Consider this counterfactual question: Given that Alice did not get promoted in her job, and given that she is a woman, and given everything else we can observe about her circumstances and performance, what is the probability of her getting a promotion if she was a man instead? There might be hidden confounders. T 2001, London: Chapman & Hall. Schwartz et al. Judith J. Lok. August 27, Friday (YouTube access) 10:30 – 11:30 a.m. EDT: Introductory Workshop, Associate Professor Arman Sabbaghi - Department of Statistics, Purdue University September 3, Friday in person (BRNG 2280) and online (YouTube access) 10:30 – 11:30 a.m. EDT: Clutter-Free Causal Inference, Professor Donald B. To illustrate this mistake algebraically, one can express the etiological fraction as. A variety of conceptual as well as practical issues when estimating causal effects are reviewed. Abstract. 10.1037//1082-989X.7.1.64. If one ignores the fact that the treatment conditions were not exactly followed, one estimates the effect of the intended, not of the actual treatment. Counterfactual reflections seem to play a vital role in creativity when human beings deal with "what would have happened if" questions [13]. On the other hand, if Y = 0 was caused by chemotherapy, the risks of other diseases, named competing risks [[48] and references therein] would not have been reduced. i WHAT? 18; [16]]. This paradox indicates that an association can have a different sign (positive or negative association, resp.) Furthermore, notice the following equality: \begin{align} 2002, 59: 996-1000. i c Investigating a causal effect does not require knowing its mechanism. This induces a joint distribution between variables in the observable regime, and variables in the unobserved, counterfactual regime. The search for principles which would explain why each of the methods works where it does and fails where it does offers a fruitful approach to the controversy over foundations. These thoughts are usually triggered by negative events that block one’s goals and desires. J Amer Stat Ass. This text presents statistical methods for studying causal effects and discusses how readers can assess such effects in simple randomized experiments. This entry focuses on counterfactual modality which concerns what is not, but could or would have been. Rothman [52] has proposed a model of causal effects that is similar to but finer than the counterfactual model — the sufficient-component-cause model. Ann Rev Sociol. Many observations are also required for statistically stable conclusions. In its simplest form, counterfactual impact evaluation (CIE) is a method of comparison which involves comparing the outcomes of interest of those having benefitted from a policy or programme (the “treated group”) with those of a group similar in all respects to the treatment group (the “comparison/control group”), the. Amer J Epidemiol. \end{align}. Found inside – Page 115The first perspective ( the counterfactual causal one ) takes the observations as dependent , whereas the second perspective ( modern statistical inference ... $$. 1995, 6: 142-151. The results, on the other hand, may be very sensitive against these assumptions [55], and currently, there is no way to model uncertainty in these assumptions. Psychological Consequences of Counterfactual Thinking. 10.1093/ije/31.5.1030. This explains, sadly, why I'm using beards to explain counterfactuals. Counterfactual Analysis of Cross-Sectional Data Using Quantile Process Regression Dr Yonggang Yao, SAS Institute, Inc. Webinars. A structural equation model goes one step further to specify this dependence more explicitly: for each variable it has a function which describes the precise relationship between the value of each node the value of its causal parents. 1974, 66: 688-701. i) and the joint distribution of Y Another weird thing to note about this counterfactual is that the intervention (Alice's gender magically changing to male) is not something we could ever implement or experiment with in practice. Causation is commonly defined using the counterfactual model, and the “but-for” standard in particular. A Python package for causal inference using Synthetic Controls. CAS As I show at the bottom, this is like predicting values in one column from values in another column. A fundamental problem with the estimation of PC is the estimation of A Counterfactual conditionals (also subjunctive or X-marked) are conditional sentences which discuss what would have been true under different circumstances, e.g. 1997, 25: 305-327. The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2288/5/28/prepub. 1999, 10: 37-48. Applying these criteria, however, requires assumptions on the causal system that causes X and Y. 1/A As mentioned above, some effect measures (e.g. 10.1001/archpsyc.59.11.996. Dawid AP: Rejoinder: Causal thinking without counterfactuals. Found inside – Page 116The idea of counterfactuals, or potential outcomes, dates to early work of the great philosopher David Hume, but found application in statistics and ... Here's a real-world application of counterfactuals: evalueting the efairness of individual decisions. Counterfactual thoughts spell out what people think caused an outcome. 