Volume 7, Issue 1

A benefit of randomized experiments is that covariate distributions of treatment and control groups are balanced on average, resulting in simple unbiased estimators for treatment effects. However, it is possible that a particular randomization yields covariate imbalances that researchers want to address in the analysis stage through adjustment or other methods. Here we present a randomization test that conditions on covariate balance by only considering treatment assignments that are similar to the observed one in terms of covariate balance. Previous conditional randomization tests have only allowed for categorical covariates, while our randomization test allows for any type of covariate. Through extensive simulation studies, we find that our conditional randomization test is more powerful than unconditional randomization tests and other conditional tests. Furthermore, we find that our conditional randomization test is valid (1) unconditionally across levels of covariate balance, and (2) conditional on particular levels of covariate balance. Meanwhile, unconditional randomization tests are valid for (1) but not (2). Finally, we find that our conditional randomization test is similar to a randomization test that uses a model-adjusted test statistic.

A key issue in the analysis of traffic accidents is to quantify the effectiveness of a given evasive action taken by a driver to avoid crashing. Since 1977, the widely accepted definition for this effectiveness measure, which is called traffic conflict, has been “the risk of a collision if the driver movement remains unchanged.” Although the definition is expressed counterfactually, the full power of counterfactual analysis was not utilized. In this paper, we propose a counterfactual measure of traffic conflict called Counterfactual Based Conflict (CBC). The CBC is interpreted as the probability that a driver avoided a crash actually by taking an evasive action in the counterfactual situation in which the crash would have occurred if he/she had not taken an evasive action and the crash would not have occurred if he/she had taken an evasive action. The CBC captures realistic aspects of the traffic situation, and lends itself to modern causal analysis. In addition, we provide some of identification conditions for the CBC. Furthermore, we formulate bounds on the CBC when the proposed identification conditions are violated. Finally, through an application of the CBC to the 100-Car Naturalistic Driving Study, we discuss the usefulness and limitations of the proposed measure.

Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test scales at least quadratically with sample size. We therefore devise two relaxations called the Randomized Conditional Independence Test (RCIT) and the Randomized conditional Correlation Test (RCoT) which both approximate KCIT by utilizing random Fourier features. In practice, both of the proposed tests scale linearly with sample size and return accurate p-values much faster than KCIT in the large sample size context. CCD algorithms run with RCIT or RCoT also return graphs at least as accurate as the same algorithms run with KCIT but with large reductions in run time.

Mann–Whitney-type causal effects are clinically relevant, easy to interpret, and readily applicable to a wide range of study settings. This article considers estimation of such effects when the outcome variable is a survival time subject to right censoring. We derive and discuss several methods: an outcome regression method based on a regression model for the survival outcome, an inverse probability weighting method based on models for treatment assignment and censoring, and two doubly robust methods that involve both types of models and that remain valid under correct specification of the outcome model or the other two models. The methods are compared in a simulation study and applied to an observational study of hospitalized pneumonia.

Often the research interest in causal inference is on the regression causal effect, which is the mean difference in the potential outcomes conditional on the covariates. In this paper, we use sufficient dimension reduction to estimate a lower dimensional linear combination of the covariates that is sufficient to model the regression causal effect. Compared with the existing applications of sufficient dimension reduction in causal inference, our approaches are more efficient in reducing the dimensionality of covariates, and avoid estimating the individual outcome regressions. The proposed approaches can be used in three ways to assist modeling the regression causal effect: to conduct variable selection, to improve the estimation accuracy, and to detect the heterogeneity. Their usefulness are illustrated by both simulation studies and a real data example.

Although the concept of randomized assignment in order to control for extraneous confounding factors reaches back hundreds of years, the first empirical use appears to have been in an 1835 trial of homeopathic medicine. Throughout the 19 th century there was a growing awareness of the need for comparison groups, albeit often without the realization that randomization could be a clean method to achieve that goal. In the second and more crucial phase of this history, four separate but related disciplines introduced randomized control trials within a few years of one another in the 1920s: agricultural science; clinical medicine; educational psychology; and social policy (specifically political science). This brought increasing rigor to fields that were focusing more on causal relationships. In a third phase, the 1950s through 1970s saw a surge of interest in more applied randomized experiments in economics and elsewhere – both in the lab and especially in the field.

We address the characterization of problems in which a consistent estimator exists in a union of two models, also termed as a doubly robust estimator. Such estimators are important in missing information, including causal inference problems. Existing characterizations, based on the semiparametric theory of projections, have seen sufficient progress, but can still leave one’s understanding less than satisfied as to when and especially why such estimation works. We explore here a different, explanatory characterization – an exegesis based on logical operators. We show that double robustness exists if and only if we can produce consistent estimators for each contributing model based on an “AND” estimator, i. e., an estimator whose consistency generally needs both models to be correct. We show how this characterization explains double robustness through falsifiability.

Providing terminally ill patients with access to experimental treatments, as allowed by recent “right to try” laws and “expanded access” programs, poses a variety of ethical questions. While practitioners and investigators may assume it is impossible to learn the effects of these treatment without randomized trials, this paper describes a simple tool to estimate the effects of these experimental treatments on those who take them, despite the problem of selection into treatment, and without assumptions about the selection process. The key assumption is that the average outcome, such as survival, would remain stable over time in the absence of the new treatment. Such an assumption is unprovable, but can often be credibly judged by reference to historical data and by experts familiar with the disease and its treatment. Further, where this assumption may be violated, the result can be adjusted to account for a hypothesized change in the non-treatment outcome, or to conduct a sensitivity analysis. The method is simple to understand and implement, requiring just four numbers to form a point estimate. Such an approach can be used not only to learn which experimental treatments are promising, but also to warn us when treatments are actually harmful – especially when they might otherwise appear to be beneficial, as illustrated by example here. While this note focuses on experimental medical treatments as a motivating case, more generally this approach can be employed where a new treatment becomes available or has a large increase in uptake, where selection bias is a concern, and where an assumption on the change in average non-treatment outcome over time can credibly be imposed.

This paper provides empirical interpretation of the do(x)do(x) operator when applied to non-manipulable variables such as race, obesity, or cholesterol level. We view do(x)do(x) as an ideal intervention that provides valuable information on the effects of manipulable variables and is thus empirically testable. We draw parallels between this interpretation and ways of enabling machines to learn effects of untried actions from those tried. We end with the conclusion that researchers need not distinguish manipulable from non-manipulable variables; both types are equally eligible to receive the do(x)do(x) operator and to produce useful information for decision makers.