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Political scientists often turn to natural experiments to draw causal inferences with observational data. Recently, the regression discontinuity design (RD) has become a popular type of natural experiment due to its relatively weak assumptions. We study a special type of regression discontinuity design where the discontinuity in treatment assignment is geographic. In this design, which we call the Geographic Regression Discontinuity (GRD) design, a geographic or administrative boundary splits units into treated and control areas, and analysts make the case that the division into treated and control areas occurs in an as-if random fashion. We show how this design is equivalent to a standard RD with two running variables, but we also clarify several methodological differences that arise in geographical contexts. We also offer a method for estimation of geographically located treatment effects that can also be used to validate the identification assumptions using observable pretreatment characteristics. We illustrate our methodological framework with a re-examination of the effects of political advertisements on voter turnout during a presidential campaign, exploiting the exogenous variation in the volume of presidential ads that is created by media market boundaries.

Identifying causal mechanisms is a fundamental goal of social science. Researchers seek to study not only whether one variable affects another but also how such a causal relationship arises. Yet commonly used statistical methods for identifying causal mechanisms rely upon untestable assumptions and are often inappropriate even under those assumptions. Randomizing treatment and intermediate variables is also insufficient. Despite these difficulties, the study of causal mechanisms is too important to abandon. We make three contributions to improve research on causal mechanisms. First, we present a minimum set of assumptions required under standard designs of experimental and observational studies and develop a general algorithm for estimating causal mediation effects. Second, we provide a method for assessing the sensitivity of conclusions to potential violations of a key assumption. Third, we offer alternative research designs for identifying causal mechanisms under weaker assumptions. The proposed approach is illustrated using media framing experiments and incumbency advantage studies.

Causal mediation analysis is routinely conducted by applied researchers in a variety of disciplines. The goal of such an analysis is to investigate alternative causal mechanisms by examining the roles of intermediate variables that lie in the causal paths between the treatment and outcome variables. In this paper we first prove that under a particular version of sequential ignorability assumption, the average causal mediation effect (ACME) is nonparametrically identified. We compare our identification assumption with those proposed in the literature. Some practical implications of our identification result are also discussed. In particular, the popular estimator based on the linear structural equation model (LSEM) can be interpreted as an ACME estimator once additional parametric assumptions are made. We show that these assumptions can easily be relaxed within and outside of the LSEM framework and propose simple nonparametric estimation strategies. Second, and perhaps most importantly, we propose a new sensitivity analysis that can be easily implemented by applied researchers within the LSEM framework. Like the existing identifying assumptions, the proposed sequential ignorability assumption may be too strong in many applied settings. Thus, sensitivity analysis is essential in order to examine the robustness of empirical findings to the possible existence of an unmeasured confounder. Finally, we apply the proposed methods to a randomized experiment from political psychology. We also make easy-to-use software available to implement the proposed methods.

The Cox proportional hazards model is widely used to model durations in the social sciences. Although this model allows analysts to forgo choices about the form of the hazard, it demands careful attention to the proportional hazards assumption. To this end, a standard diagnostic method has been developed to test this assumption. I argue that the standard test for nonproportional hazards has been misunderstood in current practice. This test detects a variety of specification errors, and these specification errors must be corrected before one can correctly diagnose nonproportionality. In particular, unmodeled nonlinearity can appear as a violation of the proportional hazard assumption for the Cox model. Using both simulation and empirical examples, I demonstrate how an analyst might be led astray by incorrectly applying the nonproportionality test.

Dramatic world change has stimulated interest in research questions about the dynamics of politics. We have seen increases in the number of time series data sets and the length of typical time series. But three shortcomings are prevalent in published time series analysis. First, analysts often estimate models without testing restrictions implied by their specification. Second, researchers link the theoretical concept of equilibrium with cointegration and error correction models. Third, analysts often do a poor job of interpreting results. The consequences include weak connections between theory and tests, biased estimates, and incorrect inferences. We outline techniques for estimating linear dynamic regressions with stationary data and weakly exogenous regressors. We recommend analysts (1) start with general dynamic models and test restrictions before adopting a particular specification and (2) use the wide array of information available from dynamic specifications. We illustrate this strategy with data on Congressional approval and tax rates across OECD countries.

A common causal identification strategy in political science is selection on observables. This strategy assumes one observes a set of covariates that is, after statistical adjustment, sufficient to make treatment status as-if random. Under adjustment methods such as matching or inverse probability weighting, coefficients for control variables are treated as nuisance parameters and are not directly estimated. This is in direct contrast to regression approaches where estimated parameters are obtained for all covariates. Analysts often find it tempting to give a causal interpretation to all the parameters in such regression models—indeed, such interpretations are often central to the proposed research design. In this paper, we ask when we can justify interpreting two or more coefficients in a regression model as causal parameters. We demonstrate that analysts must appeal to causal identification assumptions to give estimates causal interpretations. Under selection on observables, this task is complicated by the fact that more than one causal effect might be identified. We show how causal graphs provide a framework for clearly delineating which effects are presumed to be identified and thus merit a causal interpretation, and which are not. We conclude with a set of recommendations for how researchers should interpret estimates from regression models when causal inference is the goal.

