Treatment effect bounds: An application to Swan–Ganz catheterization

We reanalyze data from the observational study by Connors et al. (1996) on the impact of Swan–Ganz catheterization on mortality outcomes. The study by Connors et al. (1996) assumes that there are no unobserved differences between patients who are catheterized and patients who are not catheterized and finds that catheterization increases patient mortality. We instead allow for such differences between patients by implementing both the instrumental variable bounds of Manski (1990), which only exploits an instrumental variable, and the bounds of Shaikh and Vytlacil (2011), which exploit mild nonparametric, structural assumptions in addition to an instrumental variable. We propose and justify the use of indicators of weekday admission as an instrument for catheterization in this context. We find that in our application, the Manski (1990) bounds do not indicate whether catheterization increases or decreases mortality, where as the Shaikh and Vytlacil (2011) bounds reveal that at least for some diagnoses, Swan–Ganz catheterization reduces mortality at 7 days after catheterization. We show that the bounds of Shaikh and Vytlacil (2011) remain valid under even weaker assumptions than those described in Shaikh and Vytlacil (2011). We also extend the analysis to exploit a further nonparametric, structural assumption–that doctors catheterize individuals with systematically worse latent health–and find that this assumption further narrows these bounds and strengthens our conclusions. In our analysis, we construct confidence regions using the methodology developed in Romano and Shaikh (2008). We show in particular that the confidence regions are uniformly consistent in level over a large class of possible distributions for the observed data that include distributions where the instrument is arbitrarily “weak”.