The causal inference seminar series is co-sponsored by the Departments of Epidemiology and Biostatistics. Speakers will be drawn from the health sciences, social sciences and statistics, from faculty in the Boston area and more broadly. The series will include both more theoretical sessions oriented towards methods development and more applied sessions which examine and critically evaluate what methods from causal inference contribute to science. All students and faculty are invited to attend and participate.

Vanessa Didelez, Ph.D.
Senior Lecturer in Statistics, Department of Mathematics, University of Bristol

"Inference under Sampling Selection"

ABSTRACT: Statistical inference from data that have been collected such that the sampling depends on some of the variables of interest can be problematic, especially when it depends on the outcome of interest. It is for example well known that case-control studies only allow estimation of odds-ratios. Other examples where the selection into the sample may hinder inference are time-to-event studies when inclusion requires subjects to be in a specific state, or studies with drop-out. By modeling the sampling process explicitly through an indicator variable, we formulate conditions that allow inference on the desired target, e.g. a causal effect. Our conditions essentially exploit collapsibility and can be regarded as 'non-parametric' in the sense that they are formulated in terms of (conditional) independencies without making use of particular parametric structures. They can therefore easily be characterized through graphical models, but inference is limited to (causal) odds-ratios or statistical tests for the presence of a (causal) association. Our approach therefore provides an important first step of an analysis, facilitating the structuring and reasoning about the problem of sampling selection.

Teppei Yamamoto, Ph.D.
Assistant Professor, Department of Political Science, Massachusetts Institute of Technology

"Sensitivity Analysis for Causal Mediation Effects under Alternative Exogeneity Assumptions"

ABSTRACT: It has been shown that the average causal mediation effects may not be identifiable even when both the treatment and mediator of interest are assumed to be exogenous. In this paper, we develop new sensitivity analyses for causal mediation effects under the exogeneity of treatment and mediator. The proposed sensitivity analysis is applicable to inference based on linear models under two alternative exogeneity assumptions that exist in the literature; (1) the parallel design of Imai et al. (2009), where two randomized experiments are conducted in parallel with one randomizing the treatment alone and the other randomizing both the treatment and mediator, and (2) the fully randomized causally interpretable structural tree graph (FRCISTG) of Robins (1986, 2003), where the mediator of interest is assumed to be exogenous conditional on the treatment and a set of alternative mediators that confound the mediator-outcome relationship.

Fabrizia Mealli, Ph.D.
Professor, Department of Statistics, University of Florence

"Using Secondary Outcomes and Covariates to Sharpen Inference in Randomized Experiments with Noncompliance"

ABSTRACT: Restrictions implied by the randomization of treatment assignment on the joint distribution of a primary outcome and an auxiliary variable are used to tighten nonparametric bounds for intention-to-treat eects on the primary outcome for some latent subpopulations, without requiring the exclusion restriction assumption of the assignment. The auxiliary variable can be a secondary outcome or a covariate, while the subpopulations are defined by the values of the potential treatment status under each value of the assignment. The derived bounds can be used to detect violations of the exclusion restriction and the magnitude of these violations in instrumental variables settings. It is shown that the reduced width of the bounds depends on the the strength of the association of the auxiliary variable with the primary outcome and the compliance status. We also show how the setup we consider oers new identifying assumptions of intention-to-treat eects without the exclusion restriction. The use of the bounds is illustrated in two real data examples of a social job training experiment and a medical randomized encouragement study.

Raluca Ionescu-Ittu, Ph.D.
Research Fellow, Department of Society, Human Development, and Health, Harvard School of Public Health

"Inference Using an Exogenous Policy: Choice of Methods and Challenges"

ABSTRACT: Policies implemented at a given time at community, provincial or country level are natural experiments that can be used to answer several interesting research questions: to estimate the causal effect of the policy on the outcome, to estimate the causal effect of an exposure affected by the policy on the outcome or to identify potential effect modifiers for the effect of the policy/exposure on the outcome. In this presentation we use as a motivating example the 2006 Canadian child benefit policy that introduced in year 2006 a universal benefit of $100/month per child <6 years of age. The presentation has two parts. In the first part, we compare and discuss the challenges and opportunities offered by two methods that rely on the use of an exogenous variable: the instrumental variable (IV) and the difference-in-difference (DID) method. We discuss and compare the structural assumptions, interpretation of estimates and sources of bias for the DID and IV estimators and show that the decision between these methods is driven by several factors including: (1) whether we are interested in the effect of the policy or the effect of the exposure; (2) whether there are any secular trends in the outcome and (3) the take-up rate of the policy. In the presence of both secular trends in the outcome and low policy take-up, the effect of the exposure on the outcome can be estimated by a modified Wald IV estimator corresponding to the ratio of two DID estimates: the DID estimate on the outcome divided by the DID estimate on the mediator. We show this estimator is equivalent to an IV estimate derived using the interaction between time (pre-post policy implementation) and eligibility for the policy benefit as the instrument and the mediator as an endogenous variable. In the second part, we present a 2-stage least squares IV model that incorporates statistical interactions between the exposure and an effect modifier and use simulations to illustrate how statistical power to detect EMM in IV and the accuracy of the IV-based estimates vary across instrument strength, EMM strength and sample size. Because (1) IV estimates have inflated variance and (2) interaction tests have low power, the IV models with EMM are subject to a dual loss of power, which may limit the applicability of IV methods for detection of EMM in real-life studies.

Karim Chalak, Ph.D.
Assistant Professor, Department of Economics, Boston College

"Causality, Conditional Independence, and Graphical Separation in Settable Systems"

ABSTRACT: We study the connections between causal relations and conditional independence within the settable systems extension of the Pearl Causal Model. Our analysis clearly distinguishes between causal notions and probabilistic notions and does not formally rely on graphical representations. We provide definitions in terms of functional dependence for direct, indirect, and total causality as well as for indirect causality via and exclusive of a set of variables. We apply these notions to formally connect causal and probabilistic conditions for conditional dependence among random vectors of interest in structural systems. We state and prove the conditional Reichenbach principle of common cause, obtaining the classical Reichenbach principle as a corollary. Finally, we apply our approach to study notions of graphical separation, such as d-separation and D-separation in the artificial intelligence and machine learning literature.

Michael Rosenblum, Ph.D.
Assistant Professor, Department of Biostatistics, Johns Hopkins School of Public Health

"Confidence Intervals for the Selected Population in Randomized Trials That Adapt the Population Enrolled"

ABSTRACT: It is a challenge to design randomized trials when it is suspected that a treatment may benefit only certain subsets of the target population. In such situations, trial designs have been proposed that modify the population enrolled based on an interim analysis, in a preplanned manner. For example, if there is early evidence that the treatment only benefits a certain subset of the population, enrollment may then be restricted to this subset. At the end of such a trial, it is desirable to draw inferences about the selected population. We focus on constructing confidence intervals for the average treatment effect in the selected population. Confidence interval methods that fail to account for the adaptive nature of the design may fail to have the desired coverage probability. We provide a new procedure for constructing confidence intervals having at least 95% coverage probability, uniformly over a large class of possible data generating distributions. We prove an optimality property for our confidence interval procedure in terms of minimizing the average confidence interval widths.