Volume 8, Issue 1

An intervention may have an effect on units other than those to which it was administered. This phenomenon is called interference and it usually goes unmodeled. In this paper, we propose to combine Lauritzen-Wermuth-Frydenberg and Andersson-Madigan-Perlman chain graphs to create a new class of causal models that can represent both interference and non-interference relationships for Gaussian distributions. Specifically, we define the new class of models, introduce global and local and pairwise Markov properties for them, and prove their equivalence. We also propose an algorithm for maximum likelihood parameter estimation for the new models, and report experimental results. Finally, we show how to compute the effects of interventions in the new models.

Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed correlations. A particularly challenging setting for assessing causal compatibility is in the presence of partial information; i.e. when some of the variables are hidden/latent. This paper introduces the possible worlds framework as a method for deciding causal compatibility in this difficult setting. We define a graphical object called a possible worlds diagram, which compactly depicts the set of all possible observations. From this construction, we demonstrate explicitly, using several examples, how to prove causal incompatibility. In fact, we use these constructions to prove causal incompatibility where no other techniques have been able to. Moreover, we prove that the possible worlds framework can be adapted to provide a complete solution to the possibilistic causal compatibility problem. Even more, we also discuss how to exploit graphical symmetries and cross-world consistency constraints in order to implement a hierarchy of necessary compatibility tests that we prove converges to sufficiency.

While the HVTN 505 trial showed no overall efficacy of the tested vaccine to prevent HIV infection over placebo, markers measuring immune response to vaccination were strongly correlated with infection. This finding generated the hypothesis that some marker-defined vaccinated subgroups were partially protected whereas others had their risk increased. This hypothesis can be assessed using the principal stratification framework (Frangakis and Rubin, 2002) for studying treatment effect modification by an intermediate response variable, using methods in the sub-field of principal surrogate (PS) analysis that studies multiple principal strata. Unfortunately, available methods for PS analysis require an augmented study design not available in HVTN 505, and make untestable structural risk assumptions, motivating a need for more robust PS methods. Fortunately, another sub-field of principal stratification, survivor average causal effect (SACE) analysis (Rubin, 2006) – which studies effects in a single principal stratum – provides many methods not requiring an augmented design and making fewer assumptions. We show how, for a binary intermediate response variable, methods developed for SACE analysis can be adapted to PS analysis, providing new and more robust PS methods. Application to HVTN 505 supports that the vaccine partially protected individuals with vaccine-induced T-cells expressing certain combinations of functions.

The causal compatibility question asks whether a given causal structure graph — possibly involving latent variables — constitutes a genuinely plausible causal explanation for a given probability distribution over the graph’s observed categorical variables. Algorithms predicated on merely necessary constraints for causal compatibility typically suffer from false negatives, i.e. they admit incompatible distributions as apparently compatible with the given graph. In 10.1515/jci-2017-0020, one of us introduced the inflation technique for formulating useful relaxations of the causal compatibility problem in terms of linear programming. In this work, we develop a formal hierarchy of such causal compatibility relaxations. We prove that inflation is asymptotically tight, i.e., that the hierarchy converges to a zero-error test for causal compatibility. In this sense, the inflation technique fulfills a longstanding desideratum in the field of causal inference. We quantify the rate of convergence by showing that any distribution which passes the n th -order inflation test must be On− 1/2$\begin{array}{} \displaystyle {O}{\left(n^{{{-}{1}}/{2}}\right)} \end{array}$-close in Euclidean norm to some distribution genuinely compatible with the given causal structure. Furthermore, we show that for many causal structures, the (unrelaxed) causal compatibility problem is faithfully formulated already by either the first or second order inflation test.

There has been increasing interest in recent years in the development of approaches to estimate causal effects when the number of potential confounders is prohibitively large. This growth in interest has led to a number of potential estimators one could use in this setting. Each of these estimators has different operating characteristics, and it is unlikely that one estimator will outperform all others across all possible scenarios. Coupling this with the fact that an analyst can never know which approach is best for their particular data, we propose a synthetic estimator that averages over a set of candidate estimators. Averaging is widely used in statistics for problems such as prediction, where there are many possible models, and averaging can improve performance and increase robustness to using incorrect models. We show that these ideas carry over into the estimation of causal effects in high-dimensional scenarios. We show theoretically that averaging provides robustness against choosing a bad model, and show empirically via simulation that the averaging estimator performs quite well, and in most cases nearly as well as the best among all possible candidate estimators. Finally, we illustrate these ideas in an environmental wide association study and see that averaging provides the largest benefit in the more difficult scenarios that have large numbers of confounders.

