24 April 2009
More seriously, it also brought to mind a paper that Bo Honore and Adriana Lleras-Muney wrote several years ago exploring the war on cancer and how we measure success. The challenge in deciding if we are winning is that everyone must die of something, thus when the Times reports large declines in cardiovascular mortality, it follows that some other cause of death must be increasing to (partially) compensate for the decrease in cardiovascular mortality. What Honore and Lleras-Muney do is that they consider the challenges in estimating competing risks models when the causes of death are not independent. In simple mortality models they find that there has been no improvement in cancer mortality from the war on cancer, but the assumptions that are needed there is that individuals who die from non-cancer causes of death are censored in their analysis and that these survival times are independent.
Their more sophisticated analysis recognizes that there are many risk factors for cancer mortality that are also risk factors for other causes of death, so the assumption that the mortality risks are independent is clearly violated. They then present two alternatives to generate more plausible estimates of the effect of the war on cancer on cancer mortality. The first method is to simply look at upper and lower bounds on survival (Manski bounds) and the second method entails making some assumptions about how the distributions of survival times for different causes of death are related. The bounding method leads to quite wide bounds and they state "that it is not possible to make any statement about whether survival from cancer increased or decreased during this period [1970-2000]."
By assuming that the marginal survival distributions follow a specific functional form, they are able to tighten the bounds considerably to draw some conclusions on the efficacy of the war on cancer. Assuming independence, they find that there has been a small improvement in cancer mortality over the period 1970 to 2000. Assuming some dependence between cardiovascular and cancer mortality, however, provides evidence that the war on cancer had a very large effect on cancer mortality of between 10 and 20%, depending on race and gender. Thus there is reasonable evidence that the war on cancer has not been a failure, but perhaps not a stunning success either. The lesson for social scientists is that every assumption matters, relaxing independence between cardiovascular and cancer mortality dramatically increased the effect of the war on cancer and may even overturn the conclusion in the New York Times article.