Nova Acta Leopoldina Band 110 Nummer 377

5.4 Local Robustness Property When the association model E(Y|Z, X; β* ) includes an intercept and main effect in Zi – as in [10] – and is fitted using standard maximum likelihood with standard generalized linear models software, the solution to a well chosen weighted estimating equation for Ψ is robust to mis- specification of the association model when the true parameter value is Ψ* = 0. Thus a valid test of the causal null hypothesis that Ψ* = 0 results even when all models are misspecified. This “local” robustness property (VANSTEELANDT and GOETGHEBEUR 2003, VANSTEELANDT et al. 2005) also guarantees small bias under model misspecification when the true exposure ef- fect is close to but not equal to zero. 5.5 COX-2 Data Analysis VANSTEELANDT et al. (2010) re-analyzed the data using the causal logistic regression model described above. Fitting the logistic association model yields: logit Ê (Yi | Xi, Zi) = –4.89+ 0.11 Xi – 0.33 Zi [12] following which the causal treatment log odds ratio is estimated as Ψ´` = – 2,508 by requiring equal distributions of [11] over different levels of Z (0 or 1 in this case). Hence for the causal odds ratio exp(Ψ´` ) = 0.081 with 95 % CI (0.010, 0.826). While the point estimate seems extreme, the confidence interval is wide but has an upper bound staying well below 1 indicating a significantly beneficial effect of COX-2 inhibitors on the risk of GI bleeds within 60 days. On the other hand, the unadjusted association logistic regression pa- rameter gives an estimated association odds ratio exp(β ^ ) = exp(0.11) = 1.12 with 95 % CI (0.849, 1.495) which goes strikingly in the opposite direction of the estimated causal odds ratio, be it that the association odds ratio is not significantly different from 1. 6. Great Expectations Today’s access to massive high quality electronic health records stirs the hope that more causal answers come within reach. Causal questions evolved too, in epigenetics or plant breeding for instance, where one now learns about the causal effect of a changeable trait, such as obesity, on an important risk (MINELLI et al. 2004, TIMPSON et al. 2009), relying on Mendelian ran- domization, or of a genetic marker or SNP itself on a trait (MOERKERKE et al. 2006). While there is definitely added potential, there is also reason to stay cautious. Several fun- damental problems are not resolved by simply having larger samples or more measured vari- ables. Key elements of the structure involve: – The timing of measurements which may still be event driven and the measurements therefore not representative of the generally evolving patient population. Hospital data suffer in par- ticular from potential informative censoring and hence missing data due to discharge from a hospital unit. – Accurate measurement may remain a problem. – Some important confounders may be unavailable, that is, remain completely unmeasured. When estimating the impact of hospital infections on (hospital) mortality, for instance, naive Causal Inference: Sense and Sensitivity versus Prior and Prejudice Nova Acta Leopoldina NF 110, Nr. 377, 47–64 (2011) 59