We discuss some causal estimands that are used to study racial discrimination in policing. A central challenge is that not all police–civilian encounters are recorded in administrative datasets and available to researchers. One possible solution is to consider the average causal effect of race conditional on the civilian already being detained by the police. We find that such an estimand can be quite different from the more familiar ones in causal inference and needs to be interpreted with caution. We propose using an estimand that is new for this context—the causal risk ratio, which has more transparent interpretation and requires weaker identification assumptions. We demonstrate this through a reanalysis of the NYPD Stop-and-Frisk dataset. Our reanalysis shows that the naive estimator that ignores the posttreatment selection in administrative records may severely underestimate the disparity in police violence between minorities and whites in these and similar data.

BackgroundPrior to the advent of Oncotype DX 21-gene recurrence score (oDX) assay, the National Comprehensive Cancer Network (NCCN) guideline supported omission of adjuvant chemotherapy in patients with ≤ 1 cm (T1b) hormone receptor-positive (HR +), human epidermal growth factor receptor 2 (HER2−) node tumors. However, around 30% of these patients would have an oDX recurrence score that warrants consideration of adjuvant chemotherapy. To clarify the potential benefit of oDX in these patients, we performed a retrospective analysis comparing clinical outcomes of women with T1a or T1b, N0 HR + HER2− according to performance of oDX.Patients and MethodsAfter receiving institutional review board (IRB) approval, an institutional database was queried to identify patients with HR + HER2− ≤ T1bN0 tumors (n = 2307) diagnosed between 2009 and 2018. Patients were further stratified by recurrence score (RS) defined as low (< 18), intermediate (18–30), or high (> 30). Log-rank, Kaplan–Meier, and inverse probability of treatment weighting (IPW) analyses were used to compare disease-free survival (DFS) and overall survival (OS) across groups.ResultsPerformance of oDX (n = 1149, 49.8%) was associated with larger tumors, younger age, and White race. On univariate analysis, performance of oDX was associated with improved OS (P < 0.01). On multivariate IPW analysis, performance of oDX lengthened DFS by an average of 16.5 months, while OS was similar between groups (P < 0.01 and P = 0.73). The improved DFS was mainly driven by those with tumors ≥ T1b.ConclusionsOverall, outcomes were excellent regardless of oDX testing. Performance of oDX testing was associated with improved DFS in patients with tumors ≥ T1b. Our results support routine use of oDX testing in patients with tumors ≥ T1b.

Emergency general surgery (EGS), a heterogeneous field of over three million admissions in the United States every year, encompasses both operative and non-operative management. 1 Emergency operations have complication rates as high as 50 % and a higher risk of mortality than elective procedures. 1,2 In recent years, literature has increasingly focused on providing data for operative versus nonoperative outcomes in the EGS population who are in clinical equipoise. 3,4 Operative treatment decisions become even more complex when considering a vulnerable population like those with serious mental illness (SMI). [...]we did not perform subgroup analyses by SMI diagnosis; however, a recent meta-analysis comparing surgical outcomes among SMI and non-SMI patients found length of stay was notably longer for patients with schizophrenia despite no difference in in-hospital or 30-day mortality when comparing outcomes within subgroups of patients with depression, anxiety, or schizophrenia. 12 Future research should further explore patient-centered outcomes and the specific factors influencing surgical success among SMI patients. [...]evidence emerges, our findings provide a data-driven foundation to support tailored, condition-specific surgical decisions in this potentially vulnerable population. Funding This research was supported by the Leonard Davis Institute Medical Student Health Services and Policy Research Summer Fellowship Program and the National Institute on Aging of the National Institutes of Health ( R01AG060612).

Pretreatment selection or censoring (\"selection on treatment\") can occur when two treatment levels are compared ignoring the third option of neither treatment, in \"censoring by death\" settings where treatment is only defined for those who survive long enough to receive it, or in general in studies where the treatment is only defined for a subset of the population. Unfortunately, the standard instrumental variable (IV) estimand is not defined in the presence of such selection, so we consider estimating a new survivor-complier causal effect. Although this effect is generally not identified under standard IV assumptions, it is possible to construct sharp bounds. We derive these bounds and give a corresponding data-driven sensitivity analysis, along with nonparametric yet efficient estimation methods. Importantly, our approach allows for high-dimensional confounding adjustment, and valid inference even after employing machine learning. Incorporating covariates can tighten bounds dramatically, especially when they are strong predictors of the selection process. We apply the methods in a UK cohort study of critical care patients to examine the mortality effects of prompt admission to the intensive care unit, using ICU bed availability as an instrument. Supplementary materials for this article are available online.