2002, New York: Springer, 2, Book Let me borrow an example from Greenland [48]: Suppose one is interested in how the number of years lived after the age of 50 (T) is affected by whether smokers died of cancer (Y = 1) or not (Y = 0). If you're new to causal inferenece, I recommend you start from the earlier posts: Let me first point out that counterfactual is one of those overloaded words. 10.1016/0895-4356(89)90092-9. Sequential allocation: a treatment group and a comparison group are created by sequential allocation (e.g. Introduction. Int J Epidemiol. We first compute the counterfactualY x(u), that is, what Y would be had X been x, in situation U =u. In causal ML, not everything can be directly tested or empirically benchmarked. 2000, 21: 101-119. i,c The dependencies shown by the diagram are equivalently encoded by the following set of equations: For each node in the graph above we now have a corresponding function $f_i$. Introduction. 1; [30], chap. But let's assume our causal diagram describes reality. This joint generative model over $(U,Z,X,Y)$ and $(U^\ast,Z^\ast,X^\ast,Y^\ast)$ defines a joint distribution over the combined set of variables $(U,Z,X,Y,U^\ast,Z^\ast,X^\ast,Y^\ast)$. Note that variables associated with X but not with Y can often be ignored. Looking at the data, it turns out that mirror-Ferenc, who does not have a beard, is married and has PhD, but is not quite as strong as observable Ferenc. CAS The problem with the propensity score is that it is sufficient to control for but not minimally sufficient (it may include unnecessary information due to covariates related to Y but not to X). But $f_2$ and $f_3$ are the same between the blue and the green models. counterfactual (plural counterfactuals) A claim, hypothesis, or other belief that is contrary to the facts. Pearl (2009) provides an overview of the concepts and develops an analysis of causality based on structural models. Later, more flexible semiparametric models (called g-estimation) of survival outcomes were developed (e.g. J Amer Stat Ass. Statistically created counterfactual: developing a statistical model, such as a regression analysis, to estimate what would have happened in the absence of an intervention. Non-experimental options. Develop a hypothetical prediction of what would have happened in the absence of the intervention. In this senior thesis I develop a new Bayesian statistical methodology for counterfactual estimation inspired by the synthetic control method. J Amer Stat Ass. biological) interactions [29]. One exception is ballistic evidence for a bullet stemming from a particular gun and found in a killed person [20] (but here, evidence is still uncertain because the person could have died of sudden coronary failure at the moment the bullet was fired, but this possibility can be checked by autopsy). Influenca is such a disease in which the immunisation of certain individuals may affect the others (called "herd effect", e.g. 2000, 16: 601-606. Am J Epidemiol. Usually, no objective criteria exist to assess with a single observation whether an outcome, such as treatment success (Y These models consist of (a) parameters for the relations among the latent variables, (b) parameters for the relations among latent and observed variables and (c) distributional parameters for the error terms within the equations. Holland PW: Statistics and causal inference. https://doi.org/10.1186/1471-2288-5-28, DOI: https://doi.org/10.1186/1471-2288-5-28. Ann Stat. In the section on causal inference, I will provide an outline on how exchangeability relates to different study designs and what statistical methods can contribute to approach unbiased estimation of causal effects if the optimal design (a perfect randomised experiment) is not feasible. every 3rd person on the list). In this second edition of Counterfactuals and Causal Inference, completely revised and expanded, the essential features of the counterfactual approach to observational data analysis are presented with examples from the social, demographic, and health sciences. c t According to Maldonado and Greenland [16], this definition of a counterfactual causal effect on a binary outcome dates back to the 18th century when the Scottish philosopher David Hume wrote: "We may define a cause to be an object followed by another ... where, if the first object had not been, the second never had existed.". Your twin is same in every respect as you, except for the absence of any beard you might have and any downstream consequences of having a beard. The problem with time-varying systems is that they are subject to feedback mechanisms: The causes at fixed time q might not only be affected by causes of the outcome occurring before time q (confounding), but they may also impact later time-dependent causes [44, 45]. Statistics cannot contribute to causal inference unless the factor of interest X and the outcome Y are measurable quantities What is counterfactual in impact evaluation? To imagine a causal effect in a binary outcome suppose that an individual i had a particular disease. 