Volume 5, Issue 2 -

In causal mediation analysis, nonparametric identification of the natural indirect effect typically relies on, in addition to no unobserved pre-exposure confounding, fundamental assumptions of (i) so-called “cross-world-counterfactuals” independence and (ii) no exposure-induced confounding. When the mediator is binary, bounds for partial identification have been given when neither assumption is made, or alternatively when assuming only (ii). We extend existing bounds to the case of a polytomous mediator, and provide bounds for the case assuming only (i). We apply these bounds to data from the Harvard PEPFAR program in Nigeria, where we evaluate the extent to which the effects of antiretroviral therapy on virological failure are mediated by a patient’s adherence, and show that inference on this effect is somewhat sensitive to model assumptions.

Abstract: In this article, we carefully examine two important implementation issues when estimating propensity scores using generalized boosted models (GBM), a promising machine learning technique. First, we examine which of the following methods for tuning GBM lead to better covariate balance and inferences about causal effects: pursuing covariate balance between the treatment groups or tuning the propensity score model on the basis of a model fit criterion. Second, we examine how well GBM can handle irrelevant covariates that are included in the estimation model. We find that chasing balance rather than model fit when estimating propensity scores yielded better covariate balance and more accurate treatment effect estimates. Additionally, we find that adding irrelevant covariates to GBM increased imbalance and bias in the treatment effects. The findings from this paper have useful implications for other work focused on improving methods for estimating propensity scores.

We provide a scheme for inferring causal relations from uncontrolled statistical data based on tools from computational algebraic geometry, in particular, the computation of Groebner bases. We focus on causal structures containing just two observed variables, each of which is binary. We consider the consequences of imposing different restrictions on the number and cardinality of latent variables and of assuming different functional dependences of the observed variables on the latent ones (in particular, the noise need not be additive). We provide an inductive scheme for classifying functional causal structures into distinct observational equivalence classes. For each observational equivalence class, we provide a procedure for deriving constraints on the joint distribution that are necessary and sufficient conditions for it to arise from a model in that class. We also demonstrate how this sort of approach provides a means of determining which causal parameters are identifiable and how to solve for these. Prospects for expanding the scope of our scheme, in particular to the problem of quantum causal inference, are also discussed.

We address several questions relating to the use of standard regression and Structural Nested Mean Model (SNMM) approach (e. g., Ten Have et al. 2007) to analyze post-randomization effect modifiers of the intent-to-treat effect of a randomized intervention on a subsequent outcome, which has not been well examined. We show through simulations that the SNMM performs better with respect to bias of estimates of the intervention and interaction effects than does the corresponding standard interaction approach when the baseline intervention is randomized and the post-randomization factors are subject to confounding, and even when there is no association between the intervention and effect modifier. However, causal inference under the SNMM makes untestable assumptions that the causal contrasts do not vary across observed levels of the intervention and post-randomization factor. In addition, the precision of the SNMM-based estimators depends on the effect of the randomized intervention on the post-randomization factor varying across baseline covariate combinations. These issues and methods are illustrated with the application of the standard and causal methods to a randomized cognitive therapy (CT) trial, for which there is a conceptual model of negative cognitive styles or distortions impacted by CT but then in turn modifying the effect of CT on subsequent suicide ideation and social problem solving outcomes.

Abstract: 1 In this paper, we study the effect of a time-varying exposure mediated by a time-varying intermediate variable. We consider general longitudinal settings, including survival outcomes. At a given time point, the exposure and mediator of interest are influenced by past covariates, mediators and exposures, and affect future covariates, mediators and exposures. Right censoring, if present, occurs in response to past history. To address the challenges in mediation analysis that are unique to these settings, we propose a formulation in terms of random interventions based on conditional distributions for the mediator. This formulation, in particular, allows for well-defined natural direct and indirect effects in the survival setting, and natural decomposition of the standard total effect. Upon establishing identifiability and the corresponding statistical estimands, we derive the efficient influence curves and establish their robustness properties. Applying Targeted Maximum Likelihood Estimation, we use these efficient influence curves to construct multiply robust and efficient estimators. We also present an inverse probability weighted estimator and a nested non-targeted substitution estimator for these parameters.

Prevented and preventable fractions have been widely used in medical science to evaluate the proportion of new diseases that can be averted by a protective exposure. However, most existing formulas used in practical situations cannot be interpreted as proportions without any further assumptions because they are obtained according to different target populations and may fall outside the range [0.000,1.000]$[0.000,1.000]$. To solve this problem, this paper proposes counterfactual-based prevented and preventable proportions. When both causal effects and observed probabilities are available, we show that the proposed measures are identifiable under the negative monotonicity assumption. Additionally, when the negative monotonicity assumption is violated, we formulate the bounds on the proposed measures. We also show that negative monotonicity together with exogeneity induces equivalence between the proposed measures and existing measures.

There are two general views in causal analysis of experimental data: the super population view that the units are an independent sample from some hypothetical infinite population, and the finite population view that the potential outcomes of the experimental units are fixed and the randomness comes solely from the treatment assignment. These two views differs conceptually and mathematically, resulting in different sampling variances of the usual difference-in-means estimator of the average causal effect. Practically, however, these two views result in identical variance estimators. By recalling a variance decomposition and exploiting a completeness-type argument, we establish a connection between these two views in completely randomized experiments. This alternative formulation could serve as a template for bridging finite and super population causal inference in other scenarios.

The structural interpretation of counterfactuals as formulated in Balke and Pearl (1994a,b) [1, 2] excludes disjunctive conditionals, such as “had X$X$ been x1 or x2$x_1~\mbox{or}~x_2$,” as well as disjunctive actions such as do(X=x1 or X=x2)$do(X=x_1~\mbox{or}~X=x_2)$. In contrast, the closest-world interpretation of counterfactuals (e.g. Lewis (1973a) [3]) assigns truth values to all counterfactual sentences, regardless of the logical form of the antecedent. This paper leverages “imaging” – a process of “mass-shifting” among possible worlds, to define disjunction in structural counterfactuals. We show that every imaging operation can be given an interpretation in terms of a stochastic policy in which agents choose actions with certain probabilities. This mapping, from the metaphysical to the physical, allows us to assess whether metaphysically-inspired extensions of interventional theories are warranted in a given decision making situation.