examined category: the surgical treatment of emergency general surgery (EGS) conditions, which refers to medical emergencies where the injury is "endogenous," such as a burst appendix. Our goal is to assess racial disparities for common outcomes after EGS treatment using an administrative database of hospital claims in New York, Florida, and Pennsylvania, and to understand the extent to which differences are attributable to patient-level risk factors versus hospital-level factors. To do so, we use a class of linear weighting estimators that re-weight white patients to have a similar distribution of baseline characteristics as Black patients. This framework nests many common approaches, including matching and linear regression, but offers important advantages over these methods in terms of controlling imbalance between groups, minimizing extrapolation, and reducing computation time. Applying this approach to the claims data, we find that disparities estimates that adjust for the admitting hospital are substantially smaller than estimates that adjust for patient baseline characteristics only, suggesting that hospital-specific factors are important drivers of racial disparities in EGS outcomes.

The clustered observational study (COS) design is the observational study counterpart to the clustered randomized trial. In a COS, a treatment is assigned to intact groups, and all units within the group are exposed to the treatment. However, the treatment is non-randomly assigned. COSs are common in both education and health services research. In education, treatments may be given to all students within some schools but withheld from all students in other schools. In health studies, treatments may be applied to clusters such as hospitals or groups of patients treated by the same physician. In this manuscript, we study the identification of causal effects in clustered observational study designs. We focus on the prospect of differential selection of units to clusters, which occurs when the units' cluster selections depend on the clusters' treatment assignments. Extant work on COSs has made an implicit assumption that rules out the presence of differential selection. We derive the identification results for designs with differential selection and that contexts with differential cluster selection require different adjustment sets than standard designs. We outline estimators for designs with and without differential selection. Using a series of simulations, we outline the magnitude of the bias that can occur with differential selection. We then present two empirical applications focusing on the likelihood of differential selection.

The Regression Discontinuity (RD) design is a widely used non-experimental method for causal inference and program evaluation. While its canonical formulation only requires a score and an outcome variable, it is common in empirical work to encounter RD analyses where additional variables are used for adjustment. This practice has led to misconceptions about the role of covariate adjustment in RD analysis, from both methodological and empirical perspectives. In this chapter, we review the different roles of covariate adjustment in RD designs, and offer methodological guidance for its correct use.