A potential outcome is the outcome for an individual under a potential treatment. The "gold standard" of a randomized experiment. I draw heavily on Hernn and Robins' Causal Inference book. Causal Effect: For each unit, the comparison of the potential outcome under treatment and the potential outcome under control The Fundamental Problem of Causal Inference: We can observe at most one of the potential outcomes for each unit. Can we still make use of analysis tools like causal trees to understand heterogeneous treatment effects? . This article is the written version of the 2004 Fisher Lecture, presented August 11, 2004 at the Joint Statistical Meetings in Toronto. The causal effect for each respondent is the potential outcome that each observation would take under treatment (denoted Y(1)) minus the potential outcome that each observation would take under control (denoted Y(0)). Causal effects are defined as comparisons of potential outcomes under different treatments on a common set of units. Observed values of the potential outcomes are revealed by the assignment mechanisma probabilistic model for the treatment each unit receives as a function of covariates and potential outcomes. Posted on March 28, 2005 12:38 AM by Andrew. For . The simplest version of this powerful model consists of four main concepts. 4.1.2 Average treatment effects From this simple definition of a treatment effect come three different parameters that are often of interest to researchers. The Fundamental Problem of Causal Inference Holland, 1986 I For each unit, we can observe at most one of the two potential outcomes, the other is missing (counterfactual) I Potential outcomes and assignments jointly determine the values of the observed and missing outcomes: Yobs i Yi(Wi) = Wi Yi(1) + (1 Wi) Yi(0) To make clear what I'm talking about, let's take the simplest possible DAG where we have some confounding. The fundamental problem of causal inference says that only one potential outcome is observed for each unit. Those versed in the potential-outcome notation ( Neyman, 1923, Rubin, 1974, Holland, 1988 ), can recognize causal expressions through the subscripts that are attached to counterfactual events and variables, e.g. The proposed concepts and methods are useful for particular problems, but it would be of concern if the theory and pra They are potential because they didn't both/all actually happen. To make causal inference using a counterfactual framework, we must now find a way to impute the missing potential outcomes either implicitly or explicitly, both of which require the counterfactual consistency theorem, and either an assumption of unconditional exchangeability or of conditional exchangeability with positivity, as detailed above. Rubin's perspective on causal inference "Causality" is a tricky concept; we all know what it is, but no one really can define it. What happens if both outcomes from control and treatment can be observed? In this course, you will learn the conceptual foundations for determining causal inference and how to work with data to understand why things happen. Similarly, is the effect of a different treatment, c or control, on a unit, u. The fundamental problem for causal inference is that, for any individual unit, we can observe only one of Y (1) or Y (0), as indicated by W; that is, we observe the value of the potential outcome under only one of the possible treatments, namely the treatment actually assigned, and the potential outcome under the other treatment is missing. 1.1.1 Treatment allocation rule; 1.1.2 Potential outcomes; 1.1.3 Switching equation; 1.2 Treatment effects. Let's suppose we . The top panel displays the data we would like to be able to see in order to determine causal eects for each person in the datasetthat is, it includes both potential outcomes for each person. We conclude by extending our presentation to over-time potential outcome variables for one or more units of analysis, as well as causal variables that take on more than two values. Indicator Variables Indicator Variables are mathematical variables used to represent discrete events. We need to compare potential outcomes, but we only have 7 since yy is the observed outcome and by definition we have y = {y(1) if z = 1, y(0) if z = 0 when z = 1z = We discuss simple estimation techniques and demonstrate the importance of considering the relationship between the potential outcomes and the process of causal exposure. It is this statement about the treatment assignment mechanism that allows us to estimate the treatment effect using only the observed outcomes, the treatment, and the covariates, even though the causal claim we want to make involves only the potential outcomes. 200 potential outcomes). This paper provides an overview on the counterfactual and related approaches. 