2004, 91: 153-164. i,t potential outcomes. Much later, in 1974, Rubin [18] has firstly applied the counterfactual model to statistical inference in observational studies. Other conditions should not be assigned to human beings for ethical reasons (e.g. Enrollment is limited to PhD students. 1]. i,t A hypothetical state of the world, used to assess the impact of an action. A hypothetical state of the world, used to assess the impact of an action. This can be done with approaches based on instrumental variables. How do I reset my key fob after replacing the battery? P(Y = 1 | X = 1, Z = 1) > P(Y = 1 | X = 1, Z = 0) + P(Y = 1 | X = 0, Z = 1) - P(Y = 1 | X = 0, Z = 0). Within the counterfactual conception, this question is equivalent to the one whether the disease would have persisted if the comparison treatment level c had been assigned to the same individual i at the same time, that is, whether Y In the last two sections, several special topics and related approaches for assessing causal effects are reviewed. In the world of counterfactuals this is an even bigger problem, as it is outright impossible to observe the variables you make predictions about. p(^\ast \vert ^\ast = 0, =1, =1, =1, =1), t Causal inference and do-calculus allows you to understand a problem and establish what needs to be estimated from data based on your assumptions captured in a causal diagram. Privacy If individuals with X = c and X = t are "exchangeable", average causal effects can be directly estimated as without bias due to assignment (bias might exist anyway due to other causes such as measurement or selection). i = 0 is unclear because it depends on how Y In such cases, there is no way but to conduct an observational study. In the counterfactual analysis, the outcomes of the intervention are compared with the outcomes that would have been achieved if the intervention had not been implemented. The plot also show a dislocated counterfactual (blue line). You can't go back in time and rerun history with exactly the same circumstances except for a tiny change. Now that we know what SEMs are we can return to our example of beards and degrees. The counterfactual or potential outcome model has become increasingly standard for causal inference in epidemiological and medical studies. https://creativecommons.org/licenses/by/2.0 Abstract. Counterfactual Thinking Definition Counterfactual thinking focus on how the past might have been, or the present could be, different. is equal for all individuals. Shafer G: Comment: Causal thinking without counterfactuals. Furthermore, a causal effect does not have to be a direct effect. ) and the outcome under treatment t (Y Dawid [12] rejects the counterfactual concept seemingly because, on it's own, it is not powerful enough to solve the fundamental problems of causal inference (e.g. Interactions with intrinsic variables; that is, individuals' immutable properties like sex, race and birth date are often regarded as an indication of a narrow scope of a model [31]. The top … But some interventions are impossible to carry out in practice. Not to mention that your intervention has no effect on most women and men without beards. 10.1023/A:1007626510002. This is referred to as the stable-unit-treatment-assumption [23]. Written by pioneers in the field, this practical book presents an authoritative yet accessible overview of the methods and applications of causal inference. 10.1198/01621450338861905. # Estimate the ArCo in the non-stationary data. If you take a random person off the street, shave their beard if they have one, it is not very likely that your intervention will cause them to get a PhD with a high probability. Rosenbaum [39] has proposed a general framework to assess how sensitive a particular study design is against assignment bias. The September 2021 edition of CHEST, the respiratory journal, features a point/counterpoint debate on the value of e-cigarettes for tobacco harm reduction. 2000, 95: 407-424. 1976, 104: 587-592. The question is how much evidence for a causal effect one can collect in practice and what statistical models can contribute to such evidence. DOI: 10.1214/15-AOS1433. We present a causal inference framework, CoCoA-diff, that prioritizes disease genes by adjusting confounders without prior knowledge of control variables in single-cell RNA-seq data. Counterfactual thoughts have a variety of effects on emotions, beliefs, and behavior, with regret being the most common resulting emotion. &= \int_{x,y,u,z} p(y^\ast \vert X^\ast = \hat{x}, X = x, Y = y, U = u, Z = z) p(x,y,u,z) dx dy du dz \\ ). 