Discussions

We are grateful for the opportunity to discuss this article. In this discussion, we (i) question the plausibility of the authors' substantive assumptions, (ii) discuss the authors' choice of scientific goals and their attainability, (iii) comment on statistical issues, and (iv) describe a sensitivity analysis approach to the authors' problem. (i) Substantive Assumptions. In Section 3, the authors show that under no interference and assumptions (I) (A, S(0), S(1)) ⊥⊥Z | X, C = 1, where C is the binary indicator of the critical event, e.g., car accident, and (II) S(1) = 1 w.p.1, an application of Bayes' Theorem implies identification of the joint distribution f(A, S | C = 1, X) from the distributions f(A | S = 1, C = 1, X) and f(S | C = 1, X). Assumption 2 stipulates a dichotomous treatment factor Z, which is guaranteed to prevent death. In the authors' example, Z was transport time to hospital, a continuous variable that was dichotomized at 10 minutes. As the authors recognize, treatments Z satisfying (II) rarely exist. For instance, a fraction of individuals injured in car accidents die almost immediately. For them, a “transport time to hospital” of less than 10 minutes cannot prevent death. Yet, the empirical analysis of Section 4 reports that no deaths occurred in subjects with transport times of less than 10 minutes. Possible explanations for the lack of deaths in the rapidly transported would include (i) ambulance paramedics appropriately transport victims found dead at the scene less quickly than injured survivors, (ii) the chosen cutpoint of 10 minutes was data driven, and (iii) the number of high-risk rapidly transported subjects (i.e., 11) was sufficiently small that all survived by chance.