Nova Acta Leopoldina Band 110 Nummer 377

extensively studied over the past decade (ROBINS and GREENLAND 1992, RUBIN 2004, DIDELEz et al. 2006, GOETGELUK et al. 2008) and come in different shapes. We mention two forms. The population averaged controlled direct effect of setting exposure X to x (versus setting X to 0) when holding K fixed at value k, is defined in terms of potential outcomes Yxk and Y0k: E(Yxk − Y0k). The so-called natural direct effect is similar but compares outcomes Y after setting exposure to x versus 0 when holding K fixed at the value K0, which is the in- termediate variable that follows from reference exposure level 0 for the same subject. In what follows we set out to estimate total effects of intervening on an exposure X, not at- tempting to stop certain natural consequences K from happening. 3. The Hazards of Observational Studies The term “Stork epidemiology” has become an insult used to point at naive causal conclusions which are driven by confounding and “allow to prove anything”. The name is taken from so called statistical “proof” that babies are delivered by storks. Not surprisingly, across nations and over time a declining density of storks is associated with declining birth rate. The associ- ation should not be seen as causal, however, since both phenomena are natural consequences of growing industrialization and increasing wealth, i.e. confounders. A recent and costly example of how badly things can go wrong if observed associations are unjustly believed to be causal, came to light as a result of “The Women’s Health Initiative”: a randomized trial of combined “estrogen and progestin” versus placebo among post- menopausal women (ROSSOUW et al. 2002). The trial was motivated by “a large body of ob- servational studies suggesting a 40 % to 50 % reduction in risk among users of either estrogen alone or, less frequently, estrogen and progestin”. The hormones had been widely prescribed for symptom relief to menopausal women. Survival curves in ROSSOUW et al. (2002) show, however, that for most and the most detrimental outcomes time to occurrence came signifi- cantly sooner on the treatment arm. Results thus contradict the promising findings of previous association analyses of observational data. Could current state of the art methods help avoid these biases? The answer is positive as convincingly demonstrated by a careful analysis per- formed by HERNAN et al. (2008) of data from the observational Nurses’ Health Study. Basic insights into the flow of causal effects have taught us to require proper adjustment for (time-varying) confounders, i.e. variables predicting both estrogen and progestin use and the harmful outcome, but NOT for intermediate variables on the causal pathway from estrogen and progestin to the harmful event under study. Since in the longitudinal setting some variables may be both, confounders and intermediate variables, this adjustment requires special methods. HERNAN et al. (2008) conduct two types of analysis to evaluate the effect of HRT on coronary heart disease (CHD). First, they mimic an intention to treat analysis by choosing a particular time point and comparing subsequent event times for the groups of women who were newly treated versus not treated at that starting point, adjusting for a large set of confounders meas- ured at the chosen starting time. They repeat this for several chosen starting times in a sequen- tial analysis. Their second analysis acknowledges that HRT status at the starting time is often not maintained. An adherence adjusted analysis therefore accounts for time-varying treatment actually observed. Assuming no unmeasured time-varying confounders, but allowing for ex- Nova Acta Leopoldina NF 110, Nr. 377, 47–64 (2011) Els Goetghebeur 52