Nova Acta Leopoldina Band 110 Nummer 377

posure variables to lie on the causal path form earlier exposure to outcome, G-estimation can be used for structural nested models, and Inverse Probability Weighting (IPW) with marginal models for current treatment effects estimation. The authors chose to censor women when they go off the treatment received at the starting point considered and used IPW under the as- sumption of no unmeasured confounders for the dropout. The latter technique reweighs per time point the different prognostic strata to reconstruct similar prognostic variables distribu- tions in each treatment arm and thus render the arms comparable. Both analyses of the observational cohort in the Nurses’ Health Study now yielded results consistent with the randomized trial conclusions. And following causal logic, estimated harm- ful effects were more pronounced when accounting for treatments actually received over time. Important effect modifications were further discovered indicating harmful effects are most present during the first years following treatment initiation. Key differences left in results be- tween observational and experimental studies were explained by differences in starting point acknowledged for HRT. 4. Marginal Estimators Following “No Unmeasured Time-Varying Confounders” We explain the quite powerful marginal model mentioned above in some detail for a more general treatment strategy. A so called dynamic treatment strategy, d, is a decision rule that dictates over time t what treatment to prescribe in response to an observed history until then of treatment and response (MURPHy et al. 2001). The treatments actually given are not fully determined a priori in as much as we cannot perfectly predict the covariate evolution. Suppose we wish to evaluate the effect of such a strategy dl. Let then – μtk,dl represent the mean outcome at time tk for dynamic strategy dl and – πk (ak | ᾱ k−1, l - k−1) be the chance in the current study population of receiving treatment Ak= ak at tk, given observed history of treatment, ᾱ k−1, and observed covariate history l - k−1 up to time tk. – pk (a* k | α− k−1, l - k−1) similarly expresses the conditional probability that A* k = a* k but now under the new dynamic strategy we wish to evaluate. If the decision rule finds treatment ac- tion is determined in function of a given history, these pk’s will take on the value 0 or 1. This is the case we will consider. – Wk,dl (ᾱk, l - k–1) = j (aj | ᾱ j−1, l - j−1) / πj (a j | ᾱ j−1, l - j−1) [5] are weights that will help transform outcomes from the observed treatment sequence to those expected under the new treatment strategy studied. Expectation of response Y* k at time tk following decision rule dl , μtk,dl, can then be estimated by solving weighted estimating equation: n Í[Wk,dl ( ) (Yik – μ tk,dl ) ] = 0 [6] i=1 where i indexes observation units in a random sample i = 1, …, n. Observed outcomes Yk who in the dataset happened to follow an observed treatment path up until tk coinciding with path dl, the decision rule of interest, are weighted inversely with the probability of following that particular path in the dataset. In so doing, we reconstruct what would have happened had the entire population followed this decision rule. One thus obtains an unbiased estimating equation Causal Inference: Sense and Sensitivity versus Prior and Prejudice Nova Acta Leopoldina NF 110, Nr. 377, 47–64 (2011) 53 ! p j "1 k # ! Ak, i...,Lk"1,i