Nova Acta Leopoldina Band 110 Nummer 377

From there, we aim to predict outcomes not just in the natural world that continues to evolve under its current structure, but after intervening on exposure in this world. Thus raises the no- tion of counterfactual outcomes: what would have happened if exposure had been different. In this paper we will start by developing the causal question as it is formally posed in terms of counterfactual outcomes. We illustrate the challenges of the field by referring to the infa- mous case of hormone replacement therapy, reminding ourselves of just how much causal in- ference can go wrong and with what dire (Euros and health misery) consequences. We then zoom in on two fundamentally different assumptions with corresponding estimating ap- proaches leading to well understood causal effect parameters: the “No unmeasured con- founders” and the “Instrumental variables” assumptions. We outline these approaches for the evaluation of effects of fixed treatment prescriptions. More ambitiously and sophisticatedly newer research lines venture into causal inference on adaptive or dynamic treatment regimes (LAVORI 2000, MURPHy et al. 2001, BUyzE et al. 2010) relying, for instance, on sequentially randomized designs. Finally, we see how the prom- ise of this technology becomes big business. We end with a reflection on the popular perception and hopes and hazards for the future of computer intensive statistical methods under the flag of data mining. 2. The Causal Question After centuries of searching for causal answers, there remains a surprising amount of confusion already at the level of formulating the causal question. Judea PEARL’S (2009) “Myth, confusion, and science in causal inference ...” leaves no mystery about this point at least. For many sci- entists, expressing causal relationships through causal graphs, where arrows represent direct causal effects (PEARL 1995, 2000) or formally in a potential outcome framework (RUBIN 1974, HOLLAND 1986, ROBINS et al. 2000) helps clarify concepts, goals and assumptions. Some col- leagues nevertheless object to a formalism that involves relationships between latent, i.e. un- observed outcomes (DAWID 2000). Below, we exploit the power of the potential outcomes framework to specify causal questions and explain the issues. The “Potential Outcomes” Framework Since we are not focusing on directly observable associations, what are we studying? In words, causal inference is concerned with a “what if” question and refers to the primary outcome Yx which would have been realized had – possibly contrary to fact – exposure been set to fixed level x. We are hence concerned with potential outcomes that are observed only on those pos- sibly rare occasions when randomly observed exposure X (typically indicated by capital letter) happens to coincide with the exposure level of interest, x, and not for the units of observation with X x. There is therefore a huge missing data problem. As a result, a simple target of inference may be unattainable, and a range of different parameters, causal estimands, is defined. We list some of the most common causal parame- ters. – First and foremost there is the population average causal effect of exposure level x versus exposure level 0, where zero stands for some well defined and meaningful reference level. Nova Acta Leopoldina NF 110, Nr. 377, 47–64 (2011) Els Goetghebeur 50