Nova Acta Leopoldina Band 110 Nummer 377

for μ tk,dl provided there are no unmeasured time-varying confounders: all time-varying vari- ables which affect simultaneously future exposure as well as future natural risk (independent of exposure) have been (accurately) measured in L - k–1. 5. An Instrumental Variables Approach – Allowing for Unmeasured Confounders To allow for the needed corrections using the above marginal structural model, one must (i) have measured all important confounders and (ii) model their impact well. Because this is hard to accomplish and guarantee completely alternative approaches have been sought and found under the quite different assumptions for ‘instrumental variables’. An instrumental vari- able, for which we will use notation Z, is predictive of exposure but not otherwise of outcome and therefore it allows for an approach inspired by the causal effect measure resulting when unbiased comparisons are made between randomized arms (ANGRIST et al. 1996, HERNAN and ROBINS 2006). 5.1 Instrumental Variables in the Experimental Setting Standard Experimental designs for the evaluation of a new treatment will randomly assign patients to (experimental) treatment or control. The randomization indicator R, is the prime example of an instrument, Z: an observed vehicle that predicts treatment received, but is not otherwise predictive of outcome. It can be used to evaluate the causal effect of treatment ac- tually received (as opposed to treatment assigned). As a rule, when treatment is (randomly) assigned one has higher chance of actually receiving it, while randomization per se, “the flip of the coin”, is independent of the natural course of disease. Consider a trial (KEMENy et al. 2002) which randomizes colon cancer patients with liver metastases over the implant of a he- patic pump – or not. The aim is to find out whether direct delivery of chemotherapy to the liver through such pump increases survival chances. If all patients receive their assigned treat- ment (experimental or standard), treatment effect is straightforwardly evaluated by the so called Intention To Treat analysis (ITT): survival chances are simply compared between groups as randomized. In practice, of the random half of patients assigned the implant, some did ultimately not receive it. The data revealed furthermore that non-receivers form a high risk subpopulation: even with a treatment similar to that of the subjects on the control arm (i. e. no pump) their es- timated survival chances are lower. This points to a selection effect. Correspondingly, the re- maining patients with implant are a low risk subset and hence no longer directly comparable to the control arm. How then can we estimate the effect of the implant on the subpopulation who actually re- ceived it? Not by directly contrasting the survival rate of “receivers” with that of the random- ized control group as a whole, since we expect the experimentally treated subpopulation to have lower death rate even if the implant has no causal effect. A general approach to IV meth- ods, models an expected contrast between observed and potential treatment free outcomes in function of treatment received involving an unknown causal effect parameter, Ψ, say. This postulated effect is then taken away from observed outcomes to yield expected treatment free outcomes. For the true parameter, the obtained distribution of expected treatment free out- comes is independent of randomized arm by virtue of the randomization assumption. There- Nova Acta Leopoldina NF 110, Nr. 377, 47–64 (2011) Els Goetghebeur 54