scholarly journals Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds

2018 ◽  
Vol 43 (5) ◽  
pp. 540-567 ◽  
Author(s):  
Jiannan Lu ◽  
Peng Ding ◽  
Tirthankar Dasgupta
Keyword(s):  
Causal Effect ◽  
Real Life ◽  
Causal Effects ◽  
Potential Outcomes ◽  
Randomized Experiments ◽  
Sharp Bounds ◽  
Average Causal Effect ◽  
Behavioral Studies ◽  
And Control ◽  
Potential Outcomes Framework

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control. However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the potential outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes and is directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.

scholarly journals Bridging Finite and Super Population Causal Inference

2017 ◽  
Vol 5 (2) ◽  
Author(s):  
Peng Ding ◽  
Xinran Li ◽  
Luke W. Miratrix
Keyword(s):  
Causal Inference ◽  
Finite Population ◽  
Causal Effect ◽  
Causal Analysis ◽  
Potential Outcomes ◽  
Alternative Formulation ◽  
Randomized Experiments ◽  
Infinite Population ◽  
Variance Estimators ◽  
Average Causal Effect

AbstractThere 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.

scholarly journals Bounds on treatment effects in regression discontinuity designs with a manipulated running variable

2020 ◽  
Vol 11 (3) ◽  
pp. 839-870 ◽  
Author(s):  
François Gerard ◽  
Miikka Rokkanen ◽  
Christoph Rothe
Keyword(s):  
Unemployment Insurance ◽  
General Model ◽  
Regression Discontinuity ◽  
Causal Effects ◽  
Potential Outcomes ◽  
Binary Decision ◽  
Sharp Bounds ◽  
Wide Range ◽  
Regression Discontinuity Designs ◽  
Disincentive Effect

The key assumption in regression discontinuity analysis is that the distribution of potential outcomes varies smoothly with the running variable around the cutoff. In many empirical contexts, however, this assumption is not credible; and the running variable is said to be manipulated in this case. In this paper, we show that while causal effects are not point identified under manipulation, one can derive sharp bounds under a general model that covers a wide range of empirical patterns. The extent of manipulation, which determines the width of the bounds, is inferred from the data in our setup. Our approach therefore does not require making a binary decision regarding whether manipulation occurs or not, and can be used to deliver manipulation‐robust inference in settings where manipulation is conceivable, but not obvious from the data. We use our methods to study the disincentive effect of unemployment insurance on (formal) reemployment in Brazil, and show that our bounds remain informative, despite the fact that manipulation has a sizable effect on our estimates of causal parameters.

11. Identification and Estimation of Causal Effects with Time-Varying Treatments and Time-Varying Outcomes

2007 ◽  
Vol 37 (1) ◽  
pp. 393-434 ◽  
Author(s):  
Jennie E. Brand ◽  
Yu Xie
Keyword(s):  
Employment Status ◽  
Causal Effect ◽  
Causal Effects ◽  
Potential Outcomes ◽  
Time Varying ◽  
Potential Outcome ◽  
Units Of Analysis ◽  
Wisconsin Longitudinal Study ◽  
Time Periods ◽  
Causal Variable

We develop an approach to identifying and estimating causal effects in longitudinal settings with time-varying treatments and time-varying outcomes. The classic potential outcome approach to causal inference generally involves two time periods: units of analysis are exposed to one of two possible values of the causal variable, treatment or control, at a given point in time, and values for an outcome are assessed some time subsequent to exposure. In this paper, we develop a potential outcome approach for longitudinal situations in which both exposure to treatment and the effects of treatment are time-varying. In this longitudinal setting, the research interest centers not on only two potential outcomes, but on a whole matrix of potential outcomes, requiring a complicated conceptualization of many potential counterfactuals. Motivated by sociological applications, we develop a simplification scheme—a weighted composite causal effect that allows identification and estimation of effects with a number of possible solutions. Our approach is illustrated via an analysis of the effects of disability on subsequent employment status using panel data from the Wisconsin Longitudinal Study.

scholarly journals Causal inference under multiple versions of treatment

2013 ◽  
Vol 1 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Tyler J. VanderWeele ◽  
Miguel A. Hernan
Keyword(s):  
Causal Inference ◽  
Treatment Effect ◽  
Indirect Effects ◽  
Causal Effect ◽  
Potential Outcomes ◽  
Direct And Indirect Effects ◽  
Treatment Variable ◽  
Effect Of Treatment ◽  
New Treatment ◽  
Potential Outcomes Framework

Abstract: In this article, we discuss causal inference when there are multiple versions of treatment. The potential outcomes framework, as articulated by Rubin, makes an assumption of no multiple versions of treatment, and here we discuss an extension of this potential outcomes framework to accommodate causal inference under violations of this assumption. A variety of examples are discussed in which the assumption may be violated. Identification results are provided for the overall treatment effect and the effect of treatment on the treated when multiple versions of treatment are present and also for the causal effect comparing a version of one treatment to some other version of the same or a different treatment. Further identification and interpretative results are given for cases in which the version precedes the treatment as when an underlying treatment variable is coarsened or dichotomized to create a new treatment variable for which there are effectively “multiple versions”. Results are also given for effects defined by setting the version of treatment to a prespecified distribution. Some of the identification results bear resemblance to identification results in the literature on direct and indirect effects. We describe some settings in which ignoring multiple versions of treatment, even when present, will not lead to incorrect inferences.