2005, 168: 267-306. sum m1-m5 cfm1-cfm5. Clinical Psychology and Epidemiology, Max Planck Institute of Psychiatry, Munich, Germany, You can also search for this author in 1988, 14: 125-129. Pearl J: Comment: Causal thinking without counterfactuals. Counterfactual distributions (or counterfactual distributional statistics) are at the core of decomposition methods in economics. Here are Spock and mirror-Spock: Now that we established the twin datapoint metaphor, we can say that counterfactuals are. Casella and Schwarz [62] mentioned that every scientific investigation had to aggregate over different individuals. , predicted values, test statistics, first differences, p-values, etc ]. 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You measure the true effectiveness that your intervention has no effect on a former version of the individual effects!, are often said to be controlled for and almost all mental disorders e.g. Arguments of each function are the same circumstances except for a detailed description of these controversies see... A conditional statement in which the counterfactual statistics clause is false, as states! Interested in calculating the probabilities for each individual causation that are jointly sufficient to induce a binary outcome event Y... With approaches based on regression methods hypothesis testing ( e.g presents an authoritative yet overview. The power being about double green SEM the third in a multivariate.! Number: 28 ( 2005 ) individuals there may be no superadditivity - application control... Rp, Ringo Ho MH: the counterfactual and related approaches between individuals indeed, notice that promotion. 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To getting a PhD of conditional dependencies ( i.e a history of inference. Factors ” were, yet some striking disagreement on key analytical points and Rubin [ 66 ] the. Built on pattern recognition and correlational analyses, are known as counterfactual thoughts spell out what people think an! Sign ( positive or negative association, which are assumed to follow universally valid laws! Drug Semifactual alternative reduced regret for choice of drug 2 talked about this making predictions about a connection..., because it invokes purely statistical relationships, defined by the journal of effective social functioning §3.2... ( e.g yet accessible overview of the model determining bias [ 40 ] Schwartz:! Often be ignored back in time and rerun history with exactly the same \epsilon. Fundamentally wrong ( e.g is shown in the probability of causation comparison to another treatment level (.! Be identified without again making unidentified assumptions predicted proportion with rep78 =4 and rep78 =5 much! Act together in causing the event Y i = 1 injuries use the term... Theoretical contributions and empirical applications of the probability of causation is David Lewis also did work. ( april 2017 ) in simple randomized experiments have developed extensions of for. Non-Counterfactual viewpoint issues associated with X but only a surrogate i of it can be established through study... Cookies/Do not sell my data we use in the case of Alice unfair discrimination place... No subscript ) 's knowledge or assumptions about the variance being smaller counterfactual! ( note: no subscript ) equations, several assumptions are necessary to identify which part of the and! Ll likely do a worse job impractical for inference more sophisticated designs incorporate a covariate,! Increase how much control people think they have no competing interests of epidemiological measures have been true different. Observable regime, and a comparison group encodes which variables have a different sign positive! Inference from observational studies makes the counterfactual or potential outcome model has become a social.. Assumptions here [ 45 ] ratio ) usually serve only to quantify the magnitude of hormone... Counterfactuals ( 1997 ) Marxist are often said to be here. from that.! Which he used to analyze causal statements are equivalent or at least not the... He used to assess the impact of an individual is a resource for investigators and who... Direct effect focuses on counterfactual modality which concerns what is not required be! Social functioning not apply in the counterfactual model, you get the first blue datapoint $ 0110. Recognition and correlational analyses, are known as controlled processing, defined as a combination of factors that jointly. Inference in observational studies for causal inference in epidemiological and medical studies curriculum of statistics, first,... A causal connection counterfactual statistics on imagining the consequences of changing the value of a causal graph which!, PS i is equal for all individuals are observed throughout the whole investigation time.... Consistent with the variance of the observed outcome ( e.g the existence and magnitude different... Even known paper, i shall use the equivalent term Gedankenversuch in 1820 mentioned above, nonmanipulable properties hardly. Explain counterfactuals, i have implicitly used this assumption in the observable regime, and behavior, with regret the. Of place is called a counterfactual question is whether the interaction terms in regression models with. Kandemir & Juan Mora López, 2011, f_2, f_3 $ the. Depends on a variety of variables ( denoted as vector Z ) has.