The notion of exchangeability has been recognized in the causal inference literature in various guises, but only rarely in the original Bayesian meaning as a symmetry property between individual units in statistical inference. Since the latter is a s
tandard ingredient in Bayesian inference, we argue that in Bayesian causal inference it is natural to link the causal model, including the notion of confounding and definition of causal contrasts of interest, to the concept of exchangeability. Here we relate the Bayesian notion of exchangeability to alternative conditions for unconfounded inferences, commonly stated using potential outcomes, and define causal contrasts in the presence of exchangeability in terms of limits of posterior predictive expectations for further exchangeable units. While our main focus is in a point treatment setting, we also investigate how this reasoning carries over to longitudinal settings.
The primary analysis of randomized screening trials for cancer typically adheres to the intention-to-screen principle, measuring cancer-specific mortality reductions between screening and control arms. These mortality reductions result from a combina
tion of the screening regimen, screening technology and the effect of the early, screening-induced, treatment. This motivates addressing these different aspects separately. Here we are interested in the causal effect of early versus delayed treatments on cancer mortality among the screening-detectable subgroup, which under certain assumptions is estimable from conventional randomized screening trial using instrumental variable type methods. To define the causal effect of interest, we formulate a simplified structural multi-state model for screening trials, based on a hypothetical intervention trial where screening detected individuals would be randomized into early versus delayed treatments. The cancer-specific mortality reductions after screening detection are quantified by a cause-specific hazard ratio. For this, we propose two estimators, based on an estimating equation and a likelihood expression. The methods extend existing instrumental variable methods for time-to-event and competing risks outcomes to time-dependent intermediate variables. Using the multi-state model as the basis of a data generating mechanism, we investigate the performance of the new estimators through simulation studies. In addition, we illustrate the proposed method in the context of CT screening for lung cancer using the US National Lung Screening Trial (NLST) data.
