If your answer was that war is the wrong metaphor, you win the prize, I suppose. Still, I found this exercise from a medical stats textbook rather interesting:
17.1. A major controversy has occurred about apparent contradictions in biostatistical data as researchers try to convince Congress to allocate more funds for intramural and extramural investigations supported by the NIH. Citing improved survival rates for conditions such as cervical cancer, breast cancer, and leukemia, clinicians claim we are “winning the war” against cancer. Citing increased incidence rates for these (and other cancers), with minimal change in mortality rates, public-health experts claim that the “war” has made little progress, and we should focus on prevention rather than cure.
17.1.1. What explanation would you offer to suggest that the rising incidence of cancer is a statistical consequence of “winning” rather than “losing” the battle?
17.1.2. What explanation would you offer to reconcile the contradictory trends for survival and mortality rates, and to suggest that both sets of results are correct?
The pessimistic explanation is that early detection detects more benign cancers, leading to inflated five-year survival stats. But the question is looking for the optimistic answer, which seems harder to grok.
Off the top of my head, one thing that comes to mind is that people can get multiple types of cancer. If you survive thyroid cancer at 60, you might die of colon cancer at 70. Since we all die of something, greater survival rates would also lead to greater incidence, but wouldn’t necessarily reduce mortality. In a world of miracle cancer cures, for instance, you might start racking up cancer later in life the way people rack up colds in their youth.
Of course, I don’t have a teacher’s edition here, so any input would be welcome — alternate theories?