- © 2004 Canadian Medical Association or its licensors
Gerry Hill's analysis of queuing for cardiac surgery1 has already been critiqued by David Naylor and associates,2 but several points deserve further clarification.
Hill's main finding — that the number of deaths in line per year (D) is independent of queuing strategy — is simply a tautology. By assuming a steady state in which N patients join the queue and S are treated yearly, Hill guarantees that D = N – S, which is constant.
Hill is incorrect in criticizing the prioritization of high-risk patients on the grounds that this strategy increases the size of the queue without reducing the number of deaths. Suppose that it takes n years to reach a steady state. At that point, nS patients have been treated, which means that n(N – S) patients have entered the queue but have not been treated. Of these, Q are alive and the rest are dead. That is, the waiting list is longer if high-risk patients are prioritized precisely because fewer patients die before steady state is reached.
Most important, Hill's model does not consider death from noncardiac causes. Consider a refined model in which the mortality rates of treated patients, low-risk patients and high-risk patients are m0, m1 and m2, where m0 < m1 < m2. With this model, it is not difficult to show that prioritizing high-risk cases leads to fewer cardiac deaths and greater overall survival. The number of deaths on the waiting list in steady state is still independent of queuing strategy, but if high-risk cases are prioritized, then a greater proportion of waiting-list deaths are of noncardiac origin.
John D. Neary Second-year Medical Student Faculty of Medicine University of Toronto Toronto, Ont.