Nova Acta Leopoldina Band 110 Nummer 377

fore, the parameter value of Ψ that best achieves equality of survival curves as measured by the logrank test statistic for instance, will become the point estimate Ψ´` . Figures 2 – 4 below illustrate this approach. Figure 2 shows non-parametrically estimated survival probabilities over time in groups as randomized and finds estimated survival chances to be systematically higher on the Standard treatment arm which had no pump assigned (even though the observed difference is not statistically significant here). Figure 3 reports separate survival curves for observed receivers and non-receivers subgroups within the intervention arm. The curve for the non-receivers is duplicated in Figure 4 for the standard arm, where it represents the survival curve under control conditions for the corresponding latent subgroup of “potential non-receivers”, i.e. those who would not get the implant if it had been assigned. It is complemented by the top curve in Figure 4 which is reconstructed to arrive at average survival chances on the control arm (averaging over both curves in the right proportions) which coincide with what the non-parametrically estimated Kaplan-Meier curve – shown in Figure 2 – finds in that arm as a whole. Note that, even though ‘potential receivers’ are not directly observed on the control arm, due to randomization this subgroup is expected to be present in the same proportion as on the intervention arm, where it is directly observed. Fig. 2 Kaplan-Meier survival curves for both randomized arms of the pump implant trial. Causal Inference: Sense and Sensitivity versus Prior and Prejudice Nova Acta Leopoldina NF 110, Nr. 377, 47–64 (2011) 55