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The effect of treatment on the treated: A decision-theoretic perspective

The target of inference in many econometric and epidemiological studies is the average treatment effect. This can be estimated straightforwardly from a controlled experiment with full compliance. However, such experiments are often pragmatically impossible to conduct. In this work we consider cases where data are gathered under passive observational conditions, and are available only for those individuals who are treated. A classic example from econometrics is when we wish to estimate the effect of a training programme on subsequent income, but participation is voluntary, the data are observational, and there is no control group because only the participants are followed up. A similar situation arises in epidemiological studies, when a new drug for chronic disease with negative side-effects is introduced: this is taken only by those willing to brave the side-effects, so administration is again voluntary; and further, as willingness to take the medication is often indicative of a stronger desire to recover, it is difficult to find a comparable control group. The average treatment effect is not estimable from such data. As an alternative, Heckman and Robb (1985) suggested estimating the effect of treatment on the treated (ETT). Within the potential response framework (Rubin 1974), this is defined as E(Y1-Y0|T=1) where Yt denotes the potenial response of an individual to treatment T = t and the expectation is taken under the joint distribution of (T, Y0, Y1). However, as at most one of the potential responses can be observed for any individual, this joint distribution cannot be fully identified from any data. As the ETT appears to depend on this joint distribution, this raises the question: Is the ETT well-defined? Further, in the above examples only T = 1, Y = Y1 will be observed. The ETT also depends on Y0. What other assumptions, if any, need to be made in order to identify the ETT? This paper addresses these questions by reinterpreting the ETT in terms of the decision-theoretic model of causal inference (Dawid 2002; Dawid 2003; Geneletti 2005; Dawid and Didelez 2005). We show that the ETT is indeed well-defined, and develop a concise formula for it in terms of observable distributions. We also show that it is not possible to identify the ETT from the kind of data available in the above examples without making further assumptions, which we discuss. We also identify the minimal data situation in which the ETT can be identified.

Speaker

Speaker 1 Biography
I am a Post doc in the department of Epidemiology and Public Health working with Nicky Best and Sylvia Richardson. I'm currently researching selection bias using graphical models with focus on case-control studies. In particular I am developing methods to detect and control for selection bias. My PhD developed aspects of causal inference using the decision theoretic model - without counterfactuals!! I do not believe that using counterfactuals is necessary for causal inference - assumptions based on their existence are not empirically verifiable. The decision theoretic approach is based on the idea that the aim of causal inference is to inform future decisions - not to answer the (unanswerable) question "what would have happened if ...." For a heated debate on the pros and cons of counterfactuals see A.P.Dawid - Causal inference without counterfactuals. With discussion. J. Amer. Statist. Ass.95 (2000), 407-448. I am especially interested in the use of graphical models in particular in methodology. Other interests are in causal inference and identifying causal effects from observational data. I consider myself to be a Bayesian - not just because it works but because the philosphy of subjective probability appeals to me - "Probability does not exist" Bruno de Finetti. Some further reading: Bruno de Finetti, Theory of Probability, (translation of 1970 book) 2 volumes, New York: Wiley, (1974-5), D.V. Lindley , Introduction to Probability and Statistics from a Bayesian Viewpoint. Cambridge University Press. For more Bayesian info see http://www.bayesian.org

Speaker 2 Biography
Philip Dawid is Professor of Statistics at Cambridge University, having been Pearson Professor of Statistics at University College London from 1989 to 2007. He is Chartered Statistician and Fellow of the Royal Statistical Society, which has awarded him Guy Medals in Bronze and Silver; elected Fellow of the Institute of Mathematical Statistics; elected Member of the International Statistical Institute; and a Member of the Organising Committee for the Valencia International Meetings on Bayesian Statistics. He has served as Editor of the Journal of the Royal Statistical Society (Series B) and of Biometrika, and is currently an Editor of Bayesian Analysis. He was President of the International Society for Bayesian Analysis for the year 2000.