Causal Inference Using Potential Outcomes Design, Modeling, Decisions. Causal inference and potential outcomes. Chapter 3 introduces the potential outcomes framework for causal inference together with the Fundamental Problem of Causal Inference, which is that only one potential outcome, can possibly be observed per study participant. I was trying to figure out what this meant, and I framed it in terms of potential outcomes. The average treatment e ect We de ne the causal e ect of a treatment via potential outcomes. To make clear what I'm talking about, let's take the simplest possible DAG where we have some confounding. Goal of causal inference: Estimate causal effects. We care about causal inference because a large proportion of real-life questions of interest are questions of causality, not correlation. The people who would survive under the treatment but would die under the control, 3. Causal effect may be the desired outcome. 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. And here it comes. . They thoroughly cover 3 different classes of conditioning-based estimators of causal effects, giving each their own chapter: matching, regression, and inverse probability weighting. In recent years, both causal inference frameworks and deep learning have seen rapid adoption across science, industry, and medicine. For a hypothetical intervention, it defines the causal effect for an individual as the difference between the outcomes that would be observed for that individual with versus without the exposure or intervention under consideration. They lay out the assumptions needed for causal inference and describe the leading analysis . Let's suppose we . Potential outcomes, causal inference, and virtual history. IBM adopts a two-step approach by separating the effect-estimating step from the potential-outcome-prediction step. For a binary treatment w2f0;1g, we de ne potential outcomes Y i(1) and Y i(0) corresponding to the outcome the i-th subject would have experienced had they respectively received the treatment or not. 1.1.1 Potential Outcomes review The following questions are designed to help you get familiar with the potential outcomes framework for causal inference that we discussed in the lecture. The people who would survive under the treatment and would survive under the control, 2. Take-Away Skills. 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. 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 . 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. Rather than infer causality based on belief of whether an estimated association can be interpreted as causal, potential-outcomes methods . For this individual, the causal effect of the treatment is the difference between the potential outcome if the individual receives the treatment and the potential outcome if she does not. Back to our example experiment, before a student randomly assigned to receive the treatment is exposed to that new reading program, there are at least two potential outcomes for that student. The causal effect, or treatment effect, is the difference between these two potential outcomes. A variety of conceptual as well as practical issues when estimating causal effects are reviewed. 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 average treatment effect often appears in the causal inference literature equivalently in its potential outcome notation \mathop\mathbb{E}[Y_1 - Y_0]. PATE. This course offers a rigorous mathematical survey of causal inference at the Master's level. Imputation approaches for potential outcomes in causal inference Authors Daniel Westreich 1 , Jessie K Edwards 2 , Stephen R Cole 2 , Robert W Platt 3 , Sunni L Mumford 4 , Enrique F Schisterman 4 Affiliations 1 Department of Epidemiology, Gillings School of Global Public Health, UNC-Chapel Hill, NC, USA, djw@unc.edu. 1.1 Rubin Causal Model. (Some authors use parenthetical expressions, e.g. 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 . More generally, the field of causal inference has given rise to a particular type of prediction as the object of inference itself: potential outcomes. 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 Statisticians Jerzey Neuman and Donald Rubin both formalized a model for investigating counterfactual queries commonly referred to as the potential outcomes model. 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. This use is particularly important in more complex settings, that is, observational studies or randomized experiments with complications such as noncompliance. (Keil & Edwards, 2018 , 437-38) As they point out, causal inference just is a special case of prediction, in contemporary epidemiological causal inference frameworks. Rubin's perspective on causal inference "Causality" is a tricky concept; we all know what it is, but no one really can define it. 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 . The proposed concepts and methods are useful for particular problems, but it would be of concern if the theory and pra is Joe's blood pressure if he takes the new pill. For simplicity, we consider an intervention , which is either absent, as indicated by , or present, indicated by . The Potential Outcomes Framework (aka the Neyman-Rubin Causal Model) is arguably the most widely used framework for causal inference in the social sciences. Rubin, 1974, 1978) in relation to new data science developments. Causal inference based on a restricted version of the potential outcomes approach reasoning is assuming an increasingly prominent place in the teaching and practice of epidemiology. 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. the potential outcome framework, also called rubin-causal-model (rcm), augments the joint distribution of (z, y)(z,y) by two random variables (y(1), y(0))(y (1),y (0)) the potential outcome pair of yy when zz is 11 and 00 respectively. In this part of the Introduction to Causal Inference course, we outline week 2's lecture and walk through what potential outcomes are. Potential outcome prediction: Every causal effect is defined by two potential outcomes. We adopt this two-step approach by separating the effect-estimating step from the potential-outcome-prediction step. Contains references to relevant resources for those who want to go deeper. In general, this notation expresses the potential outcome which results from a treatment, t, on a unit, u. Causal inference refers to the design and analysis of data for uncovering causal relationships between treatment/intervention variables and outcome variables. Y (0), Y (1), Y ( x, u) or Z ( x, y ).) 