3. Describe the difference between association and causation 3. Yx ( u) or Zxy. In general, this notation expresses the potential outcome which results from a treatment, t, on a unit, u. the potential outcomes framework (rubin or neyman-rubin causal model) uses mathematical notation to describe counterfactual outcomes and can be used to describe the causal effect of an. 2 The word "counterfactual" is sometimes used here, but we follow Rubin (1990) and use the Potential Outcomes Framework. We consider a single binary outcome , which takes values 0 or 1. Causal effect is defined as the magnitude by which an outcome variable (Y) is changed by a unit-level interventional change in treatment, in other words, the difference between outcomes in the real world and the counterfactual world. Goal of causal inference: Estimate causal effects. Express assumptions with causal graphs 4. Fundamental Problem of Causal Inference, Identification, & Assumptions The so-called "fundamental problem of causal inference" (Holland 1986) is that one can never directly observe causal effects (ACE or ICE), because we can never observe both potential outcomes for any individual. The topic of this lecture, the issue of estimating the causal effect of a treatment on a primary outcome that is "censored" by death, is another such complication. In recent years, both causal inference frameworks and deep learning have seen rapid adoption across science, industry, and medicine. Treatment and control groups, and the core role of the assignment (to treatment) mechanism. Causal inference (CI) represents the task of estimating causal effects by comparing patient outcomes under multiple counterfactual treatments. We adopt this two-step approach by separating the effect-estimating step from the potential-outcome-prediction step. Here's Ferguson making the case that potential outcomes (in statistical terminology, the "Rubin causal model") are particularly relevant to the study of historical causation: The counterfactual or potential outcome model has become increasingly standard for causal inference in epidemiological and medical studies. They are all population means. 1.2.1 Individual level treatment effects; 1.2.2 Average treatment effect on the treated; 1.3 Fundamental problem of causal inference; 1.4 Intuitive estimators, confounding . The Potential Outcomes Framework (aka the Neyman-Rubin Causal Model) is arguably the most widely used framework for causal inference in the social sciences. As an alternative to the classical paradigm, the potential-outcomes paradigm for causal inference has the distinctive feature that causal effects are explicitly defined as consequences of specific actions . Donald B Rubin Donald B. Rubin is John L. Loeb Professor of Statistics, Department of Statistics, Harvard University, Cambridge, MA 02138 . IBM adopts a two-step approach by separating the effect-estimating step from the potential-outcome-prediction step. As statisticians, we focus on study design and estimation of causal effects of a specified, well-defined intervention W W W on an outcome Y Y Y from . Some authors have even argued that as X is not manipulated in experiments where Z is randomly assigned, potential outcomes Y ( z, x) should not be considered. In this part of the Introduction to Causal Inference course, we outline week 2's lecture and walk through what potential outcomes are. Potential Outcomes Model for Causal Inference Jonathan Mummolo Stanford University Mummolo (Stanford) 1 / 32. The Fundamental Problem of Causal Inference Holland, 1986, JASA I For each unit, we can observe at most one of the two potential outcomes, the other is missing (counterfactual?) The people who would survive under the treatment and would survive under the control, 2. This use is particularly important in more complex settings, that is, observational studies or randomized experiments with complications such as noncompliance. This post gives an accessible introduction to the framework's key elements interventions, potential outcomes, estimands, assignment mechanisms, and estimators. They thoroughly cover 3 different classes of conditioning-based estimators of causal effects, giving each their own chapter: matching, regression, and inverse probability weighting. Potential outcomes and ignorability. This can be expressed in two ways: average of all differences Y1- Y0; or average of all Y1minus the average of all Y0 Causal Fundamental Problem This book provides a great combination and comparison of the potential outcomes and graphical causal models perspectives. Overview of causal inference and the Rubin "potential outcomes" causal model. This is often a real possibility in nonexperimental or observational studies of treatments because these treatments occur . The average treatment effect often appears in the causal inference literature equivalently in its potential outcome notation \mathop\mathbb{E}[Y_1 - Y_0]. Interpreting the reason for this, and its importance, is an important part of the main model for understanding causality, which is to say potential outcomes. Example I-1: Potential Outcomes and Causal Effect with One Unit: Simple Difference One of the essential problems of the causal inference is to calculate those average treatment effects in different settings, with different limitations, under different distributions of untis but with the main problem we do not know both potential outcomes for the same untis. Take-Away Skills. Consider four types of patients: 1. By far the most popular approach to mathematically defining a causal effect is based on potential outcomes, or counterfactuals. The potential outcomes framework (Rubin or Neyman-Rubin causal model) uses mathematical notation to describe counterfactual outcomes and can be used to describe the causal effect of an exposure on an outcome in statistical terms.10 The terms exposure and outcome refer to the central variables of interest where the exposure is thought to have a causal effect on the outcome .