Randomized control trials (RCTs) are the gold standard for estimating causal effects, but often use samples that are non-representative of the actual population of interest. We propose a reweighting method for estimating population average treatment effects in settings with noncompliance. Simulations show the proposed compliance-adjusted population estimator outperforms its unadjusted counterpart when compliance is relatively low and can be predicted by observed covariates. We apply the method to evaluate the effect of Medicaid coverage on health care use for a target population of adults who may benefit from expansions to the Medicaid program. We draw RCT data from the Oregon Health Insurance Experiment, where less than one-third of those randomly selected to receive Medicaid benefits actually enrolled.

Estimating the effect of a randomized treatment and the effect that is transmitted through a mediator is often complicated by treatment noncompliance. In literature, an instrumental variable (IV)-based method has been developed to study causal mediation effects in the presence of treatment noncompliance. Existing studies based on the IV-based method focus on identifying the mediated portion of the intention-to-treat effect, which relies on several identification assumptions. However, little attention has been given to assessing the sensitivity of the identification assumptions or mitigating the impact of violating these assumptions. This study proposes a two-stage joint modeling method for conducting causal mediation analysis in the presence of treatment noncompliance, in which modeling assumptions can be employed to decrease the sensitivity to violation of some identification assumptions. The use of a joint modeling method is also conducive to conducting sensitivity analyses to the violation of identification assumptions. We demonstrate our approach using the Jobs II data, in which the effect of job training on job seekers’ mental health is examined.

Suppose that we are interested in the average causal effect of a binary treatment on an outcome when this relationship is confounded by a binary confounder. Suppose that the confounder is unobserved but a nondifferential proxy of it is observed. We show that, under certain monotonicity assumption that is empirically verifiable, adjusting for the proxy produces a measure of the effect that is between the unadjusted and the true measures.

This paper elaborates on administrative sorting, a threat to internal validity that has been overlooked in the regression discontinuity (RD) literature. Variation in treatment assignment near the threshold may still not be as good as random even when individuals are unable to precisely manipulate the running variable. This can be the case when administrative procedures, beyond individuals’ control and knowledge, affect their position near the threshold non-randomly. If administrative sorting is not recognized it can be mistaken as manipulation, preventing fixing the running variable and leading to discarding viable RD research designs.

In Instrumental Variables (IV) estimation, the effect of an instrument on an endogenous variable may vary across the sample. In this case, IV produces a local average treatment effect (LATE), and if monotonicity does not hold, then no effect of interest is identified. In this paper, I calculate the weighted average of treatment effects that is identified under general first-stage effect heterogeneity, which is generally not the average treatment effect among those affected by the instrument. I then describe a simple set of data-driven approaches to modeling variation in the effect of the instrument. These approaches identify a Super-Local Average Treatment Effect (SLATE) that weights treatment effects by the corresponding instrument effect more heavily than LATE. Even when first-stage heterogeneity is poorly modeled, these approaches considerably reduce the impact of small-sample bias compared to standard IV and unbiased weak-instrument IV methods, and can also make results more robust to violations of monotonicity. In application to a published study with a strong instrument, the preferred approach reduces error by about 19% in small ( N ≈ 1, 000) subsamples, and by about 13% in larger ( N ≈ 33, 000) subsamples.

In some applications, researchers using the synthetic control method (SCM) to evaluate the effect of a policy may struggle to determine whether they have identified a “good match” between the control group and treated group. In this paper, we demonstrate the utility of the mean and maximum Absolute Standardized Mean Difference (ASMD) as a test of balance between a synthetic control unit and treated unit, and provide guidance on what constitutes a poor fit when using a synthetic control. We explore and compare other potential metrics using a simulation study. We provide an application of our proposed balance metric to the 2013 Los Angeles (LA) Firearm Study [9]. Using Uniform Crime Report data, we apply the SCM to obtain a counterfactual for the LA firearm-related crime rate based on a weighted combination of control units in a donor pool of cities. We use this counterfactual to estimate the effect of the LA Firearm Study intervention and explore the impact of changing the donor pool and pre-intervention duration period on resulting matches and estimated effects. We demonstrate how decision-making about the quality of a synthetic control can be improved by using ASMD. The mean and max ASMD clearly differentiate between poor matches and good matches. Researchers need better guidance on what is a meaningful imbalance between synthetic control and treated groups. In addition to the use of gap plots, the proposed balance metric can provide an objective way of determining fit.