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. 2 The word "counterfactual" is sometimes used here, but we follow Rubin (1990) and use the The counterfactual or potential outcome model has become increasingly standard for causal inference in epidemiological and medical studies. Formulate potential outcomes corresponding to various levels of a "treatment" 2. They are potential because they didn't both/all actually happen. Under IA "expectation of the unobserved potential outcomes is equal to the conditional expectations of the observed outcomes conditional on treatment assignment " (Keele 2015 b, 5) IA allows us connect unobservable potential outcomes to observable quantities in the data IA is linked to the "assignment mechanism" 22 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)). Express assumptions with causal graphs 4. 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. Consider four types of patients: 1. Example I-1: Potential Outcomes and Causal Effect with One Unit: Simple Difference 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. 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. As for the notation, we use an additional subscript: Overview of causal inference and the Rubin "potential outcomes" causal model. Treatment and control groups, and the core role of the assignment (to treatment) mechanism. For . The Potential Outcomes Framework Sometimes called the Rubin Causal Model owing to foundational work in Rubin (1974, 1976, 1977, 1979, 1990) Rooted in ideas dating back to Fisher (1918, 1925) and Neyman (1923) Three main components of the framework: 1. ABSTRACT. Causality has been of concern since the dawn of . The causal e ect of the treatment on the i-th unit is . In this paper, we systematize the emerging literature for estimating causal effects using deep neural networks within the potential outcomes framework. Formula 5. Indicator Variables Indicator Variables are mathematical variables used to represent discrete events. Also known as the Rubin causal model (RCM), the potential outcomes framework is based on the idea of potential outcomes. 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. I Causal inference under the potential outcome framework is essentiallya missing data problem I To identify causal effects from observed data, one must By far the most popular approach to mathematically defining a causal effect is based on potential outcomes, or counterfactuals. In a randomized fMRI experiment with a treatment and a control group, the potential outcomes Z (0) and Z (1) are well defined, but it is unclear how values of X in Y ( z, x) are set. 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. Emphasis on potential outcome prediction. 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. Introduction to Modern Methods for Causal Inference Donald Rubin. Causal effects are commonly defined as comparisons of the potential outcomes under treatment and control, but this definition is threatened by the possibility that either the treatment or the control condition is not well defined, existing instead in more than one version. Causal inference (CI) represents the task of estimating causal effects by comparing patient outcomes under multiple counterfactual treatments. They are all population means. Posted on March 28, 2005 12:38 AM by Andrew. We discuss simple estimation techniques and demonstrate the importance of considering the relationship between the potential outcomes and the process of causal exposure. Potential outcomes and ignorability. . DAG with simple confounding. In doing so, potential outcomes emerge into the graph, and enable us to (for example) check the exchangeability assumption. 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) This article discusses the fundamental ideas of causal inference under a potential outcome framework (Neyman, 1923; D.B. Causal effects are defined as comparisons of potential outcomes under different treatments on a common set of units. These include causal interactions, imperfect experiments, adjustment for . 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. Potential outcomes. A potential outcome is the outcome for an individual under a potential treatment. Also, this framework crisply separates scientific inference for causal effects and decisions based on such inference, a distinction evident in Fisher's discussion of tests of significance versus tests in an accept/reject framework. Potential Outcomes Model for Causal Inference Jonathan Mummolo Stanford University Mummolo (Stanford) 1 / 32. In particular, the causal effect is not defined in terms of comparisons of outcomes at different times, as in a before-and-after comparison of my headache before and after deciding to take or not to take the aspirin. For example, a person would have a particular . 200 potential outcomes). 3. At the end of the course, learners should be able to: 1. Potential Outcomes is a model of comparing a hypothetical outcome with the outcome that . Under the potential outcomes framework for causal inference, the average treatment effect (ATE) is the average of the individual treatment effects of all individuals in a sample. the potential outcomes and covariates are given a Bayesian distribution to complete the model specification. 6,8 The most widely used method for CI is a . Causal inference as a missing data problem, and . However, every effect is defined by two potential (counterfactual) outcomes. The authors discuss how randomized experiments allow us to assess causal effects and then turn to observational studies. Explain the notation Y 1i Y 1 i. 1. Inferences about causation are of great importance in science, medicine, policy, and business. 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. You'll develop a framework to think about problems counterfactually using the Potential Outcomes Framework. The potential outcomes framework provides a way to quantify causal effects. An article on the potential outcomes framework, the lingua franca for treating causal questions that sets up the theoretical foundations of causal inference.