scholarly journals Data-Adaptive Causal Effects and Superefficiency

2016 ◽  
Vol 4 (2) ◽  
Author(s):  
Peter M. Aronow
Keyword(s):  
Causal Inference ◽  
Empirical Distribution ◽  
Causal Effect ◽  
Short Note ◽  
Causal Effects ◽  
Asymptotically Normal ◽  
Average Causal Effect ◽  
Population Average ◽  
Data Adaptive ◽  
Local Average

AbstractRecent approaches in causal inference have proposed estimating average causal effects that are local to some subpopulation, often for reasons of efficiency. These inferential targets are sometimes data-adaptive, in that they are dependent on the empirical distribution of the data. In this short note, we show that if researchers are willing to adapt the inferential target on the basis of efficiency, then extraordinary gains in precision can potentially be obtained. Specifically, when causal effects are heterogeneous, any asymptotically normal and root-$n$ consistent estimator of the population average causal effect is superefficient for a data-adaptive local average causal effect.

scholarly journals Emulating Target Trials to Improve Causal Inference from Agent-Based Models

2021 ◽  
Author(s):  
Eleanor J Murray ◽  
Brandon D L Marshall ◽  
Ashley L Buchanan
Keyword(s):  
Causal Inference ◽  
Disease Transmission ◽  
Causal Effect ◽  
Potential Outcomes ◽  
Emergent Properties ◽  
Target Trial ◽  
Agent Based Models ◽  
Agent Based ◽  
Effect Estimation ◽  
Potential Outcomes Framework

Abstract Agent-based models are a key tool for investigating the emergent properties of population health settings, such as infectious disease transmission, where the exposure often violates the key ‘no interference’ assumption of traditional causal inference under the potential outcomes framework. Agent-based models and other simulation-based modeling approaches have generally been viewed as a separate knowledge-generating paradigm from the potential outcomes framework, but this can lead to confusion about how to interpret the results of these models in real-world settings. By explicitly incorporating the target trial framework into the development of an agent-based or other simulation model, we can clarify the causal parameters of interest, as well as make explicit the assumptions required for valid causal effect estimation within or between populations. In this paper, we describe the use of the target trial framework for designing agent-based models when the goal is estimation of causal effects in the presence of interference, or spillover.

The Complier Average Causal Effect Parameter for Multiarmed RCTs

2020 ◽  
pp. 0193841X2097920
Author(s):  
Peter Z. Schochet
Keyword(s):  
Causal Effect ◽  
Control Group ◽  
Multiple Treatment ◽  
Intention To Treat ◽  
Treatment Services ◽  
Average Causal Effect ◽  
Key Issues ◽  
Effect Parameter ◽  
Complier Average Causal Effect ◽  
And Control

In randomized controlled trials, the complier average causal effect (CACE) parameter is often of policy interest because it pertains to intervention effects for study units that comply with their research assignments and receive a meaningful dose of treatment services. Causal inference methods for identifying and estimating the CACE parameter using an instrumental variables (IV) framework are well established for designs with a single treatment and control group. This article uses a parallel IV framework to discuss and build on the much smaller literature on estimation of CACE parameters for designs with multiple treatment groups. The key finding is that the conditions to identify and estimate CACE parameters are much more complex for multiarmed designs and may not be tractable in some cases. Practical steps are provided on how to proceed, and a case study demonstrates key issues. The results suggest that ensuring compliance is particularly important in multiarmed trials so that intention-to-treat estimates on the offer of intervention services (which can be identified) can provide meaningful information on the CACE parameters.

scholarly journals Instrumental variables based on twin births are by definition not valid (v.3.0)

2017 ◽  
Author(s):  
Stefan Öberg
Keyword(s):  
Instrumental Variables ◽  
Natural Experiment ◽  
Causal Effect ◽  
Potential Outcomes ◽  
Number Of Children ◽  
Biased Estimates ◽  
Potential Outcomes Framework

Twin births are a well-known and widespread example of a so-called “natural experiment”. Instrumental variables based on twin births have been used in many studies to estimate the causal effect of the number of children on the parents or siblings. I use the potential outcomes framework to show that these instrumental variables do not work as intended. They are fundamentally flawed and will always lead to severely biased estimates without any meaningful interpretation. This has been overlooked in previous research because too little attention has been paid to defining the treatment in this natural experiment. I analyze three different possible interpretations of the treatment and show that they all lead to inherent violations of the necessary assumptions. The effect of the number of on the parents or siblings is a policy relevant and theoretically important issue. The scientific record should therefore be corrected to not lead to misguided decisions.

Estimating Causal Effects From Multilevel Group-Allocation Data

2005 ◽  
Vol 30 (4) ◽  
pp. 397-412 ◽  
Author(s):  
Alix I. Gitelman
Keyword(s):  
Group Membership ◽  
Causal Effect ◽  
Hierarchical Linear Model ◽  
Dynamic Effect ◽  
Educational Interventions ◽  
Causal Effects ◽  
Group Dynamic ◽  
Average Causal Effect ◽  
Effect Of Treatment ◽  
Group Allocation

In group-allocation studies for comparing behavioral, social, or educational interventions, subjects in the same group necessarily receive the same treatment, whereby a group and/or group-dynamic effect can confound the treatment effect. General counterfactual outcomes that depend on group characteristics, group membership, and treatment are developed to provide a structure for specifying causal effects of treatment in the multilevel setting. An average causal effect of treatment cannot be specified, however, without a simplifying assumption of group-membership invariance (i.e., no group-dynamic effect). Under group-membership invariance and ignorability assumptions, the average causal effect is then connected to estimable quantities of the hierarchical linear model (HLM). Furthermore, it is shown that the typical specification of the HLM involves conditional independence assumptions that actually preclude the group-dynamic effect.

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