Unmeasured confounding is one of the most important threats to the validity of observational studies. In this paper we scrutinize a recently proposed sensitivity analysis for unmeasured confounding. The analysis requires specification of two parameters, loosely defined as the maximal strength of association that an unmeasured confounder may have with the exposure and with the outcome, respectively. The E-value is defined as the strength of association that the confounder must have with the exposure and the outcome, to fully explain away an observed exposure-outcome association. We derive the feasible region of the sensitivity analysis parameters, and we show that the bounds produced by the sensitivity analysis are not always sharp. We finally establish a region in which the bounds are guaranteed to be sharp, and we discuss the implications of this sharp region for the interpretation of the E-value. We illustrate the theory with a real data example and a simulation.

The problem of missingness in observational data is ubiquitous. When the confounders are missing at random, multiple imputation is commonly used; however, the method requires congeniality conditions for valid inferences, which may not be satisfied when estimating average causal treatment effects. Alternatively, fractional imputation, proposed by Kim 2011, has been implemented to handling missing values in regression context. In this article, we develop fractional imputation methods for estimating the average treatment effects with confounders missing at random. We show that the fractional imputation estimator of the average treatment effect is asymptotically normal, which permits a consistent variance estimate. Via simulation study, we compare fractional imputation’s accuracy and precision with that of multiple imputation.

This paper discusses identification and estimation of causal intensive margin effects. The causal intensive margin effect is defined as the treatment effect on the outcome of individuals with a positive outcome irrespective of whether they are treated or not, and is of interest for outcomes with corner solutions. The main issue is to deal with a potential selection problem that arises when conditioning on positive outcomes. We propose using difference-in-difference methods - conditional on positive outcomes - to estimate causal intensive margin effects. We derive sufficient conditions under which the difference-in-difference estimator identifies the causal intensive margin effect. We apply the methodology to estimate the causal intensive margin effect of reaching the full retirement age on working hours.

Direct effects in mediation analysis quantify the effect of an exposure on an outcome not mediated by a certain intermediate. When estimating direct effects through measured data, misclassification may occur in the outcomes, exposures, and mediators. In mediation analysis, any such misclassification may lead to biased estimates in the direct effects. Basing on the conditional dependence between the mismeasured variable and other variables given the true variable, misclassification mechanisms can be divided into non-differential misclassification and differential misclassification. In this article, several scenarios of differential misclassification will be discussed and sensitivity analysis results on direct effects will be derived for those eligible scenarios. According to our findings, the estimated direct effects are not necessarily biased in intuitively predictable directions when the misclassification is differential. The bounds of the true effects are functions of measured effects and sensitivity parameters. An example from the 2018 NCHS data will illustrate how to conduct sensitivity analyses with our results on misclassified outcomes, gestational hypertension and eclampsia, when the exposure is Hispanic women versus non-Hispanic White women and the mediator is weights gain during pregnancy.

Doubly robust (DR) estimators are an important class of statistics derived from a theory of semiparametric efficiency. They have become a popular tool in causal inference, including applications to dynamic treatment regimes. The doubly robust estimators for the mean response to a dynamic treatment regime may be conceived through the augmented inverse probability weighted (AIPW) estimating function, defined as the sum of the inverse probability weighted (IPW) estimating function and an augmentation term. The IPW estimating function of the causal estimand via marginal structural model is defined as the complete-case score function for those subjects whose treatment sequence is consistent with the dynamic regime in question divided by the probability of observing the treatment sequence given the subject's treatment and covariate histories. The augmentation term is derived by projecting the IPW estimating function onto the nuisance tangent space and has mean-zero under the truth. The IPW estimator of the causal estimand is consistent if (i) the treatment assignment mechanism is correctly modeled and the AIPW estimator is consistent if either (i) is true or (ii) nested functions of intermediate and final outcomes are correctly modeled. Hence, the AIPW estimator is doubly robust and, moreover, the AIPW is semiparametric efficient if both (i) and (ii) are true simultaneously. Unfortunately, DR estimators can be inferior when either (i) or (ii) is true and the other false. In this case, the misspecified parts of the model can have a detrimental effect on the variance of the DR estimator. We propose an improved DR estimator of causal estimand in dynamic treatment regimes through a technique originally developed by [4] which aims to mitigate the ill-effects of model misspecification through a constrained optimization. In addition to solving a doubly robust system of equations, the improved DR estimator simultaneously minimizes the asymptotic variance of the estimator under a correctly specified treatment assignment mechanism but misspecification of intermediate and final outcome models. We illustrate the desirable operating characteristics of the estimator through Monte Carlo studies and apply the methods to data from a randomized study of integrilin therapy for patients undergoing coronary stent implantation. The methods proposed here are new and may be used to further improve personalized medicine, in general.