8.18 Fighting cancer. Congress wants the medical establishment to show that progress is being made in fighting cancer. Here are some variables that might be used:
1. Total deaths from cancer. These have risen sharply over time, from 331,000 in 1970, to 505,000 in 1990, to 572,000 in 2011.
2. The percentage of all Americans who die from cancer. The percentage of deaths due to cancer rose steadily, from 17.2% in 1970 to 23.5% in 1990, then leveled off around 23.2% in 2007.
3. The percentage of cancer patients who survive for five years from the time the disease is discovered. These rates are rising slowly. The five-year survival rate was 50% in the 1975 to 1977 period and 66.5% from 2005 to 2011.
None of these variables is fully valid as a measure of the effectiveness of cancer treatment. Explain why Variables 1 and 2 could increase even if treatment is getting more effective and why Variable 3 could increase even if treatment